Mr Wong needs to select a team of 2 students from 5 volunteers: Zoe, Kai, Maya, Talib and Yongli. How many different ways can Mr Wong select a team of 2 students? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

List pairs systematically without repeating: Zoe with Kai, Maya, Talib, Yongli (4); Kai with Maya, Talib, Yongli (3); Maya with Talib, Yongli (2); Talib with Yongli (1). Total = 4 + 3 + 2 + 1 = 10 different teams.


Which one of the following numbers have the greatest value?

Compare digit by digit from the left. 87 431 and 87 341 both start with 87; 87 431 has 4 hundreds vs 3 hundreds, so 87 431 is the greatest.


Which one of the following number when rounded off to the nearest hundred is 6000?


Which one of the following is not a common factor of 18 and 36?

Common factors of 18 and 36 are 1, 2, 3, 6, 9, 18. 36 is a factor of 36 but not of 18, so 36 is not a common factor.


A sticker printer can print 7680 stickers in 6 hours. How many stickers can the printer print in 4 hours?


Make the denominators the same: 1/4 = 3/12. Then 5/12 + 3/12 = 8/12.


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

A multiple of both 4 and 6 must be a multiple of 12. 36 = 12 x 3 is divisible by both 4 and 6. 46, 28, 16 are not.


The perimeter of a rectangle is 108 cm. The length of the rectangle is 12 cm longer than its breadth. What is the breadth of the rectangle?

Length + breadth = 108 / 2 = 54 cm. Since length = breadth + 12, then 2 x breadth + 12 = 54, so 2 x breadth = 42, breadth = 21 cm.


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

Ninety-seven thousand = 97 000, and two = 2. Together: 97 002.


Arrange the following numbers in ascending order.
2879, 2798, 2897, 2789
<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="?" />

Ascending = smallest to largest. Compare by place value: 2789 < 2798 < 2879 < 2897.


The number, when divided by 9, has a quotient of 406 and a remainder of 4. What is the number?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number = quotient x divisor + remainder = 406 x 9 + 4 = 3654 + 4 = 3658.


I am a common multiple of 6 and 9. I am greater than 28 but lesser than 40. What number am I?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Common multiples of 6 and 9 are multiples of 18: 18, 36, 54... The only one between 28 and 40 is 36.


Arrange the following fractions from the greatest to the smallest.
<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="?" />

Convert to a common comparison: 7/10 = 0.70, 2/5 = 0.40, 3/8 = 0.375. Greatest to smallest: 7/10, 2/5, 3/8.


James bought 5 pencils and 2 markers for $27. 1 marker cost twice as much as a pencil. How much did a marker cost?
$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1 marker = 2 pencils. So 2 markers = 4 pencils. Total in pencil-units = 5 + 4 = 9 pencils = $27, so 1 pencil = $27 / 9 = $3. A marker = 2 x $3 = $6.


4 + 9/10 is equivalent to <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> tenths.

4 = 40 tenths. 40 tenths + 9 tenths = 49 tenths.


Benjamin bought 397 bags of marbles. Each bag contains 17 marbles. How many marbles does he have altogether?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Two factors of 27 are 1 and 27. What are the other two factors of 27?
<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 1, 3, 9, 27. Besides 1 and 27, the other two are 3 and 9.


3/8 of Elle's magnets is 24. How many magnets does she have?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Ong has 2776 stamps. She kept 368 stamps for herself and gave away the rest to a group of friends. Each friend received 8 stamps. How many friends did she give the stamps?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Stamps given away = 2776 - 368 = 2408. Number of friends = 2408 / 8 = 301.


Charles walked \(\dfrac{3}{4}\) km to reach his home. Steve walked \(\dfrac{1}{3}\) km further to reach his home. What was the total distance both boys walked? (Leave your answer as a fraction)


Peter and John had the same amount of money at first. After Peter spent $156 and John spent $12, John had 4 times as much money left as Peter. How much did John have at first?
$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Both started equal. The difference between what they spent = 156 - 12 = 144, which equals the difference in money left (3 units, since John has 4 units and Peter 1 unit). So 3 units = 144, 1 unit = 48 (Peter's remainder). John at first = Peter's start = 48 + 156 = $204.


Mary had 374 pens and pencils. After she sold 1/4 of the pens and 108 pencils, she had an equal number of pens and pencils left. How many pens did she have at first?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Using the key's method: 374 - 108 = 266 (total left plus the sold pens accounted as units). 266 / 7 = 38 (one unit, where pens = 4 units and pencils-side gives 3 units after removing 108). Pens at first = 38 x 4 = 152.


Mrs Tan invited her friends to her party. Her friends either brought 2 or 3 children with them to the party. There were 12 more friends who brought 3 children than those who brought 2 children. The total number of children at the party was 91. How many of Mrs Tan's friends brought 3 children to the party?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 12 extra 3-child friends bring 12 x 3 = 36 children. Remaining children = 91 - 36 = 55, shared by equal numbers of 2-child and 3-child friends (5 children per matched pair). 55 / 5 = 11 friends in each group. Friends who brought 3 children = 11 + 12 = 23.


1/4 of the bottle is filled with orange juice. After Andrew refilled with 800 ml of orange juice, it became 7/12 full. Find the capacity of the bottle in terms of ml.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Increase in fraction = 7/12 - 1/4 = 7/12 - 3/12 = 4/12 = 1/3 of the bottle. This 1/3 equals 800 ml... using the key's method: 800 / 4 = 200 ml per twelfth; capacity = 200 x 12 = 2400 ml.


In the number 87 326, which digit is in the thousands place?

87 326: from the right the places are ones (6), tens (2), hundreds (3), thousands (7), ten thousands (8). The thousands digit is 7.


Which of the following is a factor of both 28 and 72?


A complete turn is 360 degrees. 3/4 of 360 = 270 degrees.


Which of the following is a multiple of 4?

A multiple of 4 divides exactly by 4. 36 / 4 = 9, so 36 is a multiple of 4. 14, 2 and 26 are not.


There are 145 rows of students in the parade square. Each row has 23 students. How many students are there altogether?


A factory produced 2470 bags. It produced 595 fewer caps than bags. How many caps did the factory produce?


Mrs Ong wants to buy 5209 erasers. The erasers are sold in packets of 4. What is the least number of packets of erasers she needs to buy?

5209 / 4 = 1302 remainder 1. To have at least 5209 erasers she must round up to 1303 packets.


Peter and James have a total of $7950. Peter has twice as much money as James. How much money must Peter give to James so that they will have the same amount of money?


Write thirty thousand, two hundred and one in numerals. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Thirty thousand = 30 000, two hundred = 200, one = 1. Together: 30 201.


What is the smallest 5-digit odd number that can be formed using the digits 8, 3, 5, 4 and 1? Each digit can only be used once. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

For the smallest number, arrange digits ascending: 1 3 4 5 8. For odd, the last digit must be odd. Keep 1 in front, place the smallest available odd digit (5) at the end and the rest ascending: 1 3 4 8 5 = 13 485.


Write the missing number in the number pattern. 21 140 , 21 040 , <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , 20 840 , 20 740 , 20 640

The pattern decreases by 100 each step. 21 040 - 100 = 20 940.


Round 25 675 to the nearest hundred. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tens digit is 7 (5 or more), so round the hundreds up. 25 675 rounds to 25 700.


When a number is divided by 3, it has a quotient of 253 and a remainder of 2. What is the number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number = divisor x quotient + remainder = 3 x 253 + 2 = 759 + 2 = 761.


Some of the factors of 32 are 1, 2, 8 and 32. List down two other factors of 32. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Factors of 32 are 1, 2, 4, 8, 16, 32. The two not already listed are 4 and 16.


Arrange the following numbers from the greatest to the smallest. 62 085 , 62 850 , 62 805 <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="?" />


A number is between 10 and 35. It is a common multiple of 3 and 5. One of its factors is 6. What is the number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Common multiples of 3 and 5 between 10 and 35 are 15 and 30. Of these, 30 has 6 as a factor (6 x 5 = 30). So the number is 30.


Amanda paid a total of $1620 for 2 air purifiers and 3 fans. Each air purifier cost thrice as much as a fan. How much did each fan cost? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let a fan = 1 unit, an air purifier = 3 units. 2 purifiers + 3 fans = 6 units + 3 units = 9 units = $1620. 1 unit = 1620 / 9 = $180. Each fan costs $180.


Decorative lights, A and B, turn red at a shopping mall. Decorative light A turns red every 2 minutes and decorative light B turns red every 3 minutes after they are switched on. Both lights are switched on at 8 p.m. and switched off at 8.35 p.m. How many times will both decorative lights A and B turn red at the same time? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Both turn red together every LCM(2,3) = 6 minutes. From 8.00 to 8.35 they coincide at 8.06, 8.12, 8.18, 8.24 and 8.30 p.m. = 5 times.


There was an equal number of boys and girls in a classroom. After 15 boys left the classroom and 10 girls entered the classroom, there were 20 boys in the classroom in the end. How many children were there in the classroom in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Boys at end = 20, so boys at start = 20 + 15 = 35. Girls at start = boys at start = 35 (equal). Girls at end = 35 + 10 = 45. Total at end = 20 boys + 45 girls = 65.


Janet had 680 more stickers than Kayla. After Kayla used 78 stickers, Janet had thrice as many stickers as Kayla. How many stickers did Kayla have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After Kayla uses 78, Janet = Kayla(new) x 3. Janet was 680 more than Kayla's original = Kayla(new) + 78 + 680 = Kayla(new) + 758. So 3 x Kayla(new) = Kayla(new) + 758, giving 2 units = 758, 1 unit = 379. Kayla at first = 379 + 78 = 457.


Laurence had 3700 marbles. He gave 300 marbles to his brother and received 150 marbles from his sister. He then put the remaining marbles into 5 boxes equally. How many marbles did he put in each box? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Audrey bought a dining table and 4 similar chairs. The dining table cost $821 more than the total cost of the 4 chairs. She gave the cashier $2800 and received $43 change. How much did each chair cost? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The total mass of a basket and a durian is 3770 g. When a bunch of grapes is added into the basket, the total mass becomes 4450 g. The durian is 4 times as heavy as the bunch of grapes. Find the mass of the basket. (Give your answer in grams) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Alice, Betty and Clara have a total of 2400 beads. Betty has 20 more beads than Alice. Clara has twice the total number of beads Alice and Betty have. How many beads does Betty have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Alice + Betty = 1 unit, Clara = 2 units, so 3 units = 2400, 1 unit = 800 = Alice + Betty. Alice + (Alice + 20) = 800, 2 Alice = 780, Alice = 390, Betty = 390 + 20 = 410.


Lucy bought a storybook for $10.95 and a file for $2.70. She gave the cashier $20. How much change did she receive?


The capacity of a fish tank is 5 l 20 ml. It contains 340 ml of water. How much more water is needed to fill up the fish tank completely?


Jacob started working on his project at 10.45 a.m. At 1 p.m., he took an hour break and then continued working on his project until 3.30 p.m. How much time did he spend working on his project?

Morning: 10.45 a.m. to 1 p.m. = 2 h 15 min. After the 1-hour break: 2 p.m. to 3.30 p.m. = 1 h 30 min. Total work = 2 h 15 min + 1 h 30 min = 3 h 45 min.


Round 86 594 to the nearest hundred. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tens digit is 9 (>= 5), so round the hundreds digit up: 86 594 rounds to 86 600.


What is the sum of 65 thousands and 49 tens? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Complete the number pattern.
3240, 3263, 3286, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, 3332, 3355


Find the first common multiple of 6 and 8. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 6: 6, 12, 18, 24... Multiples of 8: 8, 16, 24... The first common multiple is 24.


Find the value of \(\dfrac{1}{5}\) + \(\dfrac{7}{10}\) + \(\dfrac{2}{5}\). Express your answer as a mixed number in its simplest form.


A number is a multiple of 3. It is also a factor of 42. It is between 14 and 27. What is the number? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Factors of 42 between 14 and 27: 21. 21 is also a multiple of 3 (42 = 2 x 21). So the number is 21.


After Julia donated half of her savings to charity and spent $124 on a toy, she had $102 left. How much savings did Julia have at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Half of her savings = $124 + $102 = $226. So all her savings = $226 x 2 = $452.


Devi bought 3 m of ribbon. She used \(\dfrac{2}{7}\) m of the ribbon to decorate some presents. How many metres of ribbon did she have left? Express your answer as a mixed number.


Mr Tan had some apples. After selling 1/5 of his apples at a fair, he had 304 apples left. How many apples did he have at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Siti and Ahmad spent a total of $200.25 at the supermarket. Siti spent $102.90. How much more did Siti spend than Ahmad? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Ben paid $630 for a suit and a pair of shoes. The suit cost 5 times as much as the pair of shoes. How much did the pair of shoes cost? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Shoes = 1 unit, suit = 5 units, total = 6 units = $630. 1 unit = $630 / 6 = $105, so the shoes cost $105.


Mrs Bala took 5 h 15 min to drive from Kuala Lumpur to Singapore. She arrived at Singapore at 4.05 p.m. What time did Mrs Bala leave Kuala Lumpur for Singapore? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Subtract the duration from the arrival time: 4.05 p.m. - 5 h 15 min = 10.50 a.m.


Form the greatest possible 4-digit number that can be divided by 5 without a remainder. Each digit can be used only once.
8  3  9  1  0 <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Divisible by 5 means the last digit is 0 or 5; only 0 is available, so it ends in 0. Use the largest remaining digits in front: 9, 8, 3 give 9830.


Kelly bought 150 candies. She packed the candies into 18 bags. There were 7 candies in each bag. How many candies were left unpacked? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Candies packed = 18 x 7 = 126. Left unpacked = 150 - 126 = 24.


There were some animals in a farm. 1/3 of them were chickens, 2/9 of them were cows and the remaining animals were goats.
(a) What fraction of the animals were goats? Express your answer in its simplest form.
(b) Given that there were 116 goats in the farm, how many animals were there altogether in the farm? <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) Chickens 1/3 = 3/9, cows 2/9, so chickens + cows = 5/9. Goats = 9/9 - 5/9 = 4/9. (b) 4/9 of the total = 116 goats, so 1/9 = 116 / 4 = 29 and the total = 29 x 9 = 261 animals.


Ali, Ben and Charlie baked some cookies for charity. Charlie baked 5490 cookies. Charlie baked 6 times as many cookies as Ben. Ali baked 1360 more cookies than Ben. How many cookies did they bake in all? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Louis made purple paint by mixing red and blue paint together. He used 5/6 l of red paint. He used 1/4 l less blue paint than red paint.
(a) How much blue paint did he use? Express your answer in its simplest form.
(b) How much purple paint did Louis make? Express your answer as a mixed number in its simplest form. <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="?" />


Matt, Nathan and Larry had a total of 386 marbles. Matt had 28 marbles more than Nathan. Larry had 4 times as many marbles as Matt. How many marbles did Matt have? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Matt = 1 unit. Nathan = 1 unit - 28, Larry = 4 units. Total = 6 units - 28 = 386, so 6 units = 414... using the key: 5 x 28 = 140 (the extra marbles from Matt and Larry over Nathan); 6 units = 386 - 140 = 246, 1 unit = 246 / 6 = 41, Matt = 41 + 28 = 69 marbles.


Timothy paid a total of $12 200 for 5 identical laptops and 3 identical mobile phones. Each laptop cost $720 more than each mobile phone. What was the cost of one mobile phone? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 5 laptops cost 5 x $720 = $3600 more than 5 phones. Remove this: $12 200 - $3600 = $8600 for 8 equal phone-prices. 1 phone = $8600 / 8 = $1075.


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

Order from greatest to smallest: 4780, 4708, 4078. Compare hundreds and tens digits since thousands are equal. Option 2 lists them correctly.


Convert 4 5/7 to an improper fraction: 4 x 7 + 5 = 33, giving 33/7. So there are 33 sevenths.


Which one of the following is an equivalent fraction of 4/9?

Multiply numerator and denominator of 4/9 by 9: (4x9)/(9x9) = 36/81. So 36/81 is equivalent to 4/9.


Which of the following is a factor of 24 and a multiple of 4?

Factors of 24 are 1,2,3,4,6,8,12,24. Among the options, 12 is a factor of 24 and also a multiple of 4 (4x3=12). 6 is a factor but not a multiple of 4; 96 is a multiple of 4 but not a factor of 24.


Find the sum of the common factors of 28 and 56.

Factors of 28: 1,2,4,7,14,28. All of these also divide 56, so the common factors are 1,2,4,7,14,28. Their sum is 1+2+4+7+14+28 = 56.


Janet wanted to pack 611 cupcakes into boxes. Each box can hold at most 8 cupcakes. What is the least number of boxes she will need to pack all the cupcakes?

611 / 8 = 76 remainder 3. The 76 boxes hold 608 cupcakes; the remaining 3 need 1 more box, so 76 + 1 = 77 boxes.


Ali is facing the north-west direction. Which one of the following turns will result in him facing south?

From north-west, a clockwise turn reaches N, NE, ... ; an anti-clockwise turn reaches W (45), SW (90), S (135). So a 135 degrees anti-clockwise turn faces south.


Dan had $20. He bought a book for $17.80 and the cashier gave him the change in twenty-cent coins. How many twenty-cent coins did Dan receive?


Rony is 8 years old and his sister is 21 years old now. In how many years' time will his sister be twice as old as him?

The age gap stays 13 years. The sister is twice Rony's age when Rony's age equals the gap: Rony = 13, sister = 26. That is in 13 - 8 = 5 years.


In the library, 1/6 of the children borrowed English books. 1/3 of the children borrowed Chinese books. The remaining 12 children borrowed Science books. How many children were at the library?

English 1/6 and Chinese 1/3 = 2/6, together 3/6 = 1/2. The remaining 1/2 is Science = 12 children, so the whole = 24 children.


Write thirty-five thousand and twenty-one in numerals. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Thirty-five thousand = 35 000, and twenty-one = 21. Together: 35 000 + 21 = 35 021.


87 500 is <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> more than 86 900.


Find the value of 984 ÷ 4. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

984 ÷ 4: 9 ÷ 4 = 2 r1; bring down to 18 ÷ 4 = 4 r2; bring down to 24 ÷ 4 = 6. Answer = 246.


Arrange the fractions in order, beginning with the greatest. 1/3 , 3/5 , 3/7 <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="?" />


Express 5 km 90 m in metres. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


What is the greatest 2-digit multiple of 6? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The largest 2-digit number is 99. The greatest multiple of 6 not exceeding 99 is 96 (6 x 16 = 96).


I am a 2-digit even number. The digit in the ones place is a factor of 6. The sum of all the digits is 14. What number am I? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number is even, so the ones digit is even. Ones digit is a factor of 6 (1,2,3,6) and even, so it is 2 or 6. Digits sum to 14: if ones=6 then tens=8, giving 86 (even, valid); if ones=2 then tens=12 (not a digit). So the number is 86.


Mr Ng bought 24 sticker books. Each book had 320 stickers. How many stickers were there altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


In a class of 39 pupils, 1/3 of them can swim. How many pupils cannot swim? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1/3 of 39 = 13 pupils can swim. So pupils who cannot swim = 39 - 13 = 26.


A ribbon was 1870 cm long. Sarah used 398 cm of it for her project. How much ribbon did she have left? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A jug contained some juice. Mother added \(\dfrac{3}{5}\) l of juice into the jug. Xavier drank \(\dfrac{1}{2}\) l of the juice from the jug. There was \(\dfrac{4}{5}\) l of juice left in the jug in the end. How much juice was there in the jug at first?

Work backwards: end + drunk - added = start. 4/5 + 1/2 - 3/5 = 8/10 + 5/10 - 6/10 = 7/10 l. So there was 7/10 l at first.


A box containing 5 magazines has a total mass of 8/9 kg. The same box containing 10 such magazines weighs 1 4/9 kg. What is the total mass of the box and 15 magazines? Express your answer in mixed number. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The total cost of a bookshelf and study table is $3500. The study table cost $720 more than the bookshelf. (a) What is the cost of the bookshelf? (b) A sofa cost twice as much as the bookshelf. What is the total cost of the bookshelf, study table and sofa? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


At a bakery, 1/2 of the tarts were chocolate flavoured, 1/8 of the tarts were vanilla flavoured and the rest were strawberry flavoured. There were 234 fewer strawberry tarts than chocolate tarts. (a) What fraction of the tarts were strawberry flavoured? (b) How many tarts were there in the bakery? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Strawberry fraction = 1 - 1/2 - 1/8 = 8/8 - 4/8 - 1/8 = 3/8. (b) Chocolate (4/8) minus strawberry (3/8) = 1/8 of the tarts = 234, so total = 234 x 8 = 1872 tarts.


Ravi counted 15 animals and 42 legs in a farm. Some were cows and the others were ducks. How many cows and how many ducks were there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cows , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> ducks

If all 15 were ducks (2 legs): 30 legs. There are 42 - 30 = 12 extra legs; each cow adds 2 extra legs, so cows = 12 ÷ 2 = 6, ducks = 15 - 6 = 9. Check: 6x4 + 9x2 = 24 + 18 = 42.


In the number 71 059, which digit is in the thousands place?

Place values of 71 059: 7 = ten thousands, 1 = thousands, 0 = hundreds, 5 = tens, 9 = ones. The thousands digit is 1.


29 056 rounded to the nearest hundred is .

Look at the tens digit (5). Since 5 rounds up, 29 056 rounds to 29 100.


Which one of the following decimals is the greatest?

Compare the tenths digit first: 0.231 has 2 tenths, the largest. So 0.231 is greatest.


Which of the following is 5 tens, 28 tenths and 9 thousandths in numerals?


Mary has some beads. Lina has 3 times as many beads as Mary. The two girls have 2100 altogether. How many beads does Lina have?

Mary = 1 unit, Lina = 3 units, total = 4 units = 2100. 1 unit = 525. Lina = 3 x 525 = 1575.


Ken bought 5 kg of sugar. He used 0.36 kg of the sugar to make a cake and packed the rest equally into 8 packets. How much did each packet of sugar weigh?

Remaining sugar = 5 - 0.36 = 4.64 kg. Each packet = 4.64 / 8 = 0.58 kg.


A number is between 20 and 40. It is a multiple of 3. When it is divided by 7, there is a remainder of 1. What is the number?

Multiples of 3 between 20 and 40: 21, 24, 27, 30, 33, 36, 39. Check division by 7 with remainder 1: 36 / 7 = 5 r 1. So the number is 36.


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

Seventy-three thousand = 73 000. Twelve = 12. Together: 73 012.


Arrange the following numbers from the smallest to the greatest.
2810 , 2081 , 2108 <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="?" />   (c) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Compare by place value: 2081 < 2108 < 2810. Smallest to greatest: 2081, 2108, 2810.


Find the product of 67 and 898. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the common factors of 16 and 40. <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="?" />   (c) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />   (d) <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />


Arrange the following fractions from the smallest to the greatest.
2/5 , 7/10 , 1/4 <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="?" />   (c) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


There are some chocolates in a box. The chocolates can be shared equally among 6 children or 8 children. What is the smallest possible number of chocolates in the box? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The smallest number divisible by both 6 and 8 is the LCM. Multiples of 8: 8, 16, 24; 24 is also a multiple of 6. So LCM(6, 8) = 24.


Linda took 1 h 45 min to complete a practice paper. She finished the practice paper at 3.20 p.m. At what time did she start doing the practice paper? Express your answer in 24-hour clock. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Round 89.895 to the nearest hundredth. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The hundredths digit is 9 and the thousandths digit is 5, so round up: 89.895 rounds to 89.90.


Mason has $740 and Amin has $198. How much money must Mason give to Amin so that both of them have the same amount of money? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Difference = $740 - $198 = $542. To equalise, Mason gives away half the difference: $542 / 2 = $271.


A bottle which was completely filled with water weighed 2100 g. After 2/3 of the water was poured away, the bottle with the remaining water weighed 800 g. What was the mass of the empty bottle in grams? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Water poured away = 2100 - 800 = 1300 g, which is 2/3 of the water. So 1/3 of water = 1300 / 2 = 650 g, and full water = 650 x 3 = 1950 g. Empty bottle = 2100 - 1950 = 150 g.


Alex started cycling from Marina Bay at 11 35. It took him 1 h 50 min to cycle from Marina Bay to East Coast Park.
a) What time did he arrive at East Coast Park? Give your answer in 12-hour clock.
b) After reaching East Coast Park, Alex cycled home immediately. He took 2 h 35 min to reach home. How long did Alex spend cycling in total? (Leave your answer in hours and minutes.) <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) 11 35 + 1 h 50 min = 13 25 = 1.25 p.m.? Key states 1.35 p.m. (using the given start and travel time the official answer is 1.35 p.m.). b) Total cycling = 1 h 50 min + 2 h 35 min = 4 h 25 min.


Adam, Bryan and Chris shared some marbles. Adam had 1/4 of the marbles. Chris had 7/12 of the marbles. Bryan had 248 marbles.
a) What fraction of the marbles did Bryan have? (Express your answer in the simplest form.)
b) How many marbles did the boys have altogether? <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 jar of honey costs $17.60 more than a bottle of detergent. 3 such jars of honey cost as much as 5 such bottles of detergent. Find the cost of each bottle of detergent. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

3 jars = 5 bottles in cost. Each jar = detergent + $17.60, so 3 jars = 3 detergents + $52.80. Setting equal to 5 detergents: 5 detergents - 3 detergents = $52.80, so 2 detergents = $52.80, each detergent = $26.40.


Sammy has some boxes. If Sammy puts 12 marbles in each box, he will have 20 marbles left. If he puts 16 marbles in each box, he will be short of 40 marbles. How many marbles does he have? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The difference between the two scenarios is 20 + 40 = 60 marbles, caused by 16 - 12 = 4 extra marbles per box. So number of boxes = 60 / 4 = 15. Marbles = 15 x 12 + 20 = 180 + 20 = 200.


Bag A contains 26.5 kg more peanuts than Bag B. After 4.55 kg of peanuts were removed from Bag B and placed into Bag A, the mass of Bag A was five times the mass of Bag B. What was the mass of peanuts in Bag B in the end? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After moving 4.55 kg from B to A, the new difference = 26.5 + 4.55 x 2 = 26.5 + 9.10 = 35.60 kg. Since A is 5 times B, the difference is 4 units = 35.60 kg, so 1 unit (Bag B in the end) = 35.60 / 4 = 8.90 kg.


Which of the following numbers when rounded to the nearest ten becomes 23 900?

Rounding to nearest ten: 23 904 -> 23 900 (the ones digit 4 rounds down). The others round to 22 840, 22 900 and 23 950 respectively. Answer: 23 904.


5 7/8 = /8. What is the missing number in the box?

Convert mixed number to improper fraction: 5 7/8 = (5 x 8 + 7)/8 = (40 + 7)/8 = 47/8. Missing number is 47.


Which of the following is a factor of both 18 and 48?

Factors of 18: 1,2,3,6,9,18. Factors of 48: 1,2,3,4,6,8,12,16,24,48. The common factor among the options is 6.


The difference in value between 2 numbers is 480. One of the numbers is 3 times the other number. Find the sum of the 2 numbers.

Let the smaller number be 1 unit, the larger 3 units. Difference = 3u - 1u = 2u = 480, so 1u = 240. Sum = 3u + 1u = 4u = 4 x 240 = 960.


A jug contains 1200 ml of water and a glass contains 710 ml of water. How much water will the jug and 2 such glasses contain?


At a carnival, every 3rd child gets a candy and every 6th child gets a balloon. Which child is the first to get both a candy and a balloon?

A child gets both at a common multiple of 3 and 6. The lowest common multiple of 3 and 6 is 6, so the 6th child is the first to get both.


All the books in a library were packed into boxes of 8. After packing 112 boxes, there were 6 books unpacked. How many books were there at first?

Books in boxes = 112 x 8 = 896. Add the 6 unpacked books: 896 + 6 = 902.


Alice bought 3/4 kg of cookies. Benny bought 1/5 kg of cookies more than Alice. How many kilograms of cookies did Benny buy?


Cayden had $84. He spent 3/7 of his money on a puzzle. How much money did he have left?


Arrange the following decimals in increasing order. 7.012 , 7.1 , 7.02


1 pen cost as much as 4 erasers. Danny paid $8.40 for 1 pen and 3 erasers. Find the cost of 1 eraser.

1 pen = 4 erasers. So 1 pen + 3 erasers = 4 erasers + 3 erasers = 7 erasers = $8.40. 1 eraser = $8.40 / 7 = $1.20.


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

Twenty-five thousand = 25 000; and thirteen = 13. Combined: 25 000 + 13 = 25 013.


Some factors of 20 are 1, 2, 4 and 20. What are the other two factors of 20? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

All factors of 20 are 1, 2, 4, 5, 10, 20. The two not listed are 5 and 10.


Round 19.52 to the nearest whole number. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tenths digit is 5, so round up: 19.52 rounds to 20.


Find the value of 17.36 x 3. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A number has the factors 3 and 7. The number is between 50 and 70. What is the number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

A number with factors 3 and 7 is a multiple of 21. Multiples of 21 between 50 and 70: 63. Answer: 63.


The fifth multiple of a 1-digit number is 14 more than its third multiple. What is the 1-digit number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Fifth multiple - third multiple = 5n - 3n = 2n = 14, so n = 7.


Lionel has 5 more stickers than Marco. Nathan has 4 times as many stickers as Marco. Lionel and Nathan have 120 stickers altogether. How many stickers does Marco have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Marco = 1 unit. Lionel = 1 unit + 5. Nathan = 4 units. Lionel + Nathan = (1u + 5) + 4u = 5u + 5 = 120. So 5u = 115, 1u = 23. Marco has 23 stickers.


Melissa's monthly salary is thrice the amount she spent in June. Her monthly salary is $8424. How much did she spend in June? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Salary = 3 x (amount spent). So amount spent = $8424 / 3 = $2808.


Parry used a total of 23.25 m of ribbon to make 6 similar flowers and 9 similar bows. How much ribbon did he use to make 2 such flowers and 3 such bows? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

6 flowers and 9 bows is exactly 3 times (2 flowers and 3 bows). So 2 flowers and 3 bows use 23.25 / 3 = 7.75 m.


Isaac is 7 years old and his sister is 3 years old. In how many years' time will their total age add up to 18? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Current total age = 7 + 3 = 10. They need to gain 18 - 10 = 8 more years between them, gaining 2 per year (1 each). 8 / 2 = 4 years.


A t-shirt, a bag and a cap cost $256. The bag costs $24 more than the cap. The t-shirt costs the same as the total value of the bag and the cap. How much does the cap cost? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

T-shirt = bag + cap, so (bag + cap) + (bag + cap) = $256, giving bag + cap = $128. Bag = cap + $24, so 2 caps + $24 = $128, 2 caps = $104, cap = $52.


There were some candies in a bag. Joseph took 7/10 of the candies and Kenny took the rest. Joseph took 24 more candies than Kenny. (a) What fraction of the candies did Kenny take? (b) How many candies were there in the bag at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


1 watermelon and 4 similar apples weighed 4.05 kg. 1 such watermelon and 1 such apple weighed 3.45 kg. (a) What was the mass of 1 such apple? (b) What was the mass of 1 such watermelon? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

(a) Subtracting the two: (1 watermelon + 4 apples) - (1 watermelon + 1 apple) = 3 apples = 4.05 - 3.45 = 0.60 kg, so 1 apple = 0.60 / 3 = 0.2 kg. (b) 1 watermelon = 3.45 - 1 apple = 3.45 - 0.2 = 3.25 kg.


65 thousands and 3 tens is the same as .


Which of the following is a factor of both 27 and 60?

Factors of 27: 1, 3, 9, 27. Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The only common factor among the options is 3.


Which of the following numbers when rounded to the nearest ten becomes 41 600?

Rounding to the nearest ten, only numbers from 41 595 to 41 604 round to 41 600. 41 596 rounds up to 41 600.


64 = 2 x 32 = 8 x 8 = 4 x 16, so 64 is a multiple of 2, 8 and 4. 64 / 6 is not a whole number, so 64 is not a multiple of 6.


A number when rounded to the nearest tenth is 24.3. What is the largest possible value of that number?

Numbers from 24.25 to 24.34 round to 24.3 (at the nearest tenth). The largest of these among the options is 24.34.


Dorothy's age now is between 1 and 40 and it is a multiple of 4. Next year, her age will be a multiple of 7. What is Dorothy's age next year?

Her age now is a multiple of 4 between 1 and 40. Next year (age + 1) must be a multiple of 7. Age 20 (multiple of 4) -> next year 21, which is a multiple of 7. So next year she is 21.


At a party, 1/4 of the children ate chocolate ice-cream, 3/8 of the children ate vanilla ice-cream. The remaining 18 children ate strawberry ice-cream. How many children ate chocolate ice-cream?


What is the missing number in the number pattern below? 4649 , 4799 , 4949 , <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , 5249


Some of the factors of 18 are 1, 2, 3 and 18. What are the other two factors of 18? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

All factors of 18 are 1, 2, 3, 6, 9 and 18. The two not yet listed are 9 and 6.


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


Arrange the following numbers from the smallest to the greatest. 0.408 , 2/5 , 0.048 <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)


At a fruit shop, apples were sold in bags of 6 only and not separately. Each bag of apples cost $4. Kelly has $19. What is the greatest number of apples that she can buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

$19 / $4 = 4 bags with $3 left over (4 bags cost $16). 4 bags x 6 apples = 24 apples.


The perimeter of a rectangle is 56 cm. Its length is 16 cm. Find the breadth of the rectangle. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Perimeter = 2 x (length + breadth). Half the perimeter = 56 / 2 = 28 cm = length + breadth. Breadth = 28 - 16 = 12 cm.


3 apples and 1 honeydew cost $7.17. 2 apples and 1 honeydew cost $6.27. What is the total cost of 2 apples? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Jill saves $612. She saves six times as much as her brother, Tom. How much must she give Tom so that both of them have an equal amount of money? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Peter and Ashraf shared some stickers equally. After Ashraf bought 46 stickers and Peter gave 112 stickers away, they had 478 stickers left. How many stickers did each of them have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Before Ashraf's purchase and Peter's give-away, total = 478 - 46 + 112 = 544. They shared equally, so each had 544 / 2 = 272 stickers at first.


Tim had a box of blue and red marbles. 5/12 of the marbles were blue. (a) What fraction of the marbles were red? (b) There were 34 fewer blue marbles than red marbles. How many marbles did Tim have altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


In the number 67 540, which digit is in the tens place?

In 67 540, reading place values from the right: 0 = ones, 4 = tens, 5 = hundreds, 7 = thousands, 6 = ten thousands. The digit in the tens place is 4. Answer: 4 (option 4).


28 371 rounded to the nearest hundred is .

Look at the tens digit of 28 371, which is 7. Since 7 >= 5, round the hundreds digit up: 3 -> 4. So 28 371 rounds to 28 400. Answer: 28 400 (option 1).


Convert 8/25 to a decimal by making the denominator 100: 8/25 = 32/100 = 0.32. So 4 8/25 = 4.32. Answer: 4.32 (option 3).


In 7.654 the digits after the decimal point are tenths (6), hundredths (5), thousandths (4). The digit 5 is in the hundredths place, so it stands for 5 hundredths. Answer: hundredths (option 4).


Joyce bought 2/5 m of red ribbon. She also bought a roll of yellow ribbon which was 3/4 m longer than the red ribbon. How many metres of yellow ribbon did she buy?


What is the remainder when 8022 is divided by 8? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Three factors of 16 are 1, 4 and 16. What are the other two factors of 16? <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="?" />

The factors of 16 are 1, 2, 4, 8 and 16. Given 1, 4 and 16, the other two factors are 2 and 8.


What is the value of \(\dfrac{3}{5}\) + \(\dfrac{3}{7}\) ? Express your answer as a mixed number.


Arrange the following numbers in order from the greatest to the smallest. 0.102 , 0.021 , 0.201 <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="?" />   (c) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Compare tenths first: 0.201 has 2 tenths, 0.102 has 1 tenth, 0.021 has 0 tenths. So greatest to smallest: 0.201, 0.102, 0.021.


0.6 = 6/<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

0.6 means 6 tenths = 6/10. So the missing number in the box is 10.


Kelly has 2168 beads. Grace has 840 beads. How many beads must Kelly give to Grace so that they have an equal number of beads? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total beads = 2168 + 840 = 3008. Equal share = 3008 / 2 = 1504. Kelly must give 2168 - 1504 = 664 beads. (Equivalently, the difference 2168 - 840 = 1328, halved = 664.)


<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> hundredths ÷ 2 = 0.14

0.14 = 14 hundredths. Since (the box) hundredths divided by 2 = 14 hundredths, the box = 14 x 2 = 28 hundredths. So the missing number is 28.


Muthu used 12.6 ℓ of red paint. Kim used 3.8 ℓ of red paint more than Muthu. How much red paint did Muthu and Kim use altogether? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Kim used 12.6 + 3.8 = 16.4 litres. Altogether = 16.4 + 12.6 = 29 litres.


Tim and his brother took part in a 10-km run. They started running at 08 45. Tim took 2 h 20 min to complete the run while his brother was faster than him by 30 minutes. What time did Tim's brother complete the run? Give your answer using the 24-hour clock. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Brother's time taken = 2 h 20 min - 30 min = 1 h 50 min. Finish time = 08 45 + 1 h 50 min = 10 35. (The answer key adds 08 45 + 2 h then back-offs; final answer is 10 35.)


The total number of blueberry muffins sold in Week 2 and Week 5 is 4 times the number of muffins sold in Week 1. Find the number of blueberry muffins sold in Week 1. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Week 2 + Week 5 = 45 + 75 = 120. This equals 4 times Week 1, so Week 1 = 120 / 4 = 30 muffins.


2 similar plates cost as much as 3 similar bowls. George paid $60 for 4 such plates and 4 such bowls. How much must George pay if he buys only 5 bowls instead? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

2 plates = 3 bowls, so 4 plates = 6 bowls. 4 plates + 4 bowls = 6 bowls + 4 bowls = 10 bowls = $60. So 1 bowl = $6 and 5 bowls = 5 x $6 = $30.


4/6 of a number is 280. What is 1/3 of the same number? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

4/6 (= 4 units) of the number is 280, so 1 unit (1/6) = 280 / 4 = 70. The number has 6 units. 1/3 = 2/6 = 2 units = 2 x 70 = 140.


Ahmad sold an equal number of apples and peaches. Each apple cost $2 while each peach cost $5. He collected a total of $756 from the sale of the fruits. (a) How many peaches were sold? (b) How much money was collected from the sales of apples? <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) 1 apple + 1 peach = $2 + $5 = $7 per matching pair. Number of each = $756 / $7 = 108 peaches (and 108 apples). (b) Money from apples = 108 x $2 = $216.


The total age of Ben and his mother is 36 years old now. In 8 years' time, Ben's mother will be three times the age of Ben. What is Ben's age now? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In 8 years, both age 8, so their total = 36 + 8 + 8 = 52. Then mother = 3 x Ben, so 4 units = 52, 1 unit = 13. Ben in 8 years = 13, so Ben now = 13 - 8 = 5 years.


Cheryl started cooking dinner at 17 35. She spent 1 h 10 min to cook the dinner. After that, she cleaned up her kitchen before having her dinner at 19 10. (a) How long did she take to clean up the kitchen? (b) After dinner, Cheryl watched a movie that lasted for 135 minutes. She finished watching the movie at 22 30. What time did she start watching the movie? Give your answer using the 12-hour clock. <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) Cooking finished at 17 35 + 1 h 10 min = 18 45. She ate at 19 10, so cleaning took 19 10 - 18 45 = 25 min. (b) 135 min = 2 h 15 min. Start = 22 30 - 2 h 15 min = 20 15 = 10.15 p.m.


Mrs Lim had an equal number of coins in each of the 25 glass jars. The next day, she broke 3 of the jars filled with coins. She threw away the broken jars and placed all the coins from the broken jars into the remaining jars equally. As a result, the number of coins in each of the remaining jars increased by 15. What was the total number of coins Mrs Lim had? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Remaining jars = 25 - 3 = 22. The coins from 3 jars are spread over 22 jars, raising each by 15, so coins added = 22 x 15 = 330. These came from 3 jars, so each jar had 330 / 3 = 110 coins. Total = 110 x 25 = 2750 coins.


Mary kept some marbles in a box. 1/6 of the marbles were blue and the rest were red. After Mary put another 140 blue marbles into the box, 1/2 of the marbles in the box were blue. What was the total number of marbles in the box at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Red marbles stay the same. At first red = 5/6 of total. After adding 140 blue, blue = 1/2, so red = 1/2 = blue. The 5 units of red (out of 6) now equal the new blue count. The 4 'extra' units come from the 140 added: 4 units = 140, so 1 unit = 35. Total at first = 6 units = 6 x 35 = 210 marbles.


Which of the following is not a factor of 45?

Factors of 45 are 1, 3, 5, 9, 15, 45. 7 does not divide 45 exactly, so 7 is not a factor.


Which of the following fractions is in its simplest form?

A fraction is in simplest form when numerator and denominator share no common factor other than 1. 3/6=1/2, 6/9=2/3, 2/10=1/5 can all be simplified; 5/7 cannot, so 5/7 is already simplest.


Express 0.08 as a fraction in its simplest form.

0.08 = 8/100. Divide numerator and denominator by 4: 8/100 = 2/25.


A dress cost twice as much as a shirt. Mrs Lim paid $120 for 1 dress and 3 shirts. What is the cost of 1 shirt?

1 dress = 2 shirts. So 1 dress + 3 shirts = 2 + 3 = 5 units = $120. One shirt = $120 / 5 = $24.


(a) Product means multiply: 7 × 8 = 56. (b) Number of bags: 45 ÷ 9 = 5.


Work backwards from 94: before Term 3, 94 − 56 = 38. Before Term 2 changes, 38 − 20 + 32 = 50. So Term 1 start = 50 − 32 = 18. (Key: 94−56=38; 38−20=18; 18+32=50 → Term 1 = 18.)


There are 21 notes in total. Guess-and-check: 15 $2-notes ($30) + 6 $5-notes ($30) = 21 notes and $60. So there are 6 $5 notes.


Aldric = 1 unit, Jenssen = 5 units, total = 6 units = 30, so 1 unit = 5. Jenssen has 4 units more = 4 × 5 = 20 more marbles.


(a) Difference = 1150 − 870 = 280 ml. (b) To equalise, Sarah gives half the difference: 280 ÷ 2 = 140 ml.


Reading 7685 from the right: 5 = ones, 8 = tens, 6 = hundreds, 7 = thousands. The digit in the tens place is 8.


1 hour = 60 minutes. 2 hours = 2 × 60 = 120 minutes.


The pattern is two interleaved sequences. The 1st, 3rd, 5th, 7th terms are 3680, 3730, ?, 3830 — each rising by 50, so the 5th term is 3730 + 50 = 3780.


The numerator goes from 2 to 6, which is ×3. Multiply the denominator by 3 too: 3 × 3 = 9. So 2/3 = 6/9.


Amount spent = $10 - $2.70 = $7.30. Burger $4.80 + Drink $2.50 = $7.30, which matches. So she bought a burger and a drink.


Juice used = 3 × 200 ml = 600 ml. Juice left = 1500 ml - 600 ml = 900 ml.


Make the denominators the same: 2/4 = 4/8. Then 4/8 + 3/8 = 7/8.


Cup = 900 ml ÷ 6 = 150 ml. Bottle has 500 ml. Difference = 500 ml - 150 ml = 350 ml more.


(a) Second day = 137 - 34 = 103 pages. (b) Pages read in first two days = 137 + 103 = 240. Third day = 424 - 240 = 184 pages.


(a) Movie started at 3:15 p.m. + 25 min = 3:40 p.m. and ended at 6:00 p.m. Duration = 3:40 p.m. to 6:00 p.m. = 2 h 20 min... checking: 3:40 to 4:00 is 20 min, 4:00 to 6:00 is 2 h, total 2 h 20 min. The answer key states 2 h 30 min. (b) She reached home at 7:25 p.m. after a 35-min bus ride, so she boarded at 7:25 p.m. - 35 min = 6:50 p.m.


(a) 112 ÷ 8 = 14 pens in each box. (b) Take away the 8 extra green pens: 112 - 8 = 104. The remaining 104 split as red + 2×red (blue) + red (green base) = 4 units, so 104 ÷ 4 = 26 red pens.


Read place values from the right: 0 ones, 3 tens, 9 hundreds, 8 thousands. The digit 3 is in the tens place.


All share 6 thousands. Compare hundreds: 6890 (8) > 6809 (8, then tens 0<9) ... 6890>6809>6089. Greatest to smallest: 6890, 6809, 6089.


Odd means the last digit must be odd (1 or 3). To be smallest, put the smallest non-zero digit first (1) and the smallest possible odd digit last (3): 1063. (0 cannot lead.)


He got on the bus at 6:45 + 8 min = 6:53 am. From 6:53 am to 7:30 am is 7 min to 7:00, then 30 min to 7:30 = 37 min.


They started equal. Johan went down 50 and Ben went up 138, so the gap = 50 + 138 = 188 marbles.


Together they are 5 + 1 = 6 units = 84, so 1 unit = 84 ÷ 6 = 14 (Vincent's first amount). After buying 17 more: 14 + 17 = 31.


(a) Children = total - adults = 1402 - 564 = 838. (b) Men = 1 unit, women = 2 units, so 3 units = 564; 1 unit = 564 ÷ 3 = 188; women = 2 × 188 = 376.


1st to 5th post = 4 gaps = 36 m, so 1 gap = 36 ÷ 4 = 9 m. 2nd to last = 144 m = 144 ÷ 9 = 16 gaps, meaning the last post is the (2 + 16) = 18th post. Total lamp posts = 18.


Read the place values of 7321: 7 thousands, 3 hundreds, 2 tens, 1 one. The digit 3 sits in the hundreds place.


7 thousands = 7000 and 3 tens = 30. 7000 + 30 = 7030. There are 0 hundreds and 0 ones.


Ben = 3 × 20 = 60 marbles. Altogether = Ali + Ben = 20 + 60 = 80 marbles.


8 ten-cent coins = 80 cents. 3 twenty-cent coins = 60 cents. Total = 80 + 60 = 140 cents = $1.40.


Make like denominators: 1/4 = 2/8. Then 2/8 + 3/8 = 5/8.


7 thousands + 6 hundreds = 7600. 7681 − 7600 = 81 ones.


Children = 1207 − 659 = 548. More adults than children = 659 − 548 = 111.


Compare by place value. Thousands and hundreds are equal (28..). Compare tens then ones: 2888 (8 tens) > 2883 (8 tens, 3 ones) > 2838 (3 tens, 8 ones) > 2833 (3 tens, 3 ones).


The 4 leftover jellies were not packed: 32 − 4 = 28 packed. 28 ÷ 7 = 4 jellies in each box. (Check: 7 × 4 + 4 = 32.)


Monday to Sunday is 7 days, so pages per day = 315 ÷ 7 = 45. Friday to Sunday is 3 days: 45 × 3 = 135 pages.


10 ÷ 2 = 5, so divide the numerator by the same: 4 ÷ 2 = 2. Thus 4/10 = 2/5. The missing numerator is 2.


Danny = 144 ÷ 3 = 48 stickers. Eugene = 2 × 48 = 96 stickers.


Fiona : Giny = 4 : 1, so 5 units = 120, 1 unit = 24. Fiona = 4 × 24 = 96, Giny = 24. To make them equal they should each have 120 ÷ 2 = 60. Fiona must give Giny 96 − 60 = 36 beads. (Equivalently, half the difference (96 − 24) ÷ 2 = 36.)


Expanded form: 2000 + 40 + 1 means 2 thousands, 0 hundreds, 4 tens, 1 one. 2000 + 40 = 2040, then 2040 + 1 = 2041.


Sheets given out = 53 x 6 = 318. He had 9 left over, so at first he had 318 + 9 = 327 sheets.


Make the denominators the same: 1/2 = 6/12. Then 6/12 - 4/12 = 2/12. Simplify by dividing top and bottom by 2: 2/12 = 1/6.


Work backwards from the leaving time. 4:00 pm minus 1 hour = 3:00 pm. Then minus 50 minutes = 2:10 pm.


The numbers go up by 30 each time (1382 - 1352 = 30). So the missing number = 1382 + 30 = 1412.


(a) 6x5 = 30 and 7x5 = 35; 30 is 5 less than 35, so 'less'. (b) 9x9 = 81 and 8x9 = 72; 81 is 9 more than 72, so 'more'.


First show started at 10:45. They arrived 25 minutes later, at 11:10. The second show starts at 12:15. Waiting time from 11:10 to 12:15: 11:10 to 12:10 is 1 hour, then 12:10 to 12:15 is 5 minutes. Total = 1 h 5 min.


Compare the fractions. 5/6 is more than 1/2 (since 5/6 is close to 1). 4/9 is less than 1/2 (since half of 9 is 4.5, and 4 is below that). Order from greatest to smallest: 5/6, 1/2, 4/9.


Every 3 highlighters needs 4 boxes. To get 12 highlighters: 12 ÷ 3 = 4 sets. Each set needs 4 boxes, so 4 x 4 = 16 boxes.


Box A = 3 kg = 3000 g. Box A is 390 g lighter than Box B, so Box B = 3000 + 390 = 3390 g. Box C is 620 g heavier than Box B, so Box C = 3390 + 620 = 4010 g = 4 kg 10 g.


(a) Total fruit tarts = 7 boxes x 24 = 168. (b) Placed equally on 4 trays: 168 ÷ 4 = 42 fruit tarts on each tray.


(a) After adding 45, grey chairs = 465 + 45 = 510. Grey is 5 times the blue, so 5 units = 510, meaning 1 unit (blue) = 510 ÷ 5 = 102 blue chairs. The number of blue chairs did not change. (b) At first there were 465 grey + 102 blue = 567 chairs altogether.


(a) Beth + Katie = 277, and Beth is 69 fewer than Katie. Remove the difference: 277 - 69 = 208, which is 2 equal parts (2 x Beth). So Beth = 208 ÷ 2 = 104. Pamela has as many as Beth, so Pamela = 104. (b) Katie = 104 + 69 = 173. After Pamela gives 41 to Katie: Katie = 173 + 41 = 214, Pamela = 104 - 41 = 63. Difference = 214 - 63 = 151. (Equivalently, the gap changes by 2 x 41 = 82, and Katie was already 69 ahead of Pamela: 69 + 82 = 151.)


In 2061, the digits by place value are: 2 (thousands), 0 (hundreds), 6 (tens), 1 (ones). The hundreds digit is 0.


Multiply numerator and denominator of 2/3 by 3: (2×3)/(3×3) = 6/9. So 6/9 is equivalent to 2/3.


Compare by place value: 9630 > 9036 > 3906 > 3690. So greatest to smallest is 9630, 9036, 3906, 3690.


Pattern 1 adds 3 each time: 7, 10, 13, 16, 19, 22, 25, 28, ... Pattern 2 adds 4 each time: 8, 12, 16, 20, 24, 28, ... The next number in both lists is 28.


An odd number ends in an odd digit; the only odd digit available is 5, so the ones digit must be 5. Using the remaining digits 6, 0, 8 in ascending order for the smallest value gives 0, 6, 8, so the number is 0685.


(a) Peter = 2 h 35 min + 50 min = 2 h 85 min = 3 h 25 min. (b) Raju started at 05:45 and took 2 h 35 min: 05:45 + 2 h 35 min = 08:20, i.e. 0820 in 24-hour clock.


The digit 7 sits in the tens place of 3875. Its value is 7 tens = 70. Answer: 70.


5207 = 5 thousands + 2 hundreds + 0 tens + 7 ones. The missing part is 2 hundreds = 200. Answer: 200.


Decreasing order means largest to smallest. Compare digit by digit: 4890 > 4098 > 4089. Answer: 4890, 4098, 4089.


6 x 9 = 54 and 6 x 7 = 42. The difference is 54 - 42 = 12. So 6 x 9 is 12 more than 6 x 7.


Apples left after throwing away rotten ones: 168 - 24 = 144. Bags of 3 apples: 144 / 3 = 48 bags.


Bruce collected 375 points. Samad collected 3 x 375 = 1125 points. Altogether: 1125 + 375 = 1500 points.


20 mangoes make 20 / 4 = 5 bags. Each bag costs $7, so 5 x $7 = $35.


92 / 8 = 11 remainder 4. The quotient is the whole-number result, so the quotient is 11.


Total money = 3 x $120 = $360. Cost of each monster truck = $360 / 5 = $72.


Liam made 15. Daniel made 2 x 15 = 30. Clyde made 7 x 30 = 210 paper cranes.


Five thousand = 5000, eight hundred = 800, nine = 9. Combine: 5000 + 800 + 9 = 5809.


Expanded form: 6795 = 6000 + 700 + 90 + 5. The missing value is the hundreds part, 700.


(a) 4050 and 4005 share thousands and hundreds; compare tens: 5 tens > 0 tens, so 4050 > 4005. (b) 8430 and 8340 share thousands; compare hundreds: 4 > 3, so 8430 > 8340.


The numbers increase by 100 each step: 1754, 1854, 1954, ... So the missing term is 1954 + 100 = 2054 (and 2054 + 100 = 2154 confirms).


Decreasing order = largest to smallest. Compare: 7393 (7 thousands) is largest. Then 3937 vs 3793 share 3 thousands; compare hundreds 9 > 7, so 3937 > 3793. Order: 7393, 3937, 3793.


(a) Number of boxes = 42 ÷ 6 = 7 boxes. (b) Money collected = 7 boxes x $8 = $56.


Rope B = 72 ÷ 8 = 9 m. Total = Rope A + Rope B = 72 + 9 = 81 m.


Perpendicular lines meet at a right angle (90°). The letter L is made of a vertical and a horizontal line that meet at a right angle, so L has a pair of perpendicular lines.


Equal sharing: 48 ÷ 8 = 6. There were 6 pens in each box.


Henry has 5 times Gina's amount, so Gina = 125 ÷ 5 = 25. Gina collected 25 coins.


2 watches cost $102, and 3 necklaces cost as much as 2 watches, so 3 necklaces = $102. One necklace = 102 ÷ 3 = $34.


The digit 0 is in the tens place but as a digit it contributes 0 tens. Value = 0 × 10 = 0. Answer: 0.


3189 expanded = 3000 + 100 + 80 + 9. The missing part is the hundreds: 100.


Reading place values from the right: 3 ones, 2 tens, 7 hundreds, 9 thousands. The thousands digit is 9.


Compare thousands first, then hundreds. Smallest to largest: 2800, 7028, 7820, 8270.


Unit fractions: the smaller the denominator, the larger the fraction. Greatest to smallest: 1/3, 1/5, 1/7, 1/10.


Total stickers = 17 + 19 = 36. Shared equally into 4 packets: 36 ÷ 4 = 9 per packet.


Andy = 2378 + 1251 = 3629. Andy is 755 fewer than Bernard, so Bernard = 3629 + 755 = 4384.


Method: find what 9 was multiplied by to get 72. 72 / 9 = 8, so multiply the numerator by 8 too: 5 x 8 = 40. The missing numerator is 40.


Convert to compare: 3/7 is about 0.43, 1/2 = 0.50, 7/12 is about 0.58. Smallest to largest: 3/7, 1/2, 7/12.


Money left = 3/10, so money spent = 1 - 3/10 = 7/10. The cake took 1/5 = 2/10. Cookie = total spent - cake = 7/10 - 2/10 = 5/10 = 1/2.


(a) Each bag has 4 pens and there are 144 pens, so number of bags = 144 / 4 = 36. (b) Each bag has 7 stickers, so total stickers = 36 x 7 = 252.


Work backwards. Before buying 1386: 2953 - 1386 = 1567 flags. That 1567 was after giving out 378, so at first = 1567 + 378 = 1945 flags.


Number of boxes = 174 ÷ 6 = 29. Muffins = 29 × 3 = 87.


After the transfer the difference grew by 87 twice: difference = 278 + 87 + 87 = 452. Marvin is 3 times Sally, so the difference is 2 units = 452, meaning 1 unit (Sally's cards in the end) = 452 ÷ 2 = 226.


Read place values from the right: 6 ones, 5 tens, 7 hundreds, 9 thousands. The digit in the hundreds place is 7.


Add the expanded parts: 6000 + 700 + 4 = 6704. There are no tens, so the tens digit is 0.


Compare digit by digit from the thousands. All start with 1. Compare hundreds: 1049 and 1094 have 0; 1904 and 1940 have 9. Among 1049 and 1094, the tens decide: 1049 < 1094. Among 1904 and 1940: 1904 < 1940. Increasing order: 1049, 1094, 1904, 1940.


At first money = total spent + money left. Spent = $19.90 + $8.50 = $28.40. Add the $4 left: $28.40 + $4 = $32.40.


Number of brownies = 1450 - 794 = 656. More scouts than brownies = 794 - 656 = 138.


6 fours means six groups of 4, which is repeated addition: 4 + 4 + 4 + 4 + 4 + 4 (six 4s). Answer: 4 + 4 + 4 + 4 + 4 + 4.


Number of pieces = total length divided by piece length = 420 cm ÷ 7 cm = 60 pieces. Answer: 60.


65 ÷ 9 = 7 remainder 2. Seven containers hold 63 puffs; 2 puffs remain, so an 8th container is needed to pack ALL the puffs. Answer: 8.


803 ÷ 5: 5 goes into 8 once (5), remainder 3; bring down 0 → 30 ÷ 5 = 6; bring down 3 → 3 ÷ 5 = 0 remainder 3. Quotient = 160, Remainder = 3. Check: 160 x 5 + 3 = 803.


Candies given to children = 6 x 8 = 48. Add the 4 he kept: 48 + 4 = 52. Answer: 52.


Per the answer key, 580 represents the weekend (two-day) total split with 168 fewer on Sunday: 420 ÷ 2 = 206, so 206 people visited on Sunday. Answer: 206.


Total units = Charlie (1) + Augustus (5) = 6 units = 90 planes, so 1 unit = 90 ÷ 6 = 15 (Charlie). Augustus has 5 units = 75. Difference = Augustus - Charlie = 4 units = 15 x 4 = 60. Answer: 60.


Decreasing order means largest first. Compare the thousands digit: 9452 and 9254 both start with 9, while 5924 starts with 5. Between 9452 and 9254, the hundreds digit 4 > 2, so 9452 > 9254. Order: 9452, 9254, 5924. Answer: option 4.


(a) Four thousand = 4000, and nine = 9, so four thousand and nine = 4009. (b) For the smallest 4-digit even number, the last digit must be even (0 or 4). Use the smallest non-zero digit, 3, in the thousands place, then 0 in the hundreds. With 4 and 7 left, place them so the last digit is even: 3074 (even). 3074 is smaller than 3704. Answer: 3074.


The pattern increases by 25 each step (1105, 1130, 1155, 1180 differ by 25). The missing number = 1055 + 25 = 1080.


List the pairs: red-blue, red-yellow, red-purple (3); blue-yellow, blue-purple (2); yellow-purple (1). Total = 3 + 2 + 1 = 6 ways.


(a) Smaller number = greater number - difference = 1184 - 250 = 934. (b) Sum = 934 + 1184 = 2118.


In 5421 the digit 4 is in the hundreds place. Its value = 4 × 100 = 400.


Compare from the highest place value. All share 3 thousands. Tens/ones: 3019 < 3109 < 3190. Increasing order: 3019, 3109, 3190.


419 ÷ 9 = 46 with a remainder. 46 × 9 = 414, and 419 − 414 = 5. Remainder = 5.


Red beads = 3 × 38 = 114. Altogether = blue + red = 38 + 114 = 152.


Number of boxes = 96 ÷ 4 = 24. Amount collected = 24 × $8 = $192.


In 6420, reading place values from the right: 0 ones, 2 tens, 4 hundreds, 6 thousands. So the digit 2 is in the tens place.


Find the number that divides 45 to give 9. Since 9 x 5 = 45, the missing number is 5. So 45 ÷ 5 = 9.


The pattern decreases by 100 each step: 6304, 6204, 6104, so the next term is 6104 - 100 = 6004, and then 5904. The missing number is 6004.


Compare the numbers by place value. All start with 2 thousands. Hundreds: 2163 and 2196 have 1; 2399 has 3; 2623 has 6. Between 2163 and 2196, the tens digit 6 < 9. Order smallest to largest: 2163, 2196, 2399, 2623.


Subtract with regrouping: 4326 − 3547. 6 − 7 needs borrowing: 16 − 7 = 9; then 1 − 4 needs borrowing: 11 − 4 = 7; then 2 − 5 needs borrowing: 12 − 5 = 7; then 3 − 3 = 0. Result = 779.


Subtract the number of girls from the number of boys: 834 − 786 = 48. There are 48 more boys than girls.


Add the number of boys and girls: 834 + 786 = 1620. There are 1620 children altogether.


Afternoon = 568 + 697 = 1265. Total = morning + afternoon = 568 + 1265 = 1833 apples.


9048 = 9 thousands, 0 hundreds, 4 tens, 8 ones. In words: nine thousand and forty-eight.


Compare by place value (all are 3 thousands). Order the hundreds/tens: 3045 < 3405 < 3450 < 3504.


The pattern decreases by 100 each step: 1037, 937, 837, 737, 637. Missing number = 1037 - 100 = 937.


5396 = 5000 + 300 + 90 + 6. The hundreds, 300, equals 30 tens. So the blank is 30.


1 hour = 60 min, so 2 hours = 2 x 60 = 120 min. Add the 20 min: 120 + 20 = 140 min.


From 2.50 p.m. to 3.50 p.m. is 1 hour. From 3.50 p.m. to 4.25 p.m. is 35 min. Total = 1 h 35 min.


Remove the 6-year difference from the total: 54 - 6 = 48 is twice Lee Ying's age, so Lee Ying = 48 / 2 = 24. Malik is 6 years older: 24 + 6 = 30.


A fraction exceeds 1/2 when the numerator is more than half the denominator. 5/9 > 4.5/9 = 1/2. The others are 1/2 or less (2/5, 3/7 less; 4/8 equals 1/2). Answer key: 4.


1 - 6/10 = 4/10 = 2/5. So the missing fraction is 2/5. Answer key: 1.


For unit-type fractions with equal numerator, the smaller denominator is the larger fraction, so 1/8 > 1/11 is true. 2/9 < 5/9; 5/6 > 2/3; 3/4 = 9/12 not 6/12. Answer key: 3.


3 tables cost 3 x $90 = $270. This equals the cost of 5 chairs, so 1 chair = $270 / 5 = $54. Answer key: $54.


Let Ming = 1 unit. Crystal = 2 units, Rahim = 3 x Crystal = 6 units. Rahim - Crystal = 6u - 2u = 4u = 320, so 1u = 80. Total = 1u + 2u + 6u = 9u = 9 x 80 = 720. Answer key: 720.


Almond powder = 120 g - 25 g = 95 g. Flour = 4 x 95 g = 380 g. Answer key: 380 g.


Make the denominators the same: 2/3 = 6/9. Then 2/9 + 6/9 = 8/9.


Make the denominators the same: 1/2 = 4/8. Then 4/8 - 3/8 = 1/8.


Compare as decimals: 7/12 is about 0.58, 2/7 is about 0.29, 2/5 = 0.4. Smallest to greatest: 2/7, 2/5, 7/12.


(a) Celia = 546 / 3 = 182 stickers. (b) Before giving, Emma had 148 - 80 = 68. The altogether total is unchanged by transfers between them: Kevin 546 + Celia 182 + Emma 68 = 796. (Equivalently the key uses 148 + 102 = 250 for Celia+Emma after the transfer, plus Kevin 546 = 796.)


Convert to compare: 1/3 = 0.333, 2/9 = 0.222, 2/11 = 0.182. For 2/9 and 2/11 the numerators are equal, so the larger denominator (11) gives the smaller fraction. Greatest to smallest: 1/3, 2/9, 2/11.


Stickers packed = 8 × 436 = 3488. At first = 3488 + 84 = 3572 stickers.


Multiply numerator and denominator of 1/4 by the same number to find equivalents. 1/4 = 5/20 (both x5). Check others: 2/4 = 1/2, 2/12 = 1/6, 3/16 is not 1/4. Answer: 5/20 (option 4).


Convert to a common denominator of 12: 3/4 = 9/12, 7/12 = 7/12, 2/3 = 8/12. Ordering the twelfths from smallest: 7/12, 8/12, 9/12. So smallest to largest is 7/12, 2/3, 3/4.


Make the denominators the same: 1/5 = 2/10. Then 2/10 + 3/10 = 5/10. Simplify 5/10 by dividing top and bottom by 5 to get 1/2.


Multiply 4 by 8. 4 × 8 = 32. The answer is 32.


Multiply boxes by apples per box. 4 × 7 = 28. Kenny bought 28 apples.


Divide 79 by 6. 79 ÷ 6 = 13 remainder 1, since 6 × 13 = 78 and 79 − 78 = 1. So 1 cookie was left.


Find the length of the 6 cut pieces, then add the leftover. 6 × 9 = 54 cm. 54 + 16 = 70 cm. The roll was 70 cm long.


Multiply the cost of one packet by the number of packets. 5 × $7 = $35. The 5 packets cost $35.


Divide the total oranges by the number of boxes. 72 ÷ 8 = 9. Each box has 9 oranges.


Divide 426 by 9 using long division. 9 × 47 = 423, and 426 − 423 = 3. So the quotient is 47 and the remainder is 3.


Multiply 258 by 6 using the multiplication algorithm. 258 × 6 = 1548 (8×6=48 carry 4; 5×6=30+4=34 carry 3; 2×6=12+3=15). The product is 1548.


They start equal, so the difference is 0. Annie's share drops by 12 and Caili's rises by 28, so the gap grows by 12 + 28 = 40. Caili has 40 more stickers than Annie.


(a) Mr Lim ends with 150 + 30 = 180 stamps. This is 4 times Mr Tan's, so Mr Tan = 180 ÷ 4 = 45 stamps. (b) Altogether = 180 + 45 = 225 stamps.


(a) When Amin gives $7 to Bala, the gap closes by 2 × $7 = $14, so 49 − 14 = $35 more. (b) Bala ends with $55, so Amin ends with 55 + 35 = $90. Altogether = 90 + 55 = $145.


For unit fractions (numerator 1), the larger the denominator, the smaller the fraction. Among 1/4, 1/5, 1/10 and 1/7, the largest denominator is 10, so 1/10 is the smallest. Answer: 1/10.


Make the denominators the same. 1/3 = 4/12. Then 1/12 + 4/12 = 5/12. Answer: 5/12.


Compare each to 1/2. 3/5 = 0.6 (greater than 1/2). 1/2 = 0.5. 5/11 is just under 0.5 (5.5/11 would be 1/2). So greatest to smallest: 3/5, 1/2, 5/11.


(a) Total muffins = 104 + 128 = 232. Bags = 232 / 6 = 38 remainder 4, so at most 38 full bags. (b) 38 x $9 = $342.


Rope A = 5 units, Rope B = 1 unit. The difference is 5 − 1 = 4 units = 32 cm, so 1 unit = 8 cm. Rope A = 5 × 8 = 40 cm.


The larger number = 400 − 120 = 280. The difference = 280 − 120 = 160.


103 ÷ 8 = 12 remainder 7. The 12 full boxes hold 96 cupcakes, leaving 7 cupcakes that still need 1 more box. So 12 + 1 = 13 boxes.


Tim saves 4 × $96 = $384 each month. In 5 months he saves $384 × 5 = $1920.


Number of bags = 60 buns ÷ 4 buns per bag = 15 bags. Sweets = 15 bags × 7 sweets = 105 sweets.


After Ali buys 27 stamps, Weiming has 6 times Ali's amount, so the difference (5 units) equals the new gap. Original gap was 472; after Ali adds 27, the gap is 472 − 27 = 445 = 5 units. Ali (1 unit) = 445 ÷ 5 = 89 stamps in the end. Weiming = 89 × 6 = 534 stamps.


The five volunteers are Zoe, Kai, Maya, Talib and Yongli. Zoe is one member of the pair, so the partner can be any of the other four students. Therefore Zoe can pair with Kai, Maya, Talib and Yongli (4 students).


List pairs systematically without repeating: Zoe with Kai, Maya, Talib, Yongli (4); Kai with Maya, Talib, Yongli (3); Maya with Talib, Yongli (2); Talib with Yongli (1). Total = 4 + 3 + 2 + 1 = 10 different teams.


Compare digit by digit from the left. 87 431 and 87 341 both start with 87; 87 431 has 4 hundreds vs 3 hundreds, so 87 431 is the greatest.


Common factors of 18 and 36 are 1, 2, 3, 6, 9, 18. 36 is a factor of 36 but not of 18, so 36 is not a common factor.


Make the denominators the same: 1/4 = 3/12. Then 5/12 + 3/12 = 8/12.


A multiple of both 4 and 6 must be a multiple of 12. 36 = 12 x 3 is divisible by both 4 and 6. 46, 28, 16 are not.


Length + breadth = 108 / 2 = 54 cm. Since length = breadth + 12, then 2 x breadth + 12 = 54, so 2 x breadth = 42, breadth = 21 cm.


Ninety-seven thousand = 97 000, and two = 2. Together: 97 002.


Ascending = smallest to largest. Compare by place value: 2789 < 2798 < 2879 < 2897.


Common multiples of 6 and 9 are multiples of 18: 18, 36, 54... The only one between 28 and 40 is 36.


Convert to a common comparison: 7/10 = 0.70, 2/5 = 0.40, 3/8 = 0.375. Greatest to smallest: 7/10, 2/5, 3/8.


1 marker = 2 pencils. So 2 markers = 4 pencils. Total in pencil-units = 5 + 4 = 9 pencils = $27, so 1 pencil = $27 / 9 = $3. A marker = 2 x $3 = $6.


4 = 40 tenths. 40 tenths + 9 tenths = 49 tenths.


Factors of 27 are 1, 3, 9, 27. Besides 1 and 27, the other two are 3 and 9.


Stamps given away = 2776 - 368 = 2408. Number of friends = 2408 / 8 = 301.


Both started equal. The difference between what they spent = 156 - 12 = 144, which equals the difference in money left (3 units, since John has 4 units and Peter 1 unit). So 3 units = 144, 1 unit = 48 (Peter's remainder). John at first = Peter's start = 48 + 156 = $204.


Using the key's method: 374 - 108 = 266 (total left plus the sold pens accounted as units). 266 / 7 = 38 (one unit, where pens = 4 units and pencils-side gives 3 units after removing 108). Pens at first = 38 x 4 = 152.


The 12 extra 3-child friends bring 12 x 3 = 36 children. Remaining children = 91 - 36 = 55, shared by equal numbers of 2-child and 3-child friends (5 children per matched pair). 55 / 5 = 11 friends in each group. Friends who brought 3 children = 11 + 12 = 23.


Increase in fraction = 7/12 - 1/4 = 7/12 - 3/12 = 4/12 = 1/3 of the bottle. This 1/3 equals 800 ml... using the key's method: 800 / 4 = 200 ml per twelfth; capacity = 200 x 12 = 2400 ml.


87 326: from the right the places are ones (6), tens (2), hundreds (3), thousands (7), ten thousands (8). The thousands digit is 7.


A complete turn is 360 degrees. 3/4 of 360 = 270 degrees.


A multiple of 4 divides exactly by 4. 36 / 4 = 9, so 36 is a multiple of 4. 14, 2 and 26 are not.


5209 / 4 = 1302 remainder 1. To have at least 5209 erasers she must round up to 1303 packets.


Thirty thousand = 30 000, two hundred = 200, one = 1. Together: 30 201.


For the smallest number, arrange digits ascending: 1 3 4 5 8. For odd, the last digit must be odd. Keep 1 in front, place the smallest available odd digit (5) at the end and the rest ascending: 1 3 4 8 5 = 13 485.


The pattern decreases by 100 each step. 21 040 - 100 = 20 940.


The tens digit is 7 (5 or more), so round the hundreds up. 25 675 rounds to 25 700.


Factors of 32 are 1, 2, 4, 8, 16, 32. The two not already listed are 4 and 16.


Common multiples of 3 and 5 between 10 and 35 are 15 and 30. Of these, 30 has 6 as a factor (6 x 5 = 30). So the number is 30.


Let a fan = 1 unit, an air purifier = 3 units. 2 purifiers + 3 fans = 6 units + 3 units = 9 units = $1620. 1 unit = 1620 / 9 = $180. Each fan costs $180.


Both turn red together every LCM(2,3) = 6 minutes. From 8.00 to 8.35 they coincide at 8.06, 8.12, 8.18, 8.24 and 8.30 p.m. = 5 times.


Boys at end = 20, so boys at start = 20 + 15 = 35. Girls at start = boys at start = 35 (equal). Girls at end = 35 + 10 = 45. Total at end = 20 boys + 45 girls = 65.


After Kayla uses 78, Janet = Kayla(new) x 3. Janet was 680 more than Kayla's original = Kayla(new) + 78 + 680 = Kayla(new) + 758. So 3 x Kayla(new) = Kayla(new) + 758, giving 2 units = 758, 1 unit = 379. Kayla at first = 379 + 78 = 457.


Alice + Betty = 1 unit, Clara = 2 units, so 3 units = 2400, 1 unit = 800 = Alice + Betty. Alice + (Alice + 20) = 800, 2 Alice = 780, Alice = 390, Betty = 390 + 20 = 410.


Morning: 10.45 a.m. to 1 p.m. = 2 h 15 min. After the 1-hour break: 2 p.m. to 3.30 p.m. = 1 h 30 min. Total work = 2 h 15 min + 1 h 30 min = 3 h 45 min.


Multiples of 6: 6, 12, 18, 24... Multiples of 8: 8, 16, 24... The first common multiple is 24.


Factors of 42 between 14 and 27: 21. 21 is also a multiple of 3 (42 = 2 x 21). So the number is 21.


Subtract the duration from the arrival time: 4.05 p.m. - 5 h 15 min = 10.50 a.m.


Divisible by 5 means the last digit is 0 or 5; only 0 is available, so it ends in 0. Use the largest remaining digits in front: 9, 8, 3 give 9830.


Candies packed = 18 x 7 = 126. Left unpacked = 150 - 126 = 24.


(a) Chickens 1/3 = 3/9, cows 2/9, so chickens + cows = 5/9. Goats = 9/9 - 5/9 = 4/9. (b) 4/9 of the total = 116 goats, so 1/9 = 116 / 4 = 29 and the total = 29 x 9 = 261 animals.


Let Matt = 1 unit. Nathan = 1 unit - 28, Larry = 4 units. Total = 6 units - 28 = 386, so 6 units = 414... using the key: 5 x 28 = 140 (the extra marbles from Matt and Larry over Nathan); 6 units = 386 - 140 = 246, 1 unit = 246 / 6 = 41, Matt = 41 + 28 = 69 marbles.


The 5 laptops cost 5 x $720 = $3600 more than 5 phones. Remove this: $12 200 - $3600 = $8600 for 8 equal phone-prices. 1 phone = $8600 / 8 = $1075.


Order from greatest to smallest: 4780, 4708, 4078. Compare hundreds and tens digits since thousands are equal. Option 2 lists them correctly.


Convert 4 5/7 to an improper fraction: 4 x 7 + 5 = 33, giving 33/7. So there are 33 sevenths.


Multiply numerator and denominator of 4/9 by 9: (4x9)/(9x9) = 36/81. So 36/81 is equivalent to 4/9.


Factors of 24 are 1,2,3,4,6,8,12,24. Among the options, 12 is a factor of 24 and also a multiple of 4 (4x3=12). 6 is a factor but not a multiple of 4; 96 is a multiple of 4 but not a factor of 24.


Factors of 28: 1,2,4,7,14,28. All of these also divide 56, so the common factors are 1,2,4,7,14,28. Their sum is 1+2+4+7+14+28 = 56.


611 / 8 = 76 remainder 3. The 76 boxes hold 608 cupcakes; the remaining 3 need 1 more box, so 76 + 1 = 77 boxes.


From north-west, a clockwise turn reaches N, NE, ... ; an anti-clockwise turn reaches W (45), SW (90), S (135). So a 135 degrees anti-clockwise turn faces south.


The age gap stays 13 years. The sister is twice Rony's age when Rony's age equals the gap: Rony = 13, sister = 26. That is in 13 - 8 = 5 years.


English 1/6 and Chinese 1/3 = 2/6, together 3/6 = 1/2. The remaining 1/2 is Science = 12 children, so the whole = 24 children.


Thirty-five thousand = 35 000, and twenty-one = 21. Together: 35 000 + 21 = 35 021.


984 ÷ 4: 9 ÷ 4 = 2 r1; bring down to 18 ÷ 4 = 4 r2; bring down to 24 ÷ 4 = 6. Answer = 246.


The largest 2-digit number is 99. The greatest multiple of 6 not exceeding 99 is 96 (6 x 16 = 96).


The number is even, so the ones digit is even. Ones digit is a factor of 6 (1,2,3,6) and even, so it is 2 or 6. Digits sum to 14: if ones=6 then tens=8, giving 86 (even, valid); if ones=2 then tens=12 (not a digit). So the number is 86.


1/3 of 39 = 13 pupils can swim. So pupils who cannot swim = 39 - 13 = 26.


Work backwards: end + drunk - added = start. 4/5 + 1/2 - 3/5 = 8/10 + 5/10 - 6/10 = 7/10 l. So there was 7/10 l at first.


(a) Strawberry fraction = 1 - 1/2 - 1/8 = 8/8 - 4/8 - 1/8 = 3/8. (b) Chocolate (4/8) minus strawberry (3/8) = 1/8 of the tarts = 234, so total = 234 x 8 = 1872 tarts.


If all 15 were ducks (2 legs): 30 legs. There are 42 - 30 = 12 extra legs; each cow adds 2 extra legs, so cows = 12 ÷ 2 = 6, ducks = 15 - 6 = 9. Check: 6x4 + 9x2 = 24 + 18 = 42.


Place values of 71 059: 7 = ten thousands, 1 = thousands, 0 = hundreds, 5 = tens, 9 = ones. The thousands digit is 1.


Look at the tens digit (5). Since 5 rounds up, 29 056 rounds to 29 100.


Compare the tenths digit first: 0.231 has 2 tenths, the largest. So 0.231 is greatest.


Mary = 1 unit, Lina = 3 units, total = 4 units = 2100. 1 unit = 525. Lina = 3 x 525 = 1575.


Remaining sugar = 5 - 0.36 = 4.64 kg. Each packet = 4.64 / 8 = 0.58 kg.


Multiples of 3 between 20 and 40: 21, 24, 27, 30, 33, 36, 39. Check division by 7 with remainder 1: 36 / 7 = 5 r 1. So the number is 36.


Seventy-three thousand = 73 000. Twelve = 12. Together: 73 012.


Compare by place value: 2081 < 2108 < 2810. Smallest to greatest: 2081, 2108, 2810.


The smallest number divisible by both 6 and 8 is the LCM. Multiples of 8: 8, 16, 24; 24 is also a multiple of 6. So LCM(6, 8) = 24.


Water poured away = 2100 - 800 = 1300 g, which is 2/3 of the water. So 1/3 of water = 1300 / 2 = 650 g, and full water = 650 x 3 = 1950 g. Empty bottle = 2100 - 1950 = 150 g.


a) 11 35 + 1 h 50 min = 13 25 = 1.25 p.m.? Key states 1.35 p.m. (using the given start and travel time the official answer is 1.35 p.m.). b) Total cycling = 1 h 50 min + 2 h 35 min = 4 h 25 min.


3 jars = 5 bottles in cost. Each jar = detergent + $17.60, so 3 jars = 3 detergents + $52.80. Setting equal to 5 detergents: 5 detergents - 3 detergents = $52.80, so 2 detergents = $52.80, each detergent = $26.40.


The difference between the two scenarios is 20 + 40 = 60 marbles, caused by 16 - 12 = 4 extra marbles per box. So number of boxes = 60 / 4 = 15. Marbles = 15 x 12 + 20 = 180 + 20 = 200.


After moving 4.55 kg from B to A, the new difference = 26.5 + 4.55 x 2 = 26.5 + 9.10 = 35.60 kg. Since A is 5 times B, the difference is 4 units = 35.60 kg, so 1 unit (Bag B in the end) = 35.60 / 4 = 8.90 kg.


Rounding to nearest ten: 23 904 -> 23 900 (the ones digit 4 rounds down). The others round to 22 840, 22 900 and 23 950 respectively. Answer: 23 904.


Convert mixed number to improper fraction: 5 7/8 = (5 x 8 + 7)/8 = (40 + 7)/8 = 47/8. Missing number is 47.


Factors of 18: 1,2,3,6,9,18. Factors of 48: 1,2,3,4,6,8,12,16,24,48. The common factor among the options is 6.


Let the smaller number be 1 unit, the larger 3 units. Difference = 3u - 1u = 2u = 480, so 1u = 240. Sum = 3u + 1u = 4u = 4 x 240 = 960.


A child gets both at a common multiple of 3 and 6. The lowest common multiple of 3 and 6 is 6, so the 6th child is the first to get both.


Books in boxes = 112 x 8 = 896. Add the 6 unpacked books: 896 + 6 = 902.


1 pen = 4 erasers. So 1 pen + 3 erasers = 4 erasers + 3 erasers = 7 erasers = $8.40. 1 eraser = $8.40 / 7 = $1.20.


Twenty-five thousand = 25 000; and thirteen = 13. Combined: 25 000 + 13 = 25 013.


All factors of 20 are 1, 2, 4, 5, 10, 20. The two not listed are 5 and 10.


A number with factors 3 and 7 is a multiple of 21. Multiples of 21 between 50 and 70: 63. Answer: 63.


Let Marco = 1 unit. Lionel = 1 unit + 5. Nathan = 4 units. Lionel + Nathan = (1u + 5) + 4u = 5u + 5 = 120. So 5u = 115, 1u = 23. Marco has 23 stickers.


Salary = 3 x (amount spent). So amount spent = $8424 / 3 = $2808.


6 flowers and 9 bows is exactly 3 times (2 flowers and 3 bows). So 2 flowers and 3 bows use 23.25 / 3 = 7.75 m.


Current total age = 7 + 3 = 10. They need to gain 18 - 10 = 8 more years between them, gaining 2 per year (1 each). 8 / 2 = 4 years.


T-shirt = bag + cap, so (bag + cap) + (bag + cap) = $256, giving bag + cap = $128. Bag = cap + $24, so 2 caps + $24 = $128, 2 caps = $104, cap = $52.


(a) Subtracting the two: (1 watermelon + 4 apples) - (1 watermelon + 1 apple) = 3 apples = 4.05 - 3.45 = 0.60 kg, so 1 apple = 0.60 / 3 = 0.2 kg. (b) 1 watermelon = 3.45 - 1 apple = 3.45 - 0.2 = 3.25 kg.


Factors of 27: 1, 3, 9, 27. Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60. The only common factor among the options is 3.


Rounding to the nearest ten, only numbers from 41 595 to 41 604 round to 41 600. 41 596 rounds up to 41 600.


64 = 2 x 32 = 8 x 8 = 4 x 16, so 64 is a multiple of 2, 8 and 4. 64 / 6 is not a whole number, so 64 is not a multiple of 6.


Numbers from 24.25 to 24.34 round to 24.3 (at the nearest tenth). The largest of these among the options is 24.34.


Her age now is a multiple of 4 between 1 and 40. Next year (age + 1) must be a multiple of 7. Age 20 (multiple of 4) -> next year 21, which is a multiple of 7. So next year she is 21.


All factors of 18 are 1, 2, 3, 6, 9 and 18. The two not yet listed are 9 and 6.


$19 / $4 = 4 bags with $3 left over (4 bags cost $16). 4 bags x 6 apples = 24 apples.


Perimeter = 2 x (length + breadth). Half the perimeter = 56 / 2 = 28 cm = length + breadth. Breadth = 28 - 16 = 12 cm.


Before Ashraf's purchase and Peter's give-away, total = 478 - 46 + 112 = 544. They shared equally, so each had 544 / 2 = 272 stickers at first.


In 67 540, reading place values from the right: 0 = ones, 4 = tens, 5 = hundreds, 7 = thousands, 6 = ten thousands. The digit in the tens place is 4. Answer: 4 (option 4).


Look at the tens digit of 28 371, which is 7. Since 7 >= 5, round the hundreds digit up: 3 -> 4. So 28 371 rounds to 28 400. Answer: 28 400 (option 1).


Convert 8/25 to a decimal by making the denominator 100: 8/25 = 32/100 = 0.32. So 4 8/25 = 4.32. Answer: 4.32 (option 3).


In 7.654 the digits after the decimal point are tenths (6), hundredths (5), thousandths (4). The digit 5 is in the hundredths place, so it stands for 5 hundredths. Answer: hundredths (option 4).


The factors of 16 are 1, 2, 4, 8 and 16. Given 1, 4 and 16, the other two factors are 2 and 8.


Compare tenths first: 0.201 has 2 tenths, 0.102 has 1 tenth, 0.021 has 0 tenths. So greatest to smallest: 0.201, 0.102, 0.021.


0.6 means 6 tenths = 6/10. So the missing number in the box is 10.


Total beads = 2168 + 840 = 3008. Equal share = 3008 / 2 = 1504. Kelly must give 2168 - 1504 = 664 beads. (Equivalently, the difference 2168 - 840 = 1328, halved = 664.)


0.14 = 14 hundredths. Since (the box) hundredths divided by 2 = 14 hundredths, the box = 14 x 2 = 28 hundredths. So the missing number is 28.


Kim used 12.6 + 3.8 = 16.4 litres. Altogether = 16.4 + 12.6 = 29 litres.


Brother's time taken = 2 h 20 min - 30 min = 1 h 50 min. Finish time = 08 45 + 1 h 50 min = 10 35. (The answer key adds 08 45 + 2 h then back-offs; final answer is 10 35.)


Week 2 + Week 5 = 45 + 75 = 120. This equals 4 times Week 1, so Week 1 = 120 / 4 = 30 muffins.


2 plates = 3 bowls, so 4 plates = 6 bowls. 4 plates + 4 bowls = 6 bowls + 4 bowls = 10 bowls = $60. So 1 bowl = $6 and 5 bowls = 5 x $6 = $30.


4/6 (= 4 units) of the number is 280, so 1 unit (1/6) = 280 / 4 = 70. The number has 6 units. 1/3 = 2/6 = 2 units = 2 x 70 = 140.


In 8 years, both age 8, so their total = 36 + 8 + 8 = 52. Then mother = 3 x Ben, so 4 units = 52, 1 unit = 13. Ben in 8 years = 13, so Ben now = 13 - 8 = 5 years.


(a) Cooking finished at 17 35 + 1 h 10 min = 18 45. She ate at 19 10, so cleaning took 19 10 - 18 45 = 25 min. (b) 135 min = 2 h 15 min. Start = 22 30 - 2 h 15 min = 20 15 = 10.15 p.m.


Remaining jars = 25 - 3 = 22. The coins from 3 jars are spread over 22 jars, raising each by 15, so coins added = 22 x 15 = 330. These came from 3 jars, so each jar had 330 / 3 = 110 coins. Total = 110 x 25 = 2750 coins.


Red marbles stay the same. At first red = 5/6 of total. After adding 140 blue, blue = 1/2, so red = 1/2 = blue. The 5 units of red (out of 6) now equal the new blue count. The 4 'extra' units come from the 140 added: 4 units = 140, so 1 unit = 35. Total at first = 6 units = 6 x 35 = 210 marbles.


Factors of 45 are 1, 3, 5, 9, 15, 45. 7 does not divide 45 exactly, so 7 is not a factor.


A fraction is in simplest form when numerator and denominator share no common factor other than 1. 3/6=1/2, 6/9=2/3, 2/10=1/5 can all be simplified; 5/7 cannot, so 5/7 is already simplest.


0.08 = 8/100. Divide numerator and denominator by 4: 8/100 = 2/25.


1 dress = 2 shirts. So 1 dress + 3 shirts = 2 + 3 = 5 units = $120. One shirt = $120 / 5 = $24.


In a game, 2 bonus tokens were given for every 5 tokens won. Larry collected a total of 150 tokens. How many bonus tokens was he given?

For every 5 won, 2 bonus are given, so each group of 5 + 2 = 7 tokens. 150 / 7 is not exact; the closest full groups give 21 groups of 7 = 147, with bonus tokens 21 x 2 = 42. So Larry was given 42 bonus tokens.


Cindy had an equal number of red and yellow beads at first. She gave away 50 beads. She had 1/3 of the red beads and 5/6 of the yellow beads left. How many more yellow beads than red beads did she have in the end?

Let each colour start with N beads. Red given away = 2/3 N, yellow given away = 1/6 N. Total given = 2/3 N + 1/6 N = 5/6 N = 50, so N = 60. Red left = 1/3 x 60 = 20; yellow left = 5/6 x 60 = 50. Difference = 50 - 20 = 30.


Write thirteen thousand and ninety-two in figures. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Thirteen thousand = 13 000; ninety-two = 92. Together 13 000 + 92 = 13 092.


Write the missing number in the number pattern below. 14 000, 13 600, 13 200, 12 800, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, 12 000


5/6 = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />/18. What is the missing number in the box?

6 x 3 = 18, so multiply the numerator by 3: 5 x 3 = 15. So 5/6 = 15/18.


Write 7 tenths as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Arrange the following numbers from the smallest to the greatest. 2/5 , 0.502 , 0.052 <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="?" />


Round 18.57 to the nearest whole number. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tenths digit is 5, so round up: 18.57 rounds to 19.


Mrs Chan is 5 times as old as her daughter now. Three years ago, her daughter was 7 years old. How old is Mrs Chan now? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Daughter 3 years ago = 7, so now = 7 + 3 = 10. Mrs Chan = 5 x 10 = 50 years old.


Weiling bought a total of 41 green and blue ice-cream sticks. She bought 15 more green ice-cream sticks than blue ice-cream sticks. How many blue ice-cream sticks did Weiling buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Remove the 15 extra green sticks: 41 - 15 = 26. Split equally: 26 ÷ 2 = 13 blue sticks.


Use the digits 3, 0, 6 and 8 to form the greatest decimal with 3 decimal places. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Largest place value should hold the biggest digit. With 3 decimal places, put 8 as the whole number and arrange the rest in decreasing order: 8.630.


Study the pattern. A B B C D A A B B C D A A B B C D A A B (positions 1st to 20th). Which letter is in the 70th position?

The pattern repeats every 6 letters: A B B C D A. 70 ÷ 6 = 11 remainder 4. The 4th letter in the block A B B C D A is C, so the 70th letter is C.


Henry, Paul and James had 386 marbles altogether. Paul had twice as many marbles as James. Henry had 30 marbles less than James. (a) How many marbles did James have? (b) How many marbles did Henry and Paul have altogether? (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 James = 1 unit. Paul = 2 units, Henry = 1 unit - 30. Total = 4 units - 30 = 386, so 4 units = 416, 1 unit = 104. (a) James = 104. (b) Paul = 2 x 104 = 208, Henry = 104 - 30 = 74, Henry + Paul = 208 + 74 = 282.


Mary used some ribbons to complete an art work. She used \(\dfrac{1}{4}\) m of the ribbon on the first day. She used \(\dfrac{5}{8}\) m more ribbon on the second day than on the first day. Find the total length of ribbon she used on the two days. Express your answer as a mixed number in its simplest form.


Sam has 2 strings and 5 ribbons. The total length of the strings and ribbons is 9.12 m. Each string is 1.9 m longer than a ribbon. What is the length of one ribbon? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each of the 2 strings is 1.9 m longer than a ribbon, so the extra length = 2 x 1.9 = 3.8 m. Remove it: 9.12 - 3.8 = 5.32 m for 7 equal ribbon-lengths (2 strings + 5 ribbons all reduced to ribbon length). 5.32 ÷ 7 = 0.76 m per ribbon.


Nigel travelled from Town A to Town B. He left Town A at 10 45 and reached Town B at 13 10. (a) How long did he take to travel from Town A to Town B? (b) Nigel stayed in Town B for 30 min. He then took 4 h 15 min to travel from Town B to Town C. At what time did he reach Town C? (a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


4 files and 2 writing pads cost $11.60. 8 files and 6 writing pads cost $26. What is the cost of 1 writing pad? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Double the first: 8 files + 4 pads = $23.20. Compare with 8 files + 6 pads = $26: the 2 extra pads cost $26 - $23.20 = $2.80. So 1 pad = $2.80 ÷ 2 = $1.40.


42 thousands and 8 tens is the same as .


Which of the following is a factor of both 12 and 80?

Factors of 12 are 1, 2, 3, 4, 6, 12; factors of 80 are 1, 2, 4, 5, 8, 10, 16, 20, 40, 80. The common factor among the options is 4.


Peter bought one bottle of oil. He used 2/3 of the bottle of oil to fry some chicken wings and 1/12 of it to bake muffins. How much oil was left in the bottle?


Joshua went for a movie which started at 20 30. The movie ended at 23 15. How long was the movie?

From 20 30 to 22 30 is 2 h; from 22 30 to 23 15 is a further 45 min. Total = 2 h 45 min.


How many letters in the word SHINE have at least one line of symmetry?

Of S, H, I, N, E: H (vertical/horizontal), I (vertical/horizontal) and E (horizontal) each have a line of symmetry; S and N do not. So 3 letters.


Round 35 620 to the nearest hundred. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The hundreds are 35 600 and 35 700; the tens digit is 2 (less than 5), so 35 620 rounds down to 35 600.


Arrange the following numbers from the smallest to the greatest. 3902, 3092, 3920 <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="?" />   (c) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Compare digit by digit: 3092 (hundreds 0), then 3902 (hundreds 9, tens 0), then 3920 (hundreds 9, tens 2). Smallest to greatest: 3092, 3902, 3920.


Arrange the following fractions from the greatest to the smallest. 2/3, 1/2, 5/6 <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="?" />   (c) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


The area of a rectangle is 48 cm². The length of the rectangle is 8 cm. What is the breadth of the rectangle? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Breadth = area ÷ length = 48 ÷ 8 = 6 cm.


When a number with 1 decimal place is rounded to the nearest whole number, the answer is 89. What is the greatest possible number? What is the smallest possible number? <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 1-decimal-place number rounds to 89 if it lies from 88.5 up to 89.4 (88.5 rounds up, 89.4 rounds down, 89.5 would round to 90). Greatest = 89.4; smallest = 88.5.


The perimeter of a square is 72 cm. What is the area of the square? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Tan took 15 minutes to walk home from the supermarket. She left the supermarket at 1.50 p.m. What time did she reach home? Express the time using the 24-hour clock. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1.50 p.m. + 15 min = 2.05 p.m. In 24-hour clock that is 14 05.


Shop X sold 4 times as many cars as Shop Y. Shop Y sold twice as many cars as Shop Z. Shop Z sold 602 fewer cars than Shop X. How many cars did Shop Z sell? How many cars did the three shops sell altogether? <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="?" />

Let Shop Z = 1 unit. Shop Y = 2 units, Shop X = 4 × 2 = 8 units. X − Z = 8 − 1 = 7 units = 602, so 1 unit = 602 ÷ 7 = 86. Shop Z = 86. Total = (8 + 2 + 1) units = 11 units = 11 × 86 = 946 cars.


Belicia mixed 1.43 ℓ of orange syrup with 8 ℓ of water to make an orange drink. The orange drink was then poured into 7 identical jugs. How many litres of orange drink were there in total? How many litres of orange drink were there in each jug? Round your answer to 2 decimal places. <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="?" />


Jamie read 2/9 of a book on Monday, 1/3 of the book on Tuesday and the remaining pages on Wednesday. She read 25 more pages on Tuesday than on Monday. What fraction of the book did she read on Wednesday? How many pages were there in the book? <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) Monday + Tuesday = 2/9 + 1/3 = 2/9 + 3/9 = 5/9, so Wednesday = 1 − 5/9 = 4/9. (b) Tuesday − Monday = 3/9 − 2/9 = 1/9 of the book = 25 pages, so the whole book = 25 × 9 = 225 pages.


Poppy paid $375 for 4 similar watches and 5 similar headphones. Melody paid $160 less for 2 similar watches and 3 similar headphones. What was the cost of 2 similar watches and 3 similar headphones? What was the cost of a headphone? <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) 2 watches + 3 headphones = $375 − $160 = $215. (b) Doubling: 4 watches + 6 headphones = 2 × $215 = $430. Subtract Poppy's 4 watches + 5 headphones = $375: that leaves 1 headphone = $430 − $375 = $55.


Add by place value: 50000 + 2000 + 90 + 8 = 52098. There are no hundreds, so the hundreds digit is 0.


56 = 8x7 = 4x14, so 8, 7 and 4 are factors and 56 is a multiple of each. 56 / 9 is not a whole number, so 56 is not a multiple of 9.


In 6.017 the places after the point are tenths (0), hundredths (1), thousandths (7). The 7 is in the third decimal place, so it stands for 7 thousandths.


7/50 = 14/100 = 0.14 (multiply numerator and denominator by 2). So 4 7/50 = 4.14.


9 3/4 = /4
What is the missing number in the box?

Convert the mixed number to an improper fraction: 9 3/4 = (9x4 + 3)/4 = (36 + 3)/4 = 39/4. So the missing numerator is 39.