Arrange the following numbers from smallest to the greatest.
\(\dfrac{2}{5}\), 0.408, 0.048
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


What is the value of \(\dfrac{3}{10}+\dfrac{4}{5}\)? Express your answer as a mixed number.


A piece of ribbon is 14 m long. Jane used \(\dfrac{3}{7}\) of it. What was the length of the ribbon left? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Fraction left = \(1-\dfrac{3}{7}=\dfrac{4}{7}\). Each seventh = 14 ÷ 7 = 2 m. Length left = \(\dfrac{4}{7}\) × 14 = 4 × 2 = 8 m.


Sera was in school from 07 30 to 14 00. How long was she in school? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> h <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> min

From 07 30 to 13 30 is 6 h, then 13 30 to 14 00 is 30 min. Total = 6 h 30 min.


Mrs Tan watched a movie which ended at 01 15. The movie lasted for 2 h 30 min. What time did the movie start? Express your answer in 24h-clock. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Work backwards from 01 15. Subtract 2 h → 23 15 (previous day), then subtract 30 min → 22 45.


The area of a square is 36 cm². Find the perimeter. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Side of square: 6 × 6 = 36, so each side = 6 cm. Perimeter = 4 × 6 = 24 cm.


During a travel fair, 958 people attended it on the first day. On the second day, there were 3 times as many people as on the first day.
(a) How many people attended the travel fair on the second day?
(b) What is the total number of people who attended the fair for the two days?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Second day = 3 × 958 = 2874 people. (b) Total = first day + second day = 958 + 2874 = 3832 people.


Ms Chai bought 3 blouses and 4 skirts for $465. Each skirt costs $20 more than a blouse. What is the cost of 1 blouse? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Replace each skirt with a blouse: remove the extra $20 × 4 = $80 from the skirts. Then 3 + 4 = 7 blouses cost $465 − $80 = $385. Cost of 1 blouse = $385 ÷ 7 = $55.


Olivia used \(\dfrac{2}{3}\) kg of sugar. Shannon used \(\dfrac{1}{6}\) kg of sugar more than Olivia. Adele used \(\dfrac{1}{3}\) kg less sugar than Shannon. What was the amount of sugar used by Adele? Express your answer in its simplest form.


There are red, blue and yellow balls. \(\dfrac{1}{12}\) of the balls are red. \(\dfrac{1}{2}\) of the balls are blue and the rest of the balls are yellow. There are 680 more yellow balls than red balls. How many balls are there altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Sonya had 7 kg of cherries more than Tara. When Sonya gave away 1.5 kg of cherries and Tara gave away 0.5 kg of cherries, Sonya still had 4 times as much as Tara. How many kilograms of cherries did Tara have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After giving away, Sonya's lead over Tara = 7 − 1.5 + 0.5 = 6 kg. At that point Sonya = 4 × Tara, so the lead = 3 units = 6 kg, giving 1 unit = 2 kg = Tara after. Tara at first = 2 + 0.5 = 2.5 kg.


In which of the following numbers does the digit 7 stand for 70?

The digit 7 stands for 70 when it is in the tens place. In 4073, the 7 is in the tens place, so it stands for 70.


Which of the following is a factor of both 12 and 40?

Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 40: 1, 2, 4, 5, 8, 10, 20, 40. The common factor among the options is 4.


\(6\dfrac{7}{8}\) = \(\dfrac{ }{8}\)<br>What is the missing number in the box?

Convert the mixed number to an improper fraction: \(6\dfrac{7}{8}\) = \(\dfrac{6\times8+7}{8}\) = \(\dfrac{55}{8}\). The missing number is 55.


What is the number when 11.84 is rounded to 1 decimal place?

To round 11.84 to 1 decimal place, look at the hundredths digit (4). Since 4 is less than 5, round down: 11.8.


Which of the following letters is symmetrical?

A symmetrical letter can be folded along a line so both halves match. X has both vertical and horizontal lines of symmetry; N, S and Z do not.


Andy had 578 marbles at first. After giving 142 marbles to Shirley, he had twice the number of marbles as Shirley in the end. How many marbles did Shirley have at first?

Andy in the end: 578 - 142 = 436. This is twice Shirley's final amount, so Shirley in the end = 436 / 2 = 218. Shirley received 142, so Shirley at first = 218 - 142 = 76.


Which of the following numbers is both a factor of 16 and a multiple of 4?

Factors of 16: 1, 2, 4, 8, 16. Multiples of 4: 4, 8, 12, ... The number 4 is both a factor of 16 and a multiple of 4.


Chuan Rui is thinking of a number. When it is divided by 18, it has a quotient of 324. What is the number?

Number = quotient x divisor = 324 x 18 = 5832.


A fruit seller had 5630 oranges. He packed all the oranges into boxes of 8. How many oranges were left unpacked?

5630 / 8 = 703 remainder 6. So 703 full boxes are packed and 6 oranges are left unpacked.


Tim ate \(\dfrac{4}{9}\) of a cake. Mark ate \(\dfrac{1}{2}\) of the same cake. What fraction of the cake was left?


Amirah saved an equal amount of money each month. She saved $19.20 in 2 months. How much would she save in 7 months?


Harvey has 4 times as much money as Chris. Harvey has $147 more than Chris. How much money does Chris have?

Harvey is 4 units, Chris is 1 unit. The difference is 3 units = $147, so 1 unit = $147 / 3 = $49. Chris has $49.


Write twenty-seven thousand and seventy in figures.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Twenty-seven thousand = 27000; seventy = 70. Together: 27000 + 70 = 27070.


What is the missing number in the number pattern?<br>6849 , 7099 , 7349 , <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , 7849


What is the value of \(\dfrac{1}{3}+\dfrac{5}{6}\)?<br>Express your answer as a mixed number.


Find the value of \(1-\dfrac{1}{2}-\dfrac{1}{6}\).<br>Express your answer in the simplest form.


Arrange the following decimals in order from the smallest to the greatest.
1.08 , 0.018 , 0.081
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> (smallest) , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> (greatest)

Compare place values: 0.018 < 0.081 < 1.08. Smallest to greatest: 0.018, 0.081, 1.08.


Find the value of 27 ÷ 8, correct to 2 decimal places.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

27 ÷ 8 = 3.375. Rounded to 2 decimal places (the thousandths digit is 5), it becomes 3.38.


At a fruit shop, apples and oranges were packed into bags for sales. There were 587 bags of fruits. Each bag contains 12 apples and 6 oranges. How many apples and oranges were there altogether?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each bag has 12 + 6 = 18 fruits. Total = 587 x 18 = 10566 fruits.


Martha had $36. She had 5 times as much money as Rina. How much money did both of them have?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Ken has 600 stamps. He gave \(\dfrac{3}{5}\) of the stamps to Tom, \(\dfrac{1}{10}\) of the stamps to John and kept the rest for himself.<br>(a) What fraction of the stamps did Ken keep for himself?


Ken has 600 stamps. He gave \(\dfrac{3}{5}\) of the stamps to Tom, \(\dfrac{1}{10}\) of the stamps to John and kept the rest for himself.
(b) How many more stamps did Ken give to Tom than to John?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Magdalene and Angelina had 568 marbles altogether. Magdalene and Jeremy had 795 marbles altogether. Angelina had half the number of marbles as Jeremy. How many marbles did they have altogether?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Jeremy - Angelina = 795 - 568 = 227. Since Angelina = half of Jeremy, Jeremy - Angelina = Angelina = 227, so Angelina = 227 and Jeremy = 454. Magdalene = 568 - 227 = 341. Altogether = 227 + 341 + 454 = 1022.


Hakim, Gomez and Vignesh saved $1895 in a particular month. Hakim saved six times as much money as Gomez. Gomez saved $95 less than Vignesh. How much money did Hakim save?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


4 files cost as much as 3 notebooks. Martha paid $84.60 for 2 files and 3 notebooks.
(a) How much does 1 file cost?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Since 3 notebooks cost the same as 4 files, replace the 3 notebooks: 2 files + 4 files = 6 files = $84.60. So 1 file = $84.60 ÷ 6 = $14.10.


4 files cost as much as 3 notebooks. Martha paid $84.60 for 2 files and 3 notebooks.
(b) How much do 3 notebooks cost?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


In 89 503, the digit 5 is in the hundreds place. Its value is 5 × 100 = 500.


Thirty-four thousand and sixty-two in figures is .

Thirty-four thousand = 34 000; sixty-two = 62. So 34 000 + 62 = 34 062.


Which of the following when rounded to the nearest hundred gives 60 000?


What is the second common multiple of 4 and 6?

Common multiples of 4 and 6 are 12, 24, 36, ... The first is 12 and the second is 24.


Which of the following fractions is equivalent to \(\dfrac{4}{6}\)?


In the number 41.32, the digit is in the hundredths place.

In 41.32: 3 is in the tenths place and 2 is in the hundredths place. So the digit in the hundredths place is 2.


Mr Ng took a flight from Singapore to Japan. He boarded the plane at 23 39 and reached Japan at 06 22 the next day. How long was the flight?

From 23 39 to 24 00 (midnight) is 21 min. From 00 00 to 06 22 is 6 h 22 min. Total = 6 h 22 min + 21 min = 6 h 43 min.


Elize had a string that was 15.61 m long. She used 1.54 m to tie a parcel and cut the remaining string into 7 equal pieces. How long was each piece of string?


Kelly used \(\dfrac{3}{10}\) kg of coffee powder. She used \(\dfrac{1}{5}\) kg less coffee powder than Frances. How much coffee powder did they use altogether?


Fill in the blank with the correct number in the number pattern.<br>875 , 845 , 815 , <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , 755

The pattern decreases by 30 each time: 875 − 30 = 845, 845 − 30 = 815, 815 − 30 = 785, 785 − 30 = 755. The missing number is 785.


The perimeter of a square is 76 cm. What is the area of the square? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Liana started doing a science quiz at 12.42 p.m. There were 8 questions in this quiz. For the first 3 questions, Liana took 6 minutes to complete each question. For the remaining questions, she took 7 minutes to complete each question. At what time did Liana complete the quiz? Express your answer using the 24-hour clock. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

First 3 questions: 3 × 6 = 18 min. Remaining 5 questions: 5 × 7 = 35 min. Total = 18 + 35 = 53 min. 12.42 p.m. + 53 min = 13 35 (1.35 p.m.) in 24-hour clock.


Which two of the fractions below are in the simplest form?
\(\dfrac{2}{5}\) , \(\dfrac{3}{6}\) , \(\dfrac{5}{7}\) , \(\dfrac{6}{8}\)
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

\(\dfrac{3}{6}=\dfrac{1}{2}\) and \(\dfrac{6}{8}=\dfrac{3}{4}\) can be simplified, so they are not in simplest form. \(\dfrac{2}{5}\) and \(\dfrac{5}{7}\) cannot be simplified (numerator and denominator share no common factor), so they are in simplest form.


Find the value of \(1-\dfrac{1}{3}-\dfrac{2}{9}\).


Arrange the following numbers from the smallest to the greatest.
0.801 , 0.081 , \(\dfrac{4}{5}\)
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />   (c) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


Gareth spent $20.45 on a shirt. He spent $12.25 more on a belt than the shirt. How much money did Gareth spend on the shirt and belt altogether? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Some factors of 52 are 1, 2, 4 and 52. What are the other two factors of 52? <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Factors of 52: 1, 2, 4, 13, 26, 52. The two not listed are 13 and 26 (since 4 × 13 = 52 and 2 × 26 = 52).


Hidayah needs to pack some books into boxes of 3 or 8. The number of books is fewer than 50. What is the greatest number of books that Hidayah has to pack? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number must be a common multiple of 3 and 8, i.e. a multiple of 24: 24, 48, 72, ... The greatest one fewer than 50 is 48.


Johnny spent \(\dfrac{1}{2}\) of his salary on food and \(\dfrac{1}{7}\) on transport. In the end, he had $630 left. How much money did Johnny spend on transport? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mei Yi spent $14.90 on 4 erasers and 5 pencils. The total cost of 1 such eraser and 1 such pencil was $3.25.
(a) How much did 1 such pencil cost?
(b) Zachary bought 7 such pencils. He paid with a $50 note. How much change did Zachary receive?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Priscilla, William and Victor had a total of 680 stickers. Victor had 180 fewer stickers than Priscilla and William had 20 more stickers than Priscilla.
(a) How many stickers did Priscilla have?
(b) Victor then bought some stickers. Priscilla had twice as many stickers as him in the end. How many stickers did Victor buy?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Let Priscilla = P. Victor = P − 180, William = P + 20. Total: P + (P − 180) + (P + 20) = 680, so 3P − 160 = 680, 3P = 840, P = 280. Priscilla had 280. (b) Victor had 280 − 180 = 100. In the end Priscilla (280) = twice Victor, so Victor = 280 ÷ 2 = 140. Victor bought 140 − 100 = 40 stickers.


Aqil collected 24 more stamps than Riley at first. After Aqil gave away 60 stamps, Riley had 4 times as many stamps as him. How many stamps did Aqil have at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After giving away 60, Aqil's stamps = Riley's ÷ 4, so Riley = 4 units and Aqil(after) = 1 unit; the difference (Riley − Aqil_after) = 3 units. At first Aqil = Riley + 24; after giving away 60, Aqil_after = Riley + 24 − 60 = Riley − 36. Difference = Riley − (Riley − 36) = 36 = 3 units, so 1 unit = 12. Aqil at first = Aqil_after + 60 = 12 + 60 = 72.


Which of the following is a multiple of 6?

A multiple of 6 can be divided exactly by 6. 30 = 6 x 5, so 30 is a multiple of 6.


Which of the following decimals is the smallest?

Compare place values. 3.038 has only 3 hundredths (0.038), while 3.07 = 0.070, 3.15, 3.304 are larger. So 3.038 is the smallest.


Laura clocked 6804 steps on Friday. She clocked 2 times as many steps on Saturday as on Friday. How many steps did she clock on both days?


The total mass of a papaya and a durian is 8.2 kg. The total mass of the papaya and a watermelon is 11.4 kg. The watermelon weighs 3 times as heavy as the papaya. What is the mass of the durian?

Papaya + watermelon = 11.4 kg and watermelon = 3 x papaya, so 4 units of papaya = 11.4 kg, papaya = 2.85 kg. Durian = 8.2 - 2.85 = 5.35 kg.


At an animal shelter, there were dogs, cats and rabbits. \(\dfrac{1}{3}\) of the animals were dogs. There were 38 more cats than dogs. The remaining 56 animals were rabbits. How many animals were there altogether?

Dogs = \(\dfrac{1}{3}\) of total, so cats + rabbits = \(\dfrac{2}{3}\) of total. Cats = dogs + 38 = \(\dfrac{1}{3}\)total + 38. Then \(\dfrac{1}{3}\)total + 38 + 56 = \(\dfrac{2}{3}\)total, so \(\dfrac{1}{3}\)total = 94 and total = 282.


Round 2818 to the nearest ten. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The ones digit is 8, which is 5 or more, so round up the tens: 2818 rounds to 2820.


Write the missing number in the number pattern below.<br>17 000 , 16 100 , 15 200 , 14 300 , <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , 12 500


Find the value of 8.27 x 9. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Arrange the following fractions from the smallest to the greatest.
\(\dfrac{7}{11}\) , \(\dfrac{1}{2}\) , \(\dfrac{10}{11}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> (smallest) , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> (greatest)


Find the sum of all the common factors of 30 and 54. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mr Tan used 21 \(l\) 75 \(ml\) of petrol in the first week. He used 3 \(l\) 25 \(ml\) more petrol in the second week. He used the same amount of petrol in the second and third week. How much petrol did he use in the 3 weeks? Express your answer in litres and millilitres. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Second week = 21 l 75 ml + 3 l 25 ml = 24 l 100 ml. Third week = 24 l 100 ml. Total = 21 l 75 ml + 24 l 100 ml + 24 l 100 ml = 69 l 275 ml.


After making a \(\dfrac{1}{4}\) turn in an anti-clockwise direction, Sarah makes a 270 degree clockwise turn and is now facing north. Which direction was she facing at first?

Work backwards from facing north. Undo the 270 degree clockwise turn (turn 270 degrees anti-clockwise) to get west. Then undo the 1/4 (90 degree) anti-clockwise turn (turn 90 degrees clockwise) to get north... reworking forwards: a 1/4 anti-clockwise turn then 270 degrees clockwise is a net 180 degree clockwise turn. To end facing north, she must have started facing south.


What was the difference in temperature between the lowest and highest temperature on that day? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(\degree C\)

Highest temperature = 33 degrees C (at 3 p.m.), lowest = 23 degrees C (at 7 a.m.). Difference = 33 - 23 = 10 degrees C.


Harry planted 10 seedlings in a row. The seedlings were planted at the same distance apart. The distance between the second and the fifth seedling was 125.4 m. What was the distance between the first and the tenth seedling? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(m\)

From the 2nd to the 5th seedling there are 3 gaps = 125.4 m, so 1 gap = 125.4 div 3 = 41.8 m. From the 1st to the 10th seedling there are 9 gaps = 41.8 x 9 = 376.2 m.


3 files and 3 pens cost $32.10. I paid $40 for 4 such files and 3 such pens. Find the cost of 3 pens. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


I am a 4-digit even number. The sum of the digits is 14. I am 2250 when rounded to the nearest 10. What number am I? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Rounding to 2250 to the nearest 10 means the number is 2245 to 2254. It must be even, so it ends in 6 (2246), 8 (2248), 0/2/4 (2250, 2252, 2254). Digit sum 14: 2+2+4+6 = 14. So the number is 2246.


A tailor had 500 buttons. He sewed 7 buttons on each shirt and had 248 buttons left.
(a) How many buttons did he use? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many shirts did he sew the buttons on? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Tom had 4730 marbles and Muthu had 1240 marbles at first. Tom gave some marbles to Muthu so that Muthu would have twice as many marbles as Tom in the end. How many marbles did Tom give Muthu? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total marbles stay 4730 + 1240 = 5970. In the end Muthu has twice Tom, so 3 units = 5970, 1 unit (Tom) = 1990, Muthu = 3980. Tom gave = 3980 - 1240 = 2740 marbles.


The mass of a wooden vase is 3.3 kg. The mass of a glass vase is 4.05 kg. What is the total mass of 3 identical wooden vases and 3 identical glass vases? Give your answer to the nearest kilogram. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(kg\)

3 wooden vases = 3.3 x 3 = 9.9 kg. 3 glass vases = 4.05 x 3 = 12.15 kg. Total = 9.9 + 12.15 = 22.05 kg, which rounds to 22 kg.


The table shows the departure times from Singapore to Penang and Kuala Lumpur as well as their arrival times. SP 100 to Penang departs 10.40 p.m. and arrives 12.05 a.m. SP 246 to Kuala Lumpur departs 8.15 p.m. and arrives 9.20 p.m.
(a) How long is the flight from Singapore to Penang? Give your answer in h and min. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Mr Bala took SP 246 to Kuala Lumpur. His flight was delayed for 45 minutes. At what time did Mr Bala finally arrive in Kuala Lumpur? Leave your answer in 24-hour clock. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) From 10.40 p.m. to 12.05 a.m.: 10.40 p.m. to 11.00 p.m. is 20 min, 11.00 p.m. to 12.05 a.m. is 1 h 5 min, total 1 h 25 min. (b) Scheduled arrival 9.20 p.m. + 45 min delay = 10.05 p.m. = 2205 in 24-hour clock.


A newly opened chicken stall had a promotion. For every chicken bought, the second chicken was sold at half price. Each chicken is $4.70. Mrs Dee bought 4 chickens.
(a) How much did she pay? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) At the end of the day, the stall collected $440. There were two $100 notes, three $50 notes and some $10 notes. How many $10 notes were there? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


There are some people attending a carnival. \(\dfrac{3}{5}\) of them are children, \(\dfrac{1}{6}\) of them are men and the rest are women. There are 42 more women than men at the carnival. How many people are at the carnival? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A group of 3 adults and 5 children bought tickets to watch a concert. Each adult ticket cost $7 more than each child ticket. The group paid a total of $125. What was the cost of each adult ticket? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Replace the 3 adult tickets with child-ticket value: 3 adults cost 3 x $7 = $21 more than 3 children. So 8 child tickets cost $125 - $21 = $104. 1 child ticket = $104 div 8 = $13. 1 adult ticket = $13 + $7 = $20.


A curry puff cost $3 and a hotdog cost $4. Miss Gaya spent a total of $238 on 70 curry puffs and hotdogs. How many hotdogs did she buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Assume all 70 are curry puffs: 70 x $3 = $210. Extra spent = $238 - $210 = $28. Each hotdog costs $4 - $3 = $1 more, so number of hotdogs = $28 div $1 = 28.


What does the digit 8 stand for in 87 502?

In 87 502 the digit 8 is in the ten thousands place. It stands for 8 ten thousands (80 000).


Which of the following is not a factor of 48?

Check each: 48 ÷ 3 = 16, 48 ÷ 6 = 8, 48 ÷ 8 = 6 all exact, so they are factors. 48 ÷ 7 is not exact, so 7 is not a factor of 48.


What is 7 thousands 3 hundreds and 6 ones as a numeral?


Methodist School Walk raised an amount of $12 800 when rounded to the nearest hundred dollars. What is the smallest possible amount raised?

To round to 12 800 to the nearest hundred, the amount must be from 12 750 to 12 849. The smallest of these is 12 750. Of the options, $12 749 rounds to 12 700, $12 849 rounds to 12 800 but is larger, so the smallest valid amount is $12 760.


Miss Toh gave 405 cards to some pupils in her class. She gave 9 cards to each pupil and had 27 cards left. How many pupils did she have in her class?

Cards given out = 405 − 27 = 378. Number of pupils = 378 ÷ 9 = 42.


Use all the digits to form the largest 4-digit even number.
6, 4, 3, 7
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

For the largest number, place the biggest digits first. For an even number, the last digit must be even (4 or 6). Use 4 as the last digit and arrange the rest in descending order: 7, 6, 3 then 4 gives 7634.


Multiply 86 by 34.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> × <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> = <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


I am a whole number. I am a multiple of 7. One of my factors is 4. I am between 40 and 60. What number am I?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 7 between 40 and 60 are 42, 49, 56. The number must also have 4 as a factor, i.e. be divisible by 4. Only 56 is divisible by 4 (56 ÷ 4 = 14), so the number is 56.


Siti and Brandon had 182 books. Brandon gave 24 books to Siti. In the end, they had the same number of books. How many books did Siti have at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In the end each had 182 ÷ 2 = 91 books. Siti gained 24 books, so at first Siti had 91 − 24 = 67 books.


Mr Tan bought 3 adult and 1 child air tickets for $2800. An adult ticket cost 2 times as much as a child ticket. How much did he pay for one adult ticket?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1 adult = 2 child units. 3 adults + 1 child = 6 + 1 = 7 child units = $2800. One child unit = $2800 ÷ 7 = $400. One adult ticket = $400 × 2 = $800.


Ahmad, John, and Tina share $830. Ahmad has twice as much money as Tina and he has $40 more than John. How much money does Ahmad have?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Tina = 1 unit, so Ahmad = 2 units. John = Ahmad − $40 = 2 units − $40. Total: 1 + 2 + (2 − $40) = 5 units − $40 = $830, so 5 units = $870 and 1 unit = $174. Ahmad = 2 units = $174 × 2 = $348.


Kim had twice as many stamps as Gopal at first. Kim lost 30 stamps and she bought another 5 stamps. In the end, Gopal had three times as many stamps as Kim. How many stamps did they have altogether at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Gopal = 1 unit, Kim = 2 units at first. Kim's net change = −30 + 5 = −25, so Kim ends with 2 units − 25. Gopal is unchanged at 1 unit, and ends with three times Kim: 1 unit = 3 × (2 units − 25) = 6 units − 75, so 5 units = 75 and 1 unit = 15. At first Gopal = 15, Kim = 30, altogether = 15 + 30 = 45.


John is facing south-west. When he turns through an angle of in an anti-clockwise direction, he will be facing east.

On the 8-point compass, turning anti-clockwise from south-west: SW → S (45°) → SE (90°) → E (135°). Each step between compass points is 45°, and there are 3 steps from south-west to east going anti-clockwise, so the turn is 3 × 45° = 135°.


Mr Lim had 528 mangoes. He sold all the mangoes at 6 for $14. How much money did he receive? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number of groups of 6 mangoes = 528 ÷ 6 = 88 groups. Each group sells for $14, so total money = 88 × $14 = $1232. Mr Lim received $1232.


Mrs Tan baked three times as many banana muffins as chocolate muffins. After she gave away 16 chocolate muffins, there were 5 times as many banana muffins as chocolate muffins. How many chocolate muffins did she bake at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let chocolate at first = 3 units of banana, so banana = 3 × chocolate. After giving away 16 chocolate, banana = 5 × (new chocolate). Banana stays the same. Using units: original chocolate is 1 part of the banana's 3 parts; after removal it is 1 part of 5. The 16 removed muffins equal the difference: with 5 units → 1 unit banana, work out 1 unit = 16×3÷? Following the key: 2u → 16×3 = 48, 1u → 48÷2 = 24, chocolate at first = 24 + 16 = 40. She baked 40 chocolate muffins at first.


Rina had 5 times as many red beads as blue beads at first. She then gave away 36 red beads and bought another 36 blue beads. She had the same number of red beads and blue beads in the end. How many red beads did she have in the end? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

At first red = 5 units, blue = 1 unit. After giving away 36 red and buying 36 blue, the totals are equal. The difference at first was 5u − 1u = 4 units; the changes close a gap of 36 + 36 = 72, which equals 4 units, so 1 unit = 18. Following the key: 36 + 36 = 72 closes the gap of (5u−1u); 72÷4 = 18 per unit. Red in the end = 5×18 − 36 = 90 − 36 = 54. She had 54 red beads in the end.


Arrange the following numbers in increasing order.<br>78 512, 87 125, 78 521, 87 215

Compare digit by digit. The two 78-thousands first: 78 512 < 78 521. Then the two 87-thousands: 87 125 < 87 215. Increasing order: 78 512, 78 521, 87 125, 87 215.


Which of the following is not a common factor of 12 and 18?

Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 18: 1, 2, 3, 6, 9, 18. Common factors are 1, 2, 3, 6. 4 is a factor of 12 but not of 18, so it is not a common factor.


There were 51 072 people at a concert. Express this number to the nearest hundred.

To round 51 072 to the nearest hundred, look at the tens digit (7). Since 7 ≥ 5, round up the hundreds: 51 072 ≈ 51 100.


At a funfair, every 2nd child gets a cotton candy and every 6th child gets a cup of bubble tea. Which child is the first to get both a cotton candy and a cup of bubble tea? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Cotton candy goes to children 2, 4, 6, 8, 10, ... Bubble tea goes to children 6, 12, 18, ... The first child receiving both is the lowest common multiple of 2 and 6, which is 6. So the 6th child is first to get both.


When a number is divided by 8, it has a quotient of 219 and a remainder of 3. What is the number? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number = quotient × divisor + remainder = 219 × 8 + 3 = 1752 + 3 = 1755.


Mrs Lee has 134 pupils. She gave 12 pencils to each pupil and had 2 pencils left. How many pencils did she have at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Pencils given out = 134 × 12 = 1608. Add the 2 left over: 1608 + 2 = 1610 pencils at first.


A baker packed 3906 croissants equally in boxes. The croissants were packed in boxes of 6. How many boxes were there altogether? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number of boxes = total croissants ÷ croissants per box = 3906 ÷ 6 = 651 boxes.


A big jar contains twice as many sweets as a small jar. 4 small jars and 2 big jars contain 256 sweets. How many sweets does a big jar contain? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let a small jar = 1 unit, so a big jar = 2 units. 4 small jars + 2 big jars = 4 units + 4 units = 8 units = 256 sweets. 1 unit = 256 ÷ 8 = 32. A big jar = 2 units = 2 × 32 = 64 sweets.


Mrs Tan bought a dress and 3 similar shirts. The dress cost $272 more than the total cost of the 3 shirts. She gave the cashier a $1000 note and received $428 change. What was the cost of 1 such shirt? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total spent = $1000 − $428 = $572. Let 1 shirt = 1 unit; 3 shirts = 3 units and the dress = 3 units + $272. Dress + 3 shirts = 6 units + $272 = $572. So 6 units = $572 − $272 = $300, and 1 unit = $300 ÷ 6 = $50. One shirt costs $50.


(a) What is the value of the digit 7 in 78 031? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Round 39 492 to the nearest thousand. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Method: place value and rounding.
(a) In 78 031, the digit 7 is in the ten-thousands place, so its value is 7 × 10 000 = 70 000.
(b) 39 492: the hundreds digit is 4 (less than 5), so round down. 39 492 rounds to 39 000.


(a) Which two numbers shown are multiples of 3?
10 , 16 , 21 , 35 , 48 , 52
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
(b) Write 5 ten thousands, 91 tens and 7 ones in numerals. <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Method: test multiples of 3, then build a number from place-value parts.
(a) Digit sums: 21→3 (÷3 yes), 48→12 (÷3 yes); 10,16,35,52 are not. So 21 and 48.
(b) 5 ten thousands = 50 000; 91 tens = 910; 7 ones = 7. Total = 50 000 + 910 + 7 = 50 917.


What is the quotient when 3950 is divided by 8? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: long division. 3950 ÷ 8 = 493 remainder 6 (493 × 8 = 3944; 3950 − 3944 = 6). The quotient is 493.


There are some marbles in a tin. The marbles can be put into either bags of 4 or bags of 7 with no remainder. What is the smallest possible number of marbles in the tin? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: find the lowest common multiple of 4 and 7. Multiples of 4: 4, 8, 12, ...; multiples of 7: 7, 14, 21, 28, ... The smallest number that is a multiple of both is 4 × 7 = 28 (since 4 and 7 share no common factor). So the smallest possible number of marbles is 28.


A shopkeeper had 60 boxes of masks. There were 100 masks in each box. He sold \(\dfrac{1}{3}\) of the masks. How many masks were left? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: total then fraction left. Total masks = 100 × 60 = 6000. He sold \(\dfrac{1}{3}\), so \(\dfrac{2}{3}\) are left. 6000 ÷ 3 = 2000; 2000 × 2 = 4000. So 4000 masks were left.


\(\dfrac{3}{7}\) of the pupils in a school are boys. There are 130 more girls than boys. \(\dfrac{1}{5}\) of the girls has short hair.
(a) How many girls are there in the school? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many girls have long hair? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Method: model in units. If \(\dfrac{3}{7}\) are boys then \(\dfrac{4}{7}\) are girls, so boys = 3 units, girls = 4 units, difference = 1 unit = 130.
(a) Girls = 4 units = 4 × 130 = 520.
(b) \(\dfrac{1}{5}\) of the girls have short hair, so \(\dfrac{4}{5}\) have long hair. 520 ÷ 5 = 104; 104 × 4 = 416 girls have long hair.


Alice and Betty had 3216 stickers altogether. After Alice gave Betty 180 stickers, she had 3 times as many stickers as Betty.
(a) How many stickers did Betty have at last? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many stickers did Alice have at first? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Method: the total is unchanged at 3216. After the transfer, Alice : Betty = 3 : 1, so there are 4 equal parts.
(a) Betty (at last) = 1 part = 3216 ÷ 4 = 804.
(b) Alice at last = 3 × 804 = 2412. Before giving 180 away, Alice had 2412 + 180 = 2592 at first.


A fruit seller had 580 green apples and 235 red apples at first. After selling the same number of each type of apples, there were 4 times as many green apples as red apples left. How many of each type of apple was sold? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: the difference between green and red is unchanged when the same number is sold. Difference = 580 − 235 = 345. After selling, green = 4 units and red = 1 unit, so the difference = 3 units = 345, giving 1 unit = 345 ÷ 3 = 115 (red apples left). Red sold = 235 − 115 = 120, and the same number (120) of green was sold.


Arrange these numbers in descending order.
2.04, 4.2, 2.402, 4.204
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

Descending = largest to smallest. Compare whole-number parts then decimal places: 4.204 and 4.2 (i.e. 4.200) both start with 4; 4.204 > 4.200. Then 2.402 > 2.04 (2.040). Order: 4.204, 4.2, 2.402, 2.04.


Divide 82.23 by 3.<br>82.23 ÷ 3 = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


(a) Express 0.85 as a fraction in its simplest form. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Express \(\dfrac{7}{25}\) as a decimal. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) 0.85 = 85/100. Divide numerator and denominator by 5: 85/100 = 17/20. (b) 7/25 = 28/100 (multiply top and bottom by 4) = 0.28.


The mass of a laptop is 1.32 kg. The mass of a tablet is 0.28 kg less than the laptop. What is the mass of the tablet?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Tablet mass = laptop mass − 0.28 = 1.32 kg − 0.28 kg = 1.04 kg.


Mr Lim bought a shirt which cost $23.80 and a pair of pants which cost $49.70. He gave the cashier $100. How much change did he receive?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The total mass of a box and a book is 2.55 kg. When some files are added into the box, the total mass becomes 3.1 kg. The book is 4 times as heavy as the files.
(a) What is the mass of the files? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What is the mass of the box when it is empty? Give your answer in kilograms. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Mass of files = 3.1 kg − 2.55 kg = 0.55 kg. (b) The book is 4 times the files: book = 0.55 × 4 = 2.20 kg. Box (empty) = (box + book) − book = 2.55 − 2.20 = 0.35 kg.


A jar can contain twice as much orange juice as a bottle. 3 such bottles and 2 such jars can contain 196.21 \(l\) of orange juice in total.
(a) How much orange juice can 1 such bottle contain? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much orange juice does 2 jars contain? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

1 jar = 2 bottles, so 2 jars = 4 bottles. Total = 3 bottles + 2 jars = 3 + 4 = 7 bottles = 196.21 L. (a) 1 bottle = 196.21 ÷ 7 = 28.03 L. (b) 2 jars = 4 bottles = 28.03 × 4 = 112.12 L.


Tommy and Siti have some rice. The total mass of the rice is 789.4 kg. When Siti gives Tommy 36.8 kg of rice, they will have the same mass of rice each. What was the mass of rice Tommy had at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After the transfer they are equal, so each has 789.4 ÷ 2 = 394.7 kg. Tommy ended with 394.7 kg after receiving 36.8 kg, so at first Tommy had 394.7 − 36.8 = 357.9 kg.


Look at the hundreds digit, 4. Since 4 < 5, round down: 28 400 ≈ 28 000.


How many common multiples do 4 and 6 have between 20 and 40?

Common multiples of 4 and 6 are multiples of their LCM, 12: 12, 24, 36, 48 ... Between 20 and 40 the common multiples are 24 and 36, so there are 2.


Jia Qi is facing east. She makes a \(\dfrac{1}{2}\)-turn and then a \(\dfrac{3}{4}\)-turn clockwise. She has to turn through an angle of in an anti-clockwise direction to face east again.

A \(\dfrac{1}{2}\)-turn is 180° and a \(\dfrac{3}{4}\)-turn is 270°, total 450° clockwise. 450° = 360° + 90°, so the net rotation is 90° clockwise. To return to facing east she must turn 90° in the anti-clockwise direction.


Divide 6394 by 7. What is the remainder? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


List all the common factors of 12 and 16. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 16: 1, 2, 4, 8, 16. The common factors are 1, 2 and 4.


Alex has a number card. The number on the card is a factor of 20 and a multiple of 4. It is greater than 5. What is the number on Alex's card? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Factors of 20: 1, 2, 4, 5, 10, 20. Multiples of 4 among these: 4 and 20. The one greater than 5 is 20.


Jenny is between 20 and 45 years old. Her present age can be divided exactly by 6. In 4 years' time, her age can be divided exactly by 5. How old is Jenny now? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 6 between 20 and 45: 24, 30, 36, 42. Add 4 to each and check divisibility by 5: 24+4=28 (no), 30+4=34 (no), 36+4=40 (yes), 42+4=46 (no). So Jenny is 36 years old now.


Jason has 284 stamps. He has 4 times as many stamps as Kim. Leah has twice as many stamps as Kim. How many stamps do they have altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Tan has 81 trays of eggs. Each tray has 8 eggs. She arranges all the eggs equally into 9 baskets. (a) How many eggs are there altogether? (b) How many eggs are there in each basket? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Total eggs = 81 trays × 8 eggs = 648 eggs. (b) Eggs per basket = 648 ÷ 9 = 72 eggs.


Which of the following is not an equivalent fraction of \(\dfrac{2}{3}\)?

\(\dfrac{8}{12}=\dfrac{2}{3}\), \(\dfrac{10}{15}=\dfrac{2}{3}\) and \(\dfrac{14}{21}=\dfrac{2}{3}\). But \(\dfrac{4}{9}\) does not simplify to \(\dfrac{2}{3}\) (it would need to be \(\dfrac{6}{9}\)), so it is not equivalent.


Arrange the following fractions in increasing order.
\(\dfrac{3}{4}\), \(\dfrac{1}{2}\), \(\dfrac{5}{8}\)
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />   (c) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


Find the value of \(1 - \dfrac{7}{12} - \dfrac{1}{6}\). Express your answer in the simplest form.


Mrs Tan had 30 kg of flour. She used 10 kg of flour to make a cake. From the amount of flour left, she gave \(\dfrac{1}{5}\) of it to her sister. How much flour did she give to her sister? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Flour left = 30 kg - 10 kg = 20 kg. She gave \(\dfrac{1}{5}\) of 20 kg = 20 ÷ 5 = 4 kg to her sister.


Mary bought a bag of apples. She gave \(\dfrac{4}{9}\) of the apples to her uncle and \(\dfrac{1}{3}\) of them to her neighbour. In the end, she had 6 apples left. How many apples did Mary have at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Fraction given away = \(\dfrac{4}{9}+\dfrac{1}{3}=\dfrac{4}{9}+\dfrac{3}{9}=\dfrac{7}{9}\). Fraction left = \(\dfrac{2}{9}\), which equals 6 apples. So 1 unit (\(\dfrac{1}{9}\)) = 6 ÷ 2 = 3 apples, and 9 units = 3 × 9 = 27 apples.


Helen prepared 18 \(l\) of orange juice and mango juice in the morning. \(\dfrac{5}{6}\) of it was orange juice and the rest was mango juice. Her children drank \(\dfrac{7}{8}\) \(l\) of mango juice in the afternoon.
(a) How much mango juice did Helen prepare?
(b) How much mango juice was left?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


A number when rounded to the nearest hundred is 56 400. What is the greatest possible whole number?

Numbers from 56 350 to 56 449 round to 56 400 (nearest hundred). The greatest whole number in this range is 56 449.


Look at the number pattern.
39 400, 37 400, 37 365, 35 365, 35 330, , 33 295
What is the missing number?


What is the remainder when 7294 is divided by 8? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


16 and 64 have exactly five common factors. Three of the common factors are 1, 4 and 16. What are the other two common factors? <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Common factors of 16 and 64 are 1, 2, 4, 8 and 16. Removing the given 1, 4 and 16 leaves 2 and 8.


Find the sum of the first three common multiples of 2 and 6. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Common multiples of 2 and 6 are multiples of 6: 6, 12, 18, ... The first three are 6, 12 and 18. Their sum is 6 + 12 + 18 = 36.


Use the 5 digits to form the greatest 5-digit number. The digit in the thousands place is an even number. Use each digit only once.
1, 0, 3, 5, 8
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To make the greatest number, place the largest digit first: 8 in the ten-thousands place. The thousands digit must be even; the largest remaining even digit is 0, so put 0 in the thousands place. Arrange the rest in descending order: 5, 3, 1. This gives 80 531.


Katelyn has two six-sided dice. One is black in colour and one is white in colour. She rolls both dice and adds the two numbers shown on the dice. How many ways can she get a total of 8? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Because the two dice are different colours, order matters. Pairs (black + white) summing to 8: 2+6, 3+5, 4+4, 5+3, 6+2. That is 5 ways.


The cost of a dining table was $735. The dining table cost 5 times as much as a dining chair.
(a) How much did the dining chair cost?
(b) How much more did the dining table cost than the dining chair?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


In a group of 120 children, \(\dfrac{3}{8}\) of them are girls. How many girls are there?


Fei Ming spent \(\dfrac{4}{7}\) of his money on a guitar and had $210 left. How much did he spend on the guitar? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mary bought 4 kg of flour. She used \(\dfrac{1}{4}\) kg of flour to make cupcakes and \(\dfrac{2}{5}\) kg of it to make pizza. How much flour was left? Express your answer as a mixed number.


Ali painted \(\dfrac{2}{9}\) of a wall on Monday and \(\dfrac{2}{3}\) of the same wall on Tuesday. What fraction of the wall was not painted?


There were 20 balloons at a party. 2 of them were purple, 4 of them were blue, 11 of them were green and the rest were yellow. For each statement, write True or False.
(a) \(\dfrac{3}{20}\) of the balloons were yellow.
(b) \(\dfrac{1}{5}\) of the balloons were blue.
(c) \(\dfrac{9}{11}\) of the balloons were not green.
(d) The fraction of the balloons that were purple is greater than the fraction of the balloons that were blue.
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />   (c) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />   (d) <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

Yellow = 20 − 2 − 4 − 11 = 3, so yellow = \(\dfrac{3}{20}\) → True. Blue = 4 = \(\dfrac{4}{20}=\dfrac{1}{5}\) → True. Not green = 20 − 11 = 9 out of 20 = \(\dfrac{9}{20}\), not \(\dfrac{9}{11}\) → False. Purple \(\dfrac{2}{20}\) is less than blue \(\dfrac{4}{20}\), so 'purple greater than blue' → False.


Sumiko baked some cookies. She gave \(\dfrac{1}{6}\) of the cookies to her siblings and 45 of the cookies to her friends. She had \(\dfrac{2}{3}\) of the cookies left.
(a) How many cookies did she have left?
(b) She packed the leftover cookies into 18 bags. Some bags contained 6 cookies while the rest of the bags contained 12 cookies. How many bags contained 6 cookies?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) She gave away \(\dfrac{1}{6}\) + 45 cookies and had \(\dfrac{2}{3}\) left. Fraction given to siblings + fraction left = \(\dfrac{1}{6}+\dfrac{4}{6}=\dfrac{5}{6}\), so the 45 cookies given to friends are the remaining \(\dfrac{1}{6}\). Thus 1 unit (\(\dfrac{1}{6}\)) = 45, and the \(\dfrac{2}{3}\) = 4 units left = 4 × 45 = 180 cookies. (b) 180 cookies in 18 bags. If all 18 bags held 12, that is 216; the shortfall 216 − 180 = 36 must come from bags holding 6 instead of 12 (each such bag is 6 fewer): 36 ÷ 6 = 6 bags contained 6 cookies.


94 072 = 90 000 + + 70 + 2<br>What is the missing number in the box?


Arrange the following numbers from the greatest to the smallest.<br>58 719, 85 917, 58 197

Compare digit by digit. 85 917 has 8 ten-thousands so is largest. Between 58 719 and 58 197, the hundreds digit decides: 7 > 1, so 58 719 > 58 197. Greatest to smallest: 85 917, 58 719, 58 197.


Which of the following is not a common factor of 12 and 16?

Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 16: 1, 2, 4, 8, 16. Common factors: 1, 2, 4. So 3 is NOT a common factor.


An adult ticket cost $5 and a child ticket cost $2.
There were as many children as adults at the funfair.
The total amount of money collected from the admission tickets was $9520.
How many people were at the funfair altogether?

Equal numbers of adults and children, so pair 1 adult + 1 child = $5 + $2 = $7. Number of pairs = $9520 ÷ $7 = 1360. Each pair is 2 people, so total people = 1360 x 2 = 2720.


(a) Write thirty-two thousand and eighty in numerals.
(b) Complete the number pattern.
31 238, 36 238, 41 238, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, 51 238

(a) Thirty-two thousand and eighty = 32 080. (b) The pattern increases by 5000 each step: 41 238 + 5000 = 46 238.


(a) What is the largest multiple of 6 that is smaller than 50?
(b) What is the common factor of 15 and 24 that is greater than 1?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Multiples of 6: 42, 48, 54... The largest below 50 is 48. (b) Factors of 15: 1, 3, 5, 15. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. The common factor greater than 1 is 3.


The mass of a papaya when rounded to the nearest hundred is 300 g.
(a) What is the smallest possible mass of the papaya?
(b) What is the greatest possible mass of the papaya?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Numbers from 250 to 349 round to 300 when rounded to the nearest hundred. (a) Smallest = 250 g. (b) Greatest = 349 g (350 would round up to 400).


Mr Tan made some apple juice.
He drank 320 ml of apple juice and divided the remaining equally into 8 glasses.
Each glass contained 275 ml of apple juice.
How many millilitres of apple juice did he make?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Juice in the 8 glasses = 275 x 8 = 2200 ml. Add back what he drank: 2200 + 320 = 2520 ml.


Denzel forms 4-digit numbers using each of the digits 1, 2, 5 and 7 once.
State whether each statement is True or False.
(a) The greatest possible number he can form is 7521. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) The smallest possible number he can form is a multiple of 3. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
(c) He can form 5 different even numbers. <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

(a) Greatest = arrange digits in descending order: 7521. True. (b) Smallest = 1257; digit sum 1+2+5+7 = 15, divisible by 3, so 1257 is a multiple of 3. True. (c) An even number must end in the only even digit, 2. The other three digits (1, 5, 7) can be arranged in 3 x 2 x 1 = 6 ways, giving 6 even numbers, not 5. False.


Amelia has 9 more marbles than Caleb. She has 12 less marbles than Bala. They have 3795 marbles altogether.
(a) How many more marbles does Bala have than Caleb?
(b) How many marbles does Caleb have?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Amelia = Caleb + 9, Bala = Amelia + 12 = Caleb + 21. So Bala has 21 more than Caleb. (b) Total = Caleb + (Caleb + 9) + (Caleb + 21) = 3 x Caleb + 30 = 3795. So 3 x Caleb = 3795 - 30 = 3765, Caleb = 3765 ÷ 3 = 1255.


Paul had 24 more books than Queenie. After Queenie gave Paul 60 books, Paul had 7 times as many books as Queenie. How many books did Queenie have at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After the transfer Paul has 24 + 60 + 60 = 144 more books than Queenie (the original 24 difference plus the 60 he gained plus the 60 she lost). At that point Paul = 7 units and Queenie = 1 unit, so the difference of 6 units = 144, giving 1 unit = 144 ÷ 6 = 24 (Queenie's books after giving away 60). Queenie at first = 24 + 60 = 84.


Which of the following statements are true about a square?
A. It has 4 right angles.
B. It has 2 pairs of parallel lines.
C. Its opposite sides are equal.

A square has 4 right angles (A true), 2 pairs of parallel sides (B true) and equal opposite sides (C true). All three statements are correct, so the answer is A, B and C.


What is the value of 4 thousands + 2 hundreds + 6 ones?


What is the missing number in the box?<br>\(6\dfrac{2}{5}\) = \(\dfrac{ }{5}\)

Convert the mixed number to an improper fraction. \(6\dfrac{2}{5}\) = \(\dfrac{(6\times5)+2}{5}\) = \(\dfrac{32}{5}\), so the missing number is 32.


There are 9345 men and 8704 women in a stadium. What is the total number of people in the stadium? Round this number to the nearest 100.

Total = 9345 + 8704 = 18 049. Rounding 18 049 to the nearest 100: the tens digit is 4 (less than 5), so round down to 18 000.


Mindy had \(\dfrac{4}{5}\) kg of flour at first. After she had used some of the flour to make noodles, she had \(\dfrac{1}{3}\) kg of flour left. How much flour did she use to make noodles?

Flour used = flour at first − flour left = \(\dfrac{4}{5}\) − \(\dfrac{1}{3}\). Common denominator 15: \(\dfrac{12}{15}\) − \(\dfrac{5}{15}\) = \(\dfrac{7}{15}\) kg.


(a) In the number pattern below, what is the missing number in the box?
78 082 , <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , 82 082 , 84 082 , 86 082
(b) Andy listed the factors of 12: 1, 2, 4, 12. He missed out two factors. What were the two missing factors? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

(a) The pattern increases by 2000 each step (82 082 − 80 082 = 2000). The missing term = 78 082 + 2000 = 80 082. (b) Factors of 12 are 1, 2, 3, 4, 6, 12. The listed set 1, 2, 4, 12 leaves out 3 and 6.


Arrange the following in decreasing order.
\(\dfrac{11}{4}\) , \(1\dfrac{1}{6}\) , 1 , \(\dfrac{8}{3}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />


Mr Chen bought 6 similar dining chairs for $1428. A sofa cost 10 times as much as a dining chair. How much did the sofa cost?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Cost of 1 dining chair = $1428 ÷ 6 = $238. The sofa costs 10 times as much = 10 × $238 = $2380.


Fiona and Janet had a total of 126 cookies at first. After Janet gave away \(\dfrac{1}{3}\) of the cookies she had, she had 4 times as many cookies as Fiona. How many cookies did Janet have at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After giving away \(\dfrac{1}{3}\), Janet keeps \(\dfrac{2}{3}\) of her cookies, which equals 4 times Fiona's. The total 126 is unchanged. Take Fiona as 1 unit, so Janet's remaining = 4 units and Janet's original = 6 units (since \(\dfrac{2}{3}\) of original = 4 units → original = 6 units). Total units = 6 + 1 = 7 = 126, so 1 unit = 18. Janet at first = 6 × 18 = 108.


Alan made some lime juice on Monday and Tuesday. He made \(\dfrac{7}{8}\) \(l\) of lime juice on Monday. He made \(\dfrac{2}{5}\) \(l\) more lime juice on Monday than Tuesday.
(a) How much lime juice did he make on Tuesday?
(b) What was the total amount of lime juice that he had made on both days? Give your answer in the simplest form.
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Marilyn has some lollipops. If she packs them into bags of 7, she will be short of 1 lollipop. If she packs them into bags of 5, she will have 2 extra lollipops.
(a) What is the least number of lollipops that Marilyn has?
(b) Marilyn decides to pack all her lollipops into bags of 5. How many more lollipops does she need to fill up the last bag of 5 lollipops?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) 'Short of 1' in bags of 7 means the number is 1 less than a multiple of 7: 6, 13, 20, 27, ... '2 extra' in bags of 5 means 2 more than a multiple of 5: 7, 12, 17, 22, 27, ... The least common value is 27. (b) 27 ÷ 5 = 5 remainder 2, so the last bag has 2 lollipops; she needs 5 − 2 = 3 more to fill it.


In 12 453, the digit 4 is in the ____ place.

In 12 453, the digits from the right are 3 (ones), 5 (tens), 4 (hundreds), 2 (thousands), 1 (ten thousands). So the digit 4 is in the hundreds place.


In which of the following are the numbers arranged from the greatest to the smallest?

Order 9680, 9608, 9068 from greatest to smallest: 9680 (largest), then 9608, then 9068. Compare digit by digit from the left. Option (2) is correct.


Which of the following is a multiple of 9?

A multiple of 9 can be divided exactly by 9. 81 = 9 x 9, so 81 is a multiple of 9. (19, 39 and 3 are not.)


Judy baked 10 chocolate and 15 peanut cookies.
She packed all the cookies into equal number of boxes.
How many chocolate and peanut cookies were there in each box?

The greatest number of equal boxes is the common factor of 10 and 15, which is 5. So 10 ÷ 5 = 2 chocolate cookies and 15 ÷ 5 = 3 peanut cookies in each box.


Siti bought 369 oranges.
She packed the oranges equally into bags of 4.
What is the least number of bags of oranges she should buy?

369 ÷ 4 = 92 remainder 1. 92 bags hold 368 oranges, leaving 1 orange, so 1 more bag is needed. Least number of bags = 93.


Peter folded 1000 paper cranes.
He folded 4 times as many cranes as Alicia.
How many paper cranes must Peter give to Alicia so that they each have the same number of cranes?

Peter = 1000, which is 4 units, so 1 unit = 250 and Alicia = 250. Total = 1250, so each should have 1250 ÷ 2 = 625. Peter must give away 1000 - 625 = 375 cranes.


A number when rounded off to the nearest hundred is 3500.
What is the greatest possible number?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Numbers from 3450 to 3549 round to 3500. The greatest of these is 3549 (3550 would round up to 3600).


Jane decorated a room with red and green lights.
The red light blinks every 3 minutes and the green light blinks every 4 minutes.
Both lights are switched on at the same time.
When will both lights blink together for the first time? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> min

The lights blink together at common multiples of 3 and 4. The lowest common multiple of 3 and 4 is 12, so they first blink together after 12 minutes.


Ahmad, Ben and Clarice shared 9036 crayons equally among themselves.
Ahmad bought another 98 crayons for himself.
How many crayons would Ahmad have in the end?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each share = 9036 ÷ 3 = 3012. Ahmad then buys 98 more: 3012 + 98 = 3110 crayons.


A table cost $910 more than a chair.
Tom paid $7520 for 2 tables and 4 chairs.
How much does a table cost?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Replace each table with a chair: 2 tables = 2 chairs + 2 x $910 = 2 chairs + $1820. So 6 chairs = $7520 - $1820 = $5700, giving 1 chair = $5700 ÷ 6 = $950. A table = $950 + $910 = $1860.


Which digit in 98 150 is in the thousands place?

In 98 150 the digits are 9 (ten thousands), 8 (thousands), 1 (hundreds), 5 (tens), 0 (ones). The thousands place is 8.


Which of the following is a multiple of 7?

Multiples of 7 are 7, 14, 21, 28, ... 21 = 7 × 3, so 21 is a multiple of 7.


Which of the following is not a factor of 42?

Factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42. 8 is not a factor of 42 (42 ÷ 8 leaves a remainder).


Ninety-five thousand, seven hundred and thirty-six in numerals is

Ninety-five thousand = 95 000; seven hundred and thirty-six = 736. Together: 95 000 + 736 = 95 736.


4024 babies were born in March. The number of babies born in March was 1097 fewer than the number of babies born in January. How many babies were born in January?

March is 1097 fewer than January, so January = March + 1097 = 4024 + 1097 = 5121.


Which of the following is a multiple of both 3 and 8?

A multiple of both 3 and 8 is a multiple of 24. 24 = 3 × 8, and 24 ÷ 3 = 8, 24 ÷ 8 = 3, so 24 works.


Samantha is less than 17 years old this year. Her age last year was a multiple of 5. Her age this year is a multiple of 4. What is Samantha's age this year?

Last year a multiple of 5 means last age is 5, 10 or 15, so this year she is 6, 11 or 16. Of these, a multiple of 4 that is less than 17 is 16.


Raja wanted to buy a new piano which costs $3483. He had been saving for 9 months but he was still short of $1647. He saved an equal amount of money each month. How much did Raja save each month?


Write the missing number in the number pattern.<br>68 501, 70 501, 72 501, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, 76 501, 78 501

The pattern increases by 2000 each time. 72 501 + 2000 = 74 501.


Some factors of 36 are 1, 2, 3, 4, 6, 12, 36. What are the other two factors of 36? <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

All factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The two missing from the list are 9 and 18.


Two of the common factors of 12 and 18 are 1 and 2. What are the other 2 common factors of 12 and 18? <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Common factors of 12 and 18 are 1, 2, 3 and 6. The two missing from the list are 3 and 6.


Find the product of 283 and 28. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the quotient when 6300 is divided by 3. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

6300 ÷ 3 = 2100 (63 ÷ 3 = 21, then bring down the two zeros).


Arrange the following numbers from the smallest to the greatest.
71 095, 78 059, 69 590, 72 950
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />


The number of people in a concert rounded to the nearest hundred is 55 100. What is the greatest possible number of people in the stadium? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To round to 55 100, the number must be from 55 050 to 55 149. The greatest possible number is 55 149.


Gopal has a number card. The number on the card is a factor of 36 and a multiple of 3. It is more than 12 but less than 20. What is the number on Gopal's card? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. Those more than 12 but less than 20 give 18. 18 is also a multiple of 3.


A number is between 40 and 50. It is also a multiple of 6. When it is divided by 8, there is no remainder. What is the number? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 6 between 40 and 50 are 42 and 48. Of these, 48 ÷ 8 = 6 with no remainder, so the number is 48.


<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> × 6 = <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
<input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> × 3 = 4608
The value of <input type="text" id="input_3" class="fill-blank-input" placeholder="?" /> is

Let the star be S and the heart be H. From H × 3 = 4608, H = 4608 ÷ 3 = 1536. From S × 6 = H, S = 1536 ÷ 6 = 256. So the star equals 256.


Carrie earns $75 a day on weekdays. She is paid twice as much on Saturdays. She worked for 21 weekdays and a Saturday in a particular month. How much does Carrie earn on a Saturday? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Saturday pay is twice the weekday pay: $75 × 2 = $150.


Carrie earns $75 a day on weekdays. She is paid twice as much on Saturdays. She worked for 21 weekdays and a Saturday in a particular month. How much did Carrie earn for that month? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A fruit seller had 106 boxes of oranges. There were 24 oranges in each box. He sold all the oranges at 8 for $5. How many oranges did the fruit seller have altogether? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total oranges = 106 boxes × 24 per box = 2544.


A fruit seller had 106 boxes of oranges. There were 24 oranges in each box. He sold all the oranges at 8 for $5. How much money did he receive from the sale of all the oranges? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Siti and Alexis collected the same number of stamps. Siti gave away 64 of her stamps and Alexis gave away 121 of her stamps. In the end, Siti had 4 times as many stamps as Alexis. How many stamps did each of them collect? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

They started equal. After giving away, the difference between Siti's and Alexis's stamps is 121 - 64 = 57, and this difference equals 3 units (since Siti had 4 units and Alexis had 1 unit). So 3 units = 57, 1 unit = 19. Alexis had 19 stamps left, so each collected 19 + 121 = 140 stamps.


Write thirteen thousand and forty-three in numerals.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Thirteen thousand = 13 000. Forty-three = 43. Combine: 13 000 + 43 = 13 043.


Use the digits to form the smallest 5-digit even number. Each digit can be used only once.
9, 0, 5, 2, 1
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

For the smallest number put small digits first, but the leading digit cannot be 0, so the smallest non-zero digit (1) goes first. For an even number the last digit must be even (0 or 2); use the smaller even digit 2 last to leave smaller digits earlier. Arrange remaining 0, 5, 9 in increasing order: 1, 0, 5, 9, 2 = 10 592.


19 508 people visited the National Museum. Round this number to the nearest thousand.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Look at the hundreds digit of 19 508, which is 5. Since 5 or more rounds up, 19 508 rounds up to 20 000.


Two factors of 27 are 1 and 27. What are the other two factors of 27?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Factors of 27 are the numbers that divide it exactly: 1, 3, 9, 27. The other two (besides 1 and 27) are 3 and 9.


Complete the following number pattern.<br>63 865, 62 865, 61 865, 60 865, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


\(5\dfrac{2}{7} = \dfrac{<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />}{7}\)<br>What is the missing number in the box?

Convert the mixed number to an improper fraction: \(5\dfrac{2}{7} = \dfrac{5\times7 + 2}{7} = \dfrac{35 + 2}{7} = \dfrac{37}{7}\). The missing numerator is 37.


Find the sum of all the factors of 10.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Arrange the following fractions in decreasing order.
\(1\dfrac{1}{6}\), \(\dfrac{3}{4}\), \(\dfrac{3}{2}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


Meiling had some money. She spent \(\dfrac{5}{6}\) of the money and had $18 left. How much money did she have at first?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

She spent \(\dfrac{5}{6}\), so \(\dfrac{1}{6}\) was left = $18. That means 1 unit = $18, and the whole (6 units) = 6 × $18 = $108.


Find the first two common multiples of 4 and 6.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Multiples of 4: 4, 8, 12, 16, 20, 24... Multiples of 6: 6, 12, 18, 24... The first two common multiples are 12 and 24.


Tom and Jerry shared $1550 between them. Jerry received $90 less than Tom. How much money did Jerry receive?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Remove the $90 difference first: $1550 − $90 = $1460. Split equally between two: $1460 ÷ 2 = $730. This is Jerry's (smaller) share.


An odd number when rounded to the nearest hundred is 2800. What is the smallest possible value of this odd number?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Numbers rounding to 2800 range from 2750 to 2849. The smallest is 2750, but it is even; the smallest odd number in this range is 2751.


Eileen baked 2800 cookies. She sold them in packets of 8 for $7 each. How much money did she collect?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number of packets = 2800 ÷ 8 = 350. Money collected = 350 × $7 = $2450.


Devi bought 24 curry puffs. She gave 6 curry puffs to her neighbour and her family ate 8 curry puffs. What fraction of the curry puffs were left? Express your answer in its simplest form.

Curry puffs left = 24 − 6 − 8 = 10. Fraction left = \(\dfrac{10}{24}\), which simplifies (dividing by 2) to \(\dfrac{5}{12}\).


Alice is thrice as old as her cousin. Alice is 39 years old now. What is their total age in 2 years' time?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mr Soh planted 27 rows of papaya trees in his orchard. There were 16 trees in each row. \(\dfrac{4}{9}\) of the papaya trees bore fruit. How many papaya trees bore fruit?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total trees = 27 × 16 = 432. This is 9 units, so 1 unit = 432 ÷ 9 = 48. Trees that bore fruit = \(\dfrac{4}{9}\) = 4 units = 4 × 48 = 192.


Convert \(1\dfrac{7}{25}\) to a decimal.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of 12 ÷ 5. Give your answer as a decimal.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Arrange these numbers in increasing order.
4.206, 4.026, 4.26, 4.602
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />


A fence was 5.6 m long. 1.25 m of the fence was painted red and the rest was painted white. What was the length of the fence that was painted white?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m

White length = total − red = 5.6 − 1.25 = 4.35 m.


A number is greater than 7.85 but smaller than 7.95. The value of the digit 3 is 0.03. The digit 1 stands for \(\dfrac{1}{1000}\). What is the number? Express your answer as a decimal.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number is between 7.85 and 7.95, so it starts 7.9. The digit 3 has value 0.03, so 3 is in the hundredths place. The digit 1 stands for \(\dfrac{1}{1000}\) = 0.001, so 1 is in the thousandths place. The number is 7.931.


Wei Jia mixed 0.25 \(l\) of rose syrup with 1.2 \(l\) of milk to make Bandung drink for her guests. She then poured the Bandung drink equally into 8 glasses. How much Bandung drink was there in each glass? Give your answer correct to 2 decimal places.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> l

Total drink = 1.2 + 0.25 = 1.45 l. Per glass = 1.45 ÷ 8 = 0.181... which rounds to 0.18 l (2 decimal places).


The total mass of a box containing a watermelon and a papaya is 3.85 kg. The watermelon is twice as heavy as the papaya. The papaya is twice as heavy as the box. What is the mass of the watermelon?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

Let the box = 1 unit. Papaya = 2 units, watermelon = 2 × papaya = 4 units. Total = 1 + 2 + 4 = 7 units = 3.85 kg, so 1 unit = 3.85 ÷ 7 = 0.55 kg. Watermelon = 4 units = 4 × 0.55 = 2.2 kg.


Mrs Khan baked some cupcakes for her students. If she gave each student 3 cupcakes, she would have 5 cupcakes remaining. If she gave each student 4 cupcakes, she would need another 3 cupcakes. How many cupcakes did Mrs Khan bake?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Giving 4 instead of 3 cupcakes per student uses 1 more per student, and the surplus of 5 becomes a shortfall of 3 — a swing of 5 + 3 = 8 cupcakes. So there are 8 students. Cupcakes = 3 × 8 + 5 = 24 + 5 = 29.


Emir had $6.40. After giving $1.20 to his brother, Emir had half the amount as his brother. What was the total amount they had altogether?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After giving away $1.20, Emir had $6.40 − $1.20 = $5.20. He then had half as much as his brother, so the brother had 2 × $5.20 = $10.40. Total = $5.20 + $10.40 = $15.60. (The total is unchanged by the transfer.)


What is the value of the digit 1 in 4.123?

In 4.123, the digit 1 is in the tenths place. Its value is 1 tenth = 0.1.


\(3\dfrac{5}{6}\) = \(\dfrac{ }{6}\)<br>What is the missing number in the box?

Convert the mixed number to an improper fraction: \(3\dfrac{5}{6}\) = (3 × 6 + 5)/6 = (18 + 5)/6 = \(\dfrac{23}{6}\). The missing number is 23.


Arrange the following in increasing order.<br>\(\dfrac{4}{5}\), \(\dfrac{4}{7}\), \(\dfrac{9}{4}\)

\(\dfrac{9}{4}\) is greater than 1 (improper), so it is the largest. For \(\dfrac{4}{5}\) and \(\dfrac{4}{7}\), same numerator means the larger denominator gives the smaller fraction, so \(\dfrac{4}{7}\) < \(\dfrac{4}{5}\). Increasing order: \(\dfrac{4}{7}\), \(\dfrac{4}{5}\), \(\dfrac{9}{4}\).


Divide 5 by 8. Correct your answer to 2 decimal places.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

5 ÷ 8 = 0.625. Rounding to 2 decimal places, the third decimal digit is 5, so round up: 0.63.


The mass of a bag of potatoes is 3 \(kg\) when rounded to the nearest kilogram. What is the greatest possible value of the bag of potatoes in 1 decimal place?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Masses from 2.5 kg up to (but not including) 3.5 kg round to 3 kg. The greatest value below 3.5 kg expressed to 1 decimal place is 3.4 kg.


Andy and Ben drank a total of \(\dfrac{4}{5}\) \(l\) of juice. Andy drank \(\dfrac{1}{2}\) \(l\) of the juice. How much more juice did Andy drink than Ben?


Ray and Sherman shared a box of cards. Ray received \(\dfrac{5}{12}\) of the cards and Sherman received the remaining 105 cards. How many cards were there in the box?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Ray had \(\dfrac{5}{12}\), so Sherman had \(\dfrac{7}{12}\) = 7 units = 105 cards. 1 unit = 105 ÷ 7 = 15 cards. The whole box = 12 units = 12 × 15 = 180 cards.


The cost of a packet of sweets is twice the cost of a packet of peanuts. The cost of 2 such packets of sweets and a packet of peanuts is $18.50.
(a) What is the cost of a packet of peanuts?
(b) John bought 2 such packets of peanuts and a packet of sweets. How much did he pay?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Let 1 packet of peanuts = 1 unit; 1 packet of sweets = 2 units. 2 sweets + 1 peanut = 4 + 1 = 5 units = $18.50, so 1 unit = $18.50 ÷ 5 = $3.70 (a). (b) 2 peanuts + 1 sweet = 2 + 2 = 4 units = $3.70 × 4 = $14.80.


Which of the following is seventy thousand, three hundred and forty in numerals?


Arrange the following numbers from the largest to the smallest.<br>42 182 , 42 281 , 41 822

Largest to smallest: 42 281 > 42 182 > 41 822. Option (2).


In the following number pattern, what is the missing number?<br>21 978, _______ , 21 778, 21 678, 21 578

The pattern decreases by 100 each term: 21 978 - 100 = 21 878. Option (4).


Which of the following numbers when rounded to the nearest hundred becomes 49 000?

Round to nearest hundred: 48 965 rounds to 49 000 (tens digit 6 rounds up). 48 875 to 48 900; 49 099 to 49 100; 49 144 to 49 100. Option (2).


Which of the following is a factor of both 12 and 28?

Factors of 12: 1,2,3,4,6,12. Factors of 28: 1,2,4,7,14,28. Common factor among options: 4. Option (4).


Which of the following is a multiple of both 4 and 6?

Common multiples of 4 and 6 are multiples of 12. Among options, 12 is a multiple of both 4 and 6. Option (2).


Peter stored 3425 boxes of masks in the warehouse. He sold 625 boxes of masks on Monday and 2150 boxes of masks on Tuesday. How many boxes of masks is he left with?


The sum of two numbers is 75. One of the numbers is a multiple of 8. The other number is a factor of 21. What is the difference between the 2 numbers?

Factors of 21: 1, 3, 7, 21. The multiple of 8 = 75 - factor. 75 - 3 = 72 (a multiple of 8). So the numbers are 72 and 3; difference = 72 - 3 = 69. Option (2).


A number is 5800 when rounded to the nearest hundred. What are the smallest and greatest possible numbers?
Smallest: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
Greatest: <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Smallest rounding up to 5800: 5750 (5750 rounds to 5800). Greatest rounding down to 5800: 5849 (5849 rounds to 5800, 5850 rounds to 5900). Smallest = 5750, Greatest = 5849.


There are 2400 red and blue stickers in a shop. The number of red stickers is three times as many as the number of blue stickers. How many blue stickers are there?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Red is 3 times blue, so total = 4 units = 2400. 1 unit (blue) = 2400 / 4 = 600. Blue stickers = 600.


Mr Tan bought 125 boxes of chocolates. Each box contained 28 chocolates. How many chocolates did Mr Tan buy in total?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mr Lim bought a bag of candies for his students. If he gives each student 6 candies, he will not have any candies left. If he gives each student 8 candies, he will be short of 6 candies. How many students did he have?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Giving 8 instead of 6 needs 2 more per student, totalling a shortfall of 6 candies. Number of students = 6 / 2 = 3.


Three ovens and two printers cost $2300. A printer cost $80 more than an oven. What is the cost of an oven?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Replace 2 printers by ovens: each printer = oven + 80, so 2 printers = 2 ovens + 160. Total = 5 ovens + 160 = 2300, so 5 ovens = 2140, 1 oven = 2140 / 5 = $428.


John had twice as much money as Ken. After John spent $1064, Ken had four times as much money as John.
(a) How much money did John have in the end?
$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much money did the both of them have at first?
$<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Ken's amount is unchanged. At first John = 2 x Ken. In the end Ken = 4 x John(end), so John(end) = Ken / 4. Let Ken = 1 unit; John(start) = 2 units; John(end) = Ken/4 = 1/4 unit. John spent $1064 = John(start) - John(end) = 2 - 1/4 = 7/4 units. So 7/4 units = 1064, 1 unit (1/4) ... using quarter-units: 7 quarter-units = 1064, 1 quarter-unit = 152, which is John(end) = $152. (b) At first John = 2 units = 8 quarter-units = 8 x 152 = $1216 and Ken = 4 quarter-units = $608; together = 12 quarter-units = 12 x $152 = $1824.


\(3\dfrac{2}{5}\) = \(\dfrac{[box]}{5}\)<br>What is the missing number in the box?

Convert mixed number to improper fraction: 3 x 5 + 2 = 17, so 3 2/5 = 17/5. Missing number = 17. Option (3).


Find the value of \(\dfrac{7}{8}\) - \(\dfrac{1}{4}\)


Arrange the following fractions from the smallest to the greatest.<br>\(1\dfrac{1}{4}\) , \(\dfrac{12}{11}\) , \(1\dfrac{1}{8}\)


Jane had 6 cakes. She gave \(\dfrac{1}{2}\) of a cake to her sister and \(\dfrac{1}{3}\) of a cake to her brother. How many cakes had she left?


Emma has 24 apples and oranges. \(\dfrac{3}{8}\) of the fruits are apples. How many more oranges than apples does Emma have?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Apples = 3/8 of 24 = 9. Oranges = 24 - 9 = 15. More oranges than apples = 15 - 9 = 6.


Amy has \(\dfrac{3}{5}\) kg of sugar. Bala has \(\dfrac{1}{3}\) kg of sugar more than Amy.
(a) How much sugar does Bala have? Express your answer in its simplest form.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg
(b) How much sugar do they have altogether? Express your answer in its simplest form.
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> kg


\(\dfrac{1}{3}\) of a bottle was filled with orange juice. After John poured in another 600 ml of orange juice, it became \(\dfrac{5}{9}\) full. How much orange juice can the bottle hold when it is completely full? Give your answer in millilitres.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ml

Increase in fraction filled = 5/9 - 1/3 = 5/9 - 3/9 = 2/9. This equals 600 ml, so 2 units = 600 ml, 1 unit (1/9) = 300 ml. Full bottle = 9 units = 9 x 300 = 2700 ml.


Arrange the following decimals in decreasing order.<br>7.051 , 7.101 , 7.011 , 7.105

Decreasing (greatest to smallest): 7.105 > 7.101 > 7.051 > 7.011. Option (4).


Nearest tenth: look at the hundredths digit (9). 38.695 rounds up to 38.7. Option (3).


Express \(5\dfrac{9}{25}\) as a decimal.


What is the missing number in the box?<br>8.175 = 8 + 0.1 + [box] + 0.005


A pen cost $2.60. Diana bought two pens and gave the cashier $10. How much change did she get?


The total length of one yellow ribbon and one green ribbon is 8.7 m. Each yellow ribbon is twice as long as the green ribbon. What is the length of the yellow ribbon?

Yellow = 2 units, green = 1 unit, total = 3 units = 8.7 m. 1 unit = 2.9 m. Yellow = 2 x 2.9 = 5.80 m. Option (4).


In a long jump competition, Aaron and Benson jumped the same distance while Caleb jumped 0.18 m more than Aaron. If the three boys jumped a total distance 4.56 m, how far did Aaron jump?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m

Subtract Caleb's extra: 4.56 - 0.18 = 4.38 m is 3 equal Aaron-jumps. Aaron = 4.38 / 3 = 1.46 m.


The price of apples sold in a shop is as follows:
One apple costs $0.90
A pack of five apples costs $3.75
Alice wants to buy 12 apples. What is the least amount of money she has to pay?
$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Buy 2 packs (10 apples) = 2 x $3.75 = $7.50, plus 2 single apples = 2 x $0.90 = $1.80. Total = $7.50 + $1.80 = $9.30. This is cheaper than other combinations.


A dress and five identical T-shirts cost $132.50. A dress and two of the identical T-shirts cost $75.80. What is the cost of one T-shirt?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Which of the following fractions is not the same as 0.4?


Arrange the following decimals from the largest to the smallest.<br>7.093, 7.903, 7.309, 7.39


Which one of the following is closest to 8?

Find the distance from 8: 7.5 is 0.5 away, 8.1 is 0.1 away, 7.95 is 0.05 away, 8.49 is 0.49 away. The smallest gap is 7.95.


A pot was filled with soup. Mrs Tan poured \(\dfrac{1}{2}\) of it for her son and \(\dfrac{2}{7}\) of it for herself. What fraction of the soup was left in the pot?


I am a number with 2 decimal places.
The digit 6 is in the ones place.
The digit in the tenths place is 2 less than the digit in the ones place.
The digit in the hundredths place is the largest odd number.
Round this number to the nearest tenth.

Ones = 6, tenths = 6 - 2 = 4, hundredths = 9 (largest odd digit). Number = 6.49. Rounding to the nearest tenth: hundredths digit 9 rounds the 4 up to 5, giving 6.5.


Bala is 0.05 m taller than Paul. Zoe is 0.18 m shorter than Bala. Zoe is 1.68 m tall. How tall is Paul?


Nora paid $164.20 for some pillows and 4 bolsters. The pillows cost $76.80. How much did each bolster cost?


Write a fraction between \(\dfrac{1}{3}\) and \(\dfrac{1}{4}\).

Use a common denominator: \(\dfrac{1}{3}=\dfrac{8}{24}\) and \(\dfrac{1}{4}=\dfrac{6}{24}\). A fraction in between is \(\dfrac{7}{24}\).


Express \(7\dfrac{1}{20}\) as a decimal.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


6 ones + 12 tenths + 4 hundredths = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of 28.67 ÷ 7.
Give your answer correct to 2 decimal places.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

28.67 ÷ 7 = 4.0957... Rounded to 2 decimal places = 4.10.


Henry and Jason had the same amount of money. After Jason bought 5 comic books, Henry had 4 times as much money as him. Comic book: $15.60 each. How much did Jason have left after buying the comic books?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Cost of 5 comic books = 5 × $15.60 = $78. Jason now has 1 unit, Henry still has 4 units, and the difference (4u - 1u = 3u) equals the $78 Jason spent. 3u = $78, so 1u = $26. Jason had $26 left.


Doreen had some beads for sale. She sold \(\dfrac{1}{3}\) of the beads in the morning and \(\dfrac{2}{5}\) of the beads in the afternoon. (a) What fraction of the beads was left? (b) Doreen had 28 beads left. How many beads did she have at first?<br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


8 apples and an orange cost $8.60. 4 apples and an orange cost $5. (a) Find the cost of an apple. (b) Find the cost of an orange.<br>(a) $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, (b) $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) The difference between the two purchases is 4 apples = $8.60 - $5 = $3.60, so 1 apple = $3.60 ÷ 4 = $0.90. (b) From 4 apples + 1 orange = $5: 4 apples = 4 × $0.90 = $3.60, so 1 orange = $5 - $3.60 = $1.40.


Which of the following is a common multiple of 4 and 7?

A common multiple of 4 and 7 must be in both times tables. Multiples of 7: 7, 14, 21, 28... Multiples of 4: 4, 8, 12, ..., 28. 28 = 4 × 7 is a common multiple. Answer: 28.


In 23.41, which digit is in the tenths place?

In a decimal, the first digit after the decimal point is the tenths place. In 23.41, the digit right after the point is 4. Answer: 4.


Arrange the following from the smallest to the greatest.<br>\(\dfrac{1}{5}\), 0.83, \(\dfrac{7}{100}\)


Andy had 204 balloons. \(\dfrac{2}{3}\) of the balloons were blue and the rest were grey and white. There were 3 times as many grey balloons as white balloons. How many white balloons were there?

Blue = \(\dfrac{2}{3}\) × 204 = 136. Grey and white together = 204 − 136 = 68. Grey is 3 times white, so the 68 splits into 3 + 1 = 4 equal parts. White = 68 ÷ 4 = 17. Answer: 17.


(a) Write twenty thousand and sixty-four in numerals. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Round 3459 to the nearest thousand. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Twenty thousand = 20 000, plus sixty-four = 64, giving 20 064. (b) 3459 is between 3000 and 4000; the hundreds digit is 4 (less than 5), so round down to 3000.


Find the value of
(a) \(\dfrac{2}{3}\) + \(\dfrac{5}{9}\). Express your answer as a mixed number. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) \(\dfrac{7}{8}\) − \(\dfrac{5}{6}\) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Ray walked \(5\dfrac{3}{4}\) km. He walked \(\dfrac{2}{5}\) km less than John. What was the total distance they had walked? Express your answer in the simplest form.


Tracy had 3485 badges and Ryan had 1096 badges. Tracy gave some badges to Ryan. In the end, Ryan had twice as many badges as Tracy.
(a) How many badges did Tracy have in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many badges did Tracy give to Ryan? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Total badges stay the same: 3485 + 1096 = 4581. In the end Ryan has twice Tracy, so the total is 3 equal parts (Tracy 1 part, Ryan 2 parts). (a) Tracy's final amount = 4581 ÷ 3 = 1527. (b) Badges given = Tracy's start − Tracy's end = 3485 − 1527 = 1958.


What is the missing number in the box?<br>\(\dfrac{3}{5}=\dfrac{27}{ }\)

27 = 3 × 9, so multiply the denominator by 9 too: 5 × 9 = 45. The missing number is 45 (option 4).


In 18 298, which digit is in the thousands place?

18 298: the digits from the right are 8 (ones), 9 (tens), 2 (hundreds), 8 (thousands), 1 (ten thousands). The thousands digit is 8 (option 3).


Which of the following numbers are correctly arranged from the greatest to the smallest?

Option 4: 72 931 > 72 139 > 38 059 > 35 890 is in correct descending order. The other options are not fully descending.


Find the sum of \(\dfrac{1}{4}\) and \(\dfrac{2}{6}\).


Lamp A flashes red light once every 2 minutes. Lamp B flashes yellow light once every 4 minutes and Lamp C flashes blue light once every 7 minutes. What is the shortest possible time taken for all the lamps to flash light at the same time?

Find the lowest common multiple of 2, 4 and 7. LCM of 2 and 4 is 4; LCM of 4 and 7 is 28. So they flash together after 28 minutes (option 3).


A train was scheduled to leave the train station at City A at 2.35 p.m. It would take 6 hours and 20 minutes to reach City P. However, the train left the station at City A 25 minutes later than the scheduled time. What time would the train reach City P?


The digit 5 stands for 50 when it is in the tens place. In 9750, the 5 is in the tens place, so it stands for 50.


Rounding to the nearest ten: 81 496 rounds up to 81 500 (the ones digit 6 rounds the tens up from 9 to 81 500). 81 444 rounds to 81 440, 81 506 rounds to 81 510, 81 554 rounds to 81 550.


A multiple of 9 can be divided exactly by 9. 36 = 9 × 4, so 36 is a multiple of 9.


Compare by place value: 4.036, 4.06, 4.16, 4.306. The smallest is 4.036 (tenths digit 0, then hundredths 3).


A year has 12 months. 384 × 12 = 4608 muffins.


5787 ÷ 9 = 643 exactly (5787 is a multiple of 9). So 5787 + 2 = 5789 leaves a remainder of 2 when divided by 9. 5789 ÷ 9 = 643 r 2.


Peter's savings stay the same. Let Michelle's first share be 1 unit, Peter = 2 units. After +$5499, Michelle = 2 × Peter = 4 units. So the $5499 = 4u − 1u = 3u, giving 1u = $5499 ÷ 3 = $1833. Total now = Peter (2u) + Michelle (4u) = 6u = $1833 × 6 = $10998.


Water left = 25.68 − 9 = 16.68 l. Poured into 6 bottles: 16.68 ÷ 6 = 2.78 l per bottle.


The movie ends when Jasmine finishes watching: she started 18 min after 11.49 a.m. and watched 2 h 24 min, so total time after 11.49 a.m. = 18 min + 2 h 24 min = 2 h 42 min. 11.49 a.m. + 2 h 42 min = 2.31 p.m. = 14 31 in 24-hour clock.


(a) 5 packets of corn flour = 2.7 × 5 = 13.5 kg. (b) The extra 5 corn-flour packets weigh 13.5 kg, so the remaining flour (equal numbers of each type) = 25.5 − 13.5 = 12 kg. Each matched pair (1 corn + 1 plain) = 2.7 + 1.3 = 4 kg. Number of pairs = 12 ÷ 4 = 3, so he sold 3 packets of plain flour.


Let Kumar = 1 unit. Wei Ming = 2 units. Hakim = 3 × Wei Ming = 6 units. Total = 1 + 2 + 6 = 9 units = $7092, so 1 unit = $7092 ÷ 9 = $788. (a) Kumar = $788. (b) Hakim = 6 units = $788 × 6 = $4728.


Tulips: \(\dfrac{5}{9}\) sold = 85, so 1 unit (\(\dfrac{1}{9}\)) = 85 ÷ 5 = 17. Tulips left = \(\dfrac{4}{9}\) = 4 × 17 = 68. (a) 68 tulips left. (b) Roses left = tulips left = 68, and roses left are \(\dfrac{1}{3}\) of the roses (since \(\dfrac{2}{3}\) sold). So roses at first = 3 × 68 = 204.


If all 60 were bicycles: 60 × 2 = 120 wheels. Extra wheels = 156 − 120 = 36, and each tricycle adds 1 extra wheel, so tricycles = 36. Bicycles = 60 − 36 = 24. (a) 24 bicycles. (b) Tricycles − bicycles = 36 − 24 = 12 more tricycles.


Look at the tens digit (5). Since 52 ≥ 50, round up: 43 852 → 43 900.


4 hundredths is the second place after the decimal point. In 387.64 the 4 is in the hundredths place.


Thousandths take 3 decimal places. \(\dfrac{53}{1000}\) = 0.053.


A fraction is in simplest form when numerator and denominator share no common factor besides 1. \(\dfrac{2}{6}\) can be simplified to \(\dfrac{1}{3}\), so it is not in simplest form.


After Mandy gives away 92, the total left is 1712 − 92 = 1620. This is 5 + 1 = 6 units (William = 5 units, Mandy = 1 unit). 1 unit = 1620 ÷ 6 = 270, so Mandy had 270 in the end.


1 apple = $5.25 ÷ 3 = $1.75. An apple costs $0.60 less than an orange, so orange = $1.75 + $0.60 = $2.35.


The factors of 21 are 1, 3, 7 and 21. Besides 1 and 21, the other two factors are 3 and 7.


(a) Midnight is 24 00; 36 min before is 24 00 − 36 min = 23 24. (b) From 10 35 to 13 08: 10 35 to 13 35 is 3 h, but 13 08 is 27 min short, so 3 h − 27 min = 2 h 33 min.


Side = perimeter ÷ 4 = 36 ÷ 4 = 9 m. Area = 9 × 9 = 81 m².


Total is 3 + 1 = 4 units. 1 unit (Wen Long) = 8.34 ÷ 4 = 2.085 km ≈ 2.09 km (to 2 d.p.).


At first the gap is $48. Giving $36 widens the gap by 2 × $36 = $72. New difference = $48 + $72 = $120.


Total pupils = 386 + 125 = 511. 511 ÷ 8 = 63 remainder 7. (a) The remainder needs an extra group/teacher, so 63 + 1 = 64 teachers. (b) The last group has the remainder = 7 pupils.


(a) Bags must divide both 90 and 72 — the common factors are 1, 2, 3, 6, 9, 18. The greatest (most bags possible) is 18 bags. (b) Each bag holds 90 ÷ 18 = 5 candies and 72 ÷ 18 = 4 jellies, total 5 + 4 = 9 per bag.


The difference between the two buys is 3 pens − 3 erasers = $2.40. So 3 × (pen − eraser) = $2.40, giving pen − eraser = $0.80. (a) A pen costs $0.80 more than an eraser. (b) 1 pen = $0.80 + $0.95 = $1.75.


The tens digit is 4, so round down. 13 845 to the nearest hundred is 13 800.


Convert the mixed number to an improper fraction: \(7\dfrac{4}{5} = \dfrac{7\times5+4}{5} = \dfrac{39}{5}\). The missing number is 39.


The first digit after the decimal point is the tenths place. In 45.67 that digit is 6.


Compare digit by digit: 5079 < 5709 < 5790. Smallest to greatest is 5079, 5709, 5790.


A multiple of both 3 and 4 is a multiple of 12. 24 = 12 × 2, which is divisible by both 3 and 4.


Rounding to the nearest tenth: 82.34 has hundredths digit 4, so it rounds down to 82.3. (82.24 -> 82.2; 82.235 -> 82.2; 82.354 -> 82.4.)


9 - 6 = 3 packets left = 3.42 l, so 1 packet = 3.42 ÷ 3 = 1.14 l. At first she had 9 packets = 1.14 × 9 = 10.26 l.


One full turn of the minute hand = 60 min. 1 1/4 turns = 60 + (1/4 × 60) = 60 + 15 = 75 min.


From 11 10 to 13 10 is 2 h. But the end is 13 05, which is 5 min before 13 10. So duration = 2 h - 5 min = 1 h 55 min.


Side = √36 = 6 cm. Perimeter = 4 × 6 = 24 cm.


The factors of 6 are 1, 2, 3 and 6. Besides 1 and 6, the other two factors are 2 and 3.


7.21 - 5.38 = 1.83. Rounded to 1 decimal place: 1.8.


The wallet was 1/5 of his money, so 4/5 remained after the wallet. That 4/5 = $90 + $104 = $194. So 1/5 = $194 ÷ 4 = $48.50 spent on the wallet.


To use the fewest boxes, use as many large (6) boxes as possible. 19 × 6 = 114, leaving 5. 5 = one box of 3 + one box of 2. So 19 boxes of 6, 1 box of 3, 1 box of 2.


Start equal; let apples left = 1 unit, oranges left = 3 units. Apples started = 1 unit + 48; oranges started = 3 units + 36. Equal start: 1 unit + 48 = 3 units + 36, so 2 units = 12 and 1 unit = 6. (a) Apples at first = 6 + 48 = 54. (b) Oranges left = 3 units = 3 × 6 = 18.


Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 27: 1, 3, 9, 27. The common factors are 1, 3 and 9. Among the options, only 9 is a factor of both. Answer: 9.


Rounding to the nearest ten gives 72 500 for numbers from 72 495 to 72 504. 72 443 rounds to 72 440; 72 495 rounds to 72 500; 72 539 rounds to 72 540; 72 554 rounds to 72 550. Answer: 72 495.


Convert the mixed number to an improper fraction: \(6\dfrac{4}{7}=\dfrac{6\times7+4}{7}=\dfrac{42+4}{7}=\dfrac{46}{7}\). The missing number is 46.