Olivia used sticks to make triangles and squares. She used 6 sticks for each triangle and 8 sticks for each square. Olivia made the same number of triangles and squares. She used 14 more sticks to make the squares than the triangles. How many triangles did she make?

Each square uses 8 − 6 = 2 more sticks than each triangle. With an equal number of each shape, the extra sticks total 14, so the number of squares (and triangles) = 14 ÷ 2 = 7. She made 7 triangles.


Write the missing number in the number pattern below.<br>14 100, 13 200, 12 300, 11 400, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, 9600


Which two of the fractions below are equivalent to \(\dfrac{6}{8}\)?
\(\dfrac{12}{16}\), \(\dfrac{5}{7}\), \(\dfrac{4}{5}\), \(\dfrac{3}{4}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

\(\dfrac{6}{8}\) simplifies to \(\dfrac{3}{4}\). \(\dfrac{12}{16}\) also simplifies to \(\dfrac{3}{4}\). So the two equivalent fractions are \(\dfrac{12}{16}\) and \(\dfrac{3}{4}\).


At a funfair, \(\dfrac{5}{12}\) of the people were children, \(\dfrac{1}{3}\) of the people were men and the rest were women. What fraction of the people were women? Express your answer as a fraction in its simplest form.


Express 3 ÷ 7 as a decimal. Round your answer to the nearest hundredth.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

3 ÷ 7 = 0.4285... The thousandths digit is 8, so rounding to the nearest hundredth gives 0.43.


A train took 2 h 25 min to travel from Station A to Station B. It arrived at Station B at 23 45. What time did the train leave Station A? Express your answer using the 24-hour clock.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Subtract the travelling time from the arrival time: 23 45 − 2 h 25 min. 23 45 − 2 h = 21 45; 21 45 − 25 min = 21 20. The train left at 21 20.


The table shows the number of stickers collected by each pupil in a group. Part of the table is covered by an ink blot. There were 87 pupils who collected at least 70 stickers.
Number of stickers: 50, 60, 70, 80, 90
Number of pupils: 25, 34, 19, ?, ?
How many pupils in total collected 80 and 90 stickers?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

'At least 70 stickers' means the 70, 80 and 90 groups together = 87. The 70 group is 19, so the 80 and 90 groups together = 87 − 19 = 68.


A pair of trousers cost $132. It cost $27 more than a shirt. Mr Lee bought a pair of trousers and 4 shirts.
(a) How much did a shirt cost?
(b) How much did Mr Lee pay for a pair of trousers and 4 shirts 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="?" />


There were some stickers in a box. Mariam took \(\dfrac{3}{8}\) of the stickers and Amy took the rest. Mariam took 36 fewer stickers than Amy.
(a) What fraction of the stickers did Amy take?
(b) How many stickers were in the box in total?
(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) Amy took 1 − \(\dfrac{3}{8}\) = \(\dfrac{5}{8}\). (b) Amy's share minus Mariam's share = \(\dfrac{5}{8} - \dfrac{3}{8} = \dfrac{2}{8} = \dfrac{1}{4}\) of the total = 36 stickers. So total = 36 × 4 = 144 stickers.


Ahmad and Jack had the same amount of money at first. After Ahmad had spent $37 and Jack had received $15, Jack had 3 times as much money as Ahmad in the end.
(a) How much more money did Jack have than Ahmad in the end?
(b) How much money did Jack have at first?
(a) $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) The difference between them grew by $37 (Ahmad spent) + $15 (Jack received) = $52. So in the end Jack had $52 more than Ahmad. (b) In the end Jack = 3 × Ahmad, so the $52 difference = 2 units, 1 unit = $26 = Ahmad's end amount; Jack's end = 3 × $26 = $78. Jack at first = $78 − $15 = $63. (Key gives Jack's first amount via 52 ÷ 2 = 26 = Ahmad's end amount.)


Tina saved some money from Monday to Friday. Each day, she saved $1 more than the previous day. At the end of Wednesday, she saved a total of $38.70.
(a) How much money did Tina save on Wednesday?
(b) How much money did she save on Friday?
(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) Mon, Tue, Wed savings differ by $1. Their total $38.70 minus the extra: Tue = Wed − 1, Mon = Wed − 2. 3 × Wed − 3 = 38.70, so 3 × Wed = 41.70, Wed = $13.90. (b) Thursday = $14.90, Friday = $15.90.


Arrange the following numbers from the smallest to the largest.
3.5 , 3.05 , \(3\dfrac{1}{100}\)
<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="?" />


2 3/7 = /7
What is the missing number in the box?

Convert the mixed number to an improper fraction: 2 3/7 = (2x7 + 3)/7 = 17/7. The missing numerator is 17.


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

Order ascending: 6083 < 6803 < 6830. That is option 4.


\(\dfrac{5}{7}\) has no common factor between 5 and 7, so it is already in simplest form. The others simplify: \(\dfrac{6}{9}=\dfrac{2}{3}\), \(\dfrac{3}{6}=\dfrac{1}{2}\), \(\dfrac{4}{10}=\dfrac{2}{5}\).


Which of the following decimals is the greatest?

Compare the tenths digit first: 0.369 and 0.346 have 3 tenths, the others have 1 tenth. Between 0.369 and 0.346, the hundredths digit 6 > 4, so 0.369 is greatest.


Which of the following is a factor of both 12 and 90?


Mrs Lee had some stickers. After she gave 6 stickers to each of her 28 pupils, she had 12 stickers left. How many stickers did Mrs Lee have at first?

Stickers given out = 6 × 28 = 168. Add the 12 left over: 168 + 12 = 180.


What could be the mass of a Primary 4 Mathematics textbook?

A textbook has a mass of a few hundred grams. 33 g is far too light, 33 kg and 330 kg are far too heavy. 330 g is the sensible estimate.


Mei Ling started running a marathon at 6.35 a.m. and finished it at 11.10 a.m. How long did she take to complete the marathon?

From 6.35 a.m. to 11.35 a.m. is 5 h, but she finished at 11.10 a.m., which is 25 min earlier: 5 h − 25 min = 4 h 35 min. (From 6.35 to 11.10 = 4 h to 10.35, plus 35 min to 11.10 = 4 h 35 min.)


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

Thirteen thousand = 13 000, plus ninety-four = 94, giving 13 094.


Write the missing number in the number pattern.<br>14 000, 13 200, 12 400, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, 10 800, 10 000

The pattern decreases by 800 each time: 14 000, 13 200, 12 400, 11 600, 10 800, 10 000. The missing number is 11 600.


Find the sum of 647 and 978. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Make the denominators the same: \(\dfrac{1}{3}=\dfrac{3}{9}\). Then \(\dfrac{2}{9}+\dfrac{3}{9}=\dfrac{5}{9}\).


\(0.8=\dfrac{8}{<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />}\) What is the missing number in the box?

0.8 means 8 tenths, so \(0.8=\dfrac{8}{10}\). The missing number is 10.


Round 42.64 to the nearest whole number. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tenths digit is 6, which is 5 or more, so round up: 42.64 ≈ 43.


Which two of the fractions below are smaller than \(\dfrac{1}{2}\)?
\(\dfrac{4}{11}\), \(\dfrac{3}{4}\), \(\dfrac{5}{10}\), \(\dfrac{2}{7}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Mrs Tan took 20 min to travel from her home to the office. She spent 6 h 30 min in the office. She left her office at 18 15. What time did she leave her home in the morning? Give your answer in 24-hour clock. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Left office at 18 15. Subtract 6 h 30 min in office: 18 15 − 6 h 30 min = 11 45 (arrived at office). Subtract 20 min travel: 11 45 − 20 min = 11 25. She left home at 11 25.


PQRS is a square with perimeter 28 cm. Find its area. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

Side of square = 28 ÷ 4 = 7 cm. Area = 7 × 7 = 49 cm².


The total cost of a handbag and purse is $242. The handbag costs $20 more than the purse. Find the cost of the handbag. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Remove the extra $20: 242 − 20 = 222, which is twice the purse. Purse = 222 ÷ 2 = 111. Handbag = 111 + 20 = 131.


The chairs in the hall are arranged in rows. Each row has the same number of chairs. When Ali sits at one of the chairs, there are 6 chairs to his right and 5 chairs to his left. There are 8 chairs in front of him and 4 chairs behind him. How many chairs are there in the hall? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Chairs in Ali's row = 6 + 5 + 1 = 12. Number of rows = 8 + 4 + 1 = 13. Total chairs = 12 × 13 = 156.


Mrs Wong baked between 70 to 90 cookies. She could pack all the cookies into boxes of 5 cookies or boxes of 8 cookies without any remainder. How many cookies did Mrs Wong bake? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number must be a common multiple of 5 and 8, i.e. a multiple of 40. Between 70 and 90, the multiple of 40 is 80.


\(\dfrac{5}{12}\) of the passengers on the MRT were female.
(a) What fraction of the passengers were male?
(b) There were 40 female passengers, how many passengers were there on the MRT?
(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) Male fraction = \(\dfrac{12}{12}-\dfrac{5}{12}=\dfrac{7}{12}\). (b) \(\dfrac{5}{12}\) corresponds to 40 female passengers, so 1 unit = 40 ÷ 5 = 8, and the total = 8 × 12 = 96 passengers.


The total mass of an empty school bag and 5 similar books was 5.4 kg. The total mass of the same school bag and 2 similar books was 3 kg.
(a) What was the mass of 1 book?
(b) What was the mass of the empty school bag?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> kg

(a) The difference of 3 books = 5.4 − 3 = 2.4 kg, so 1 book = 2.4 ÷ 3 = 0.8 kg. (b) 2 books = 0.8 × 2 = 1.6 kg, so the bag = 3 − 1.6 = 1.4 kg.


Ravi had $92 more than Peter. After Ravi gave $100 to Peter, Peter had 5 times as much as Ravi.
(a) How much money did Ravi have at first?
(b) How much money did Peter have in the end?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

After the transfer the total is unchanged. Ravi gave away $100, so the difference shifts by $200: originally Ravi had $92 more, after giving $100 Peter has $108 more than Ravi. Peter = 5 × Ravi, so the difference = 4 units = $108? Using the key: Ravi's amount after = (total)÷6 of a 1:5 split. (100+8)÷4 = 27 → Ravi after = $27, Ravi at first = 27 + 100 = $127. (b) Peter at first = 127 − 92 = $35; Peter in the end = 35 + 100 = $135.


In which of the following numbers does the digit 6 stand for 600?

The digit 6 stands for 600 when it is in the hundreds place. In 8690, the 6 is in the hundreds place, so it stands for 600.


Which of the following is <b>not</b> a factor of 42?

Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. 8 is not a factor because 42 ÷ 8 does not give a whole number.


Which of the following decimals is the smallest?

All have whole-number part 4. Compare tenths: 4.056 has 0 tenths, which is smallest. So 4.056 is the smallest.


How many one-fifths are there in 4 wholes?

Each whole has 5 one-fifths. In 4 wholes there are 4 × 5 = 20 one-fifths.


The total volume of 2 identical bottles of orange juice is 9.3 litres. What is the volume of 6 such bottles of orange juice?

1 bottle = 9.3 ÷ 2 = 4.65 litres. 6 bottles = 4.65 × 6 = 27.9 litres. (Or: 6 bottles = 3 × 9.3 = 27.9 litres.)


Betty and Ken had 180 coins altogether. After Betty gave 25 coins to Ken, Ken had twice as many coins as Betty. How many coins did Ken have at first?

Total stays 180. After giving, Ken = 2 × Betty, so 3 units = 180, 1 unit = 60. Betty (after) = 60, Ken (after) = 120. Ken at first = 120 − 25 = 95.


Arrange the following numbers from the smallest to the greatest.
3504 , 3045 , 3450
<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="?" />

Compare the numbers digit by digit: 3045 < 3450 < 3504. From smallest to greatest: 3045, 3450, 3504.


Write \(3\dfrac{5}{6}\) as an improper fraction.

Multiply the whole number by the denominator and add the numerator: (3 × 6) + 5 = 23. So \(3\dfrac{5}{6} = \dfrac{23}{6}\).


Change to like denominators: \(\dfrac{3}{4} = \dfrac{6}{8}\). Then \(\dfrac{6}{8} - \dfrac{5}{8} = \dfrac{1}{8}\).


Round 14 310 to the nearest hundred.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tens digit of 14 310 is 1, which is less than 5, so round down. 14 310 rounded to the nearest hundred is 14 300.


Which two of the fractions below are in the simplest form?
\(\dfrac{3}{5}\) , \(\dfrac{4}{6}\) , \(\dfrac{5}{7}\) , \(\dfrac{6}{10}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

A fraction is in simplest form when its numerator and denominator share no common factor other than 1. \(\dfrac{4}{6}\) simplifies to \(\dfrac{2}{3}\) and \(\dfrac{6}{10}\) simplifies to \(\dfrac{3}{5}\), so they are not simplest. \(\dfrac{3}{5}\) and \(\dfrac{5}{7}\) cannot be simplified, so they are in simplest form.


Round 24.85 to 1 decimal place.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Look at the second decimal place (the hundredths digit) which is 5, so round the tenths up. 24.85 rounded to 1 decimal place is 24.9.


Jenny took 20 min to walk from her home to school in the morning. She spent 3 h 35 min in school. She left her school at 12 15. What time did she leave her home in the morning? Give your answer in 24-hour clock.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Work backwards from 12 15. Subtract 3 h 35 min in school: 12 15 − 3 h 35 min = 08 40 (arrival at school). Subtract 20 min walk: 08 40 − 20 min = 08 20. She left home at 08 20.


Siti paid $30 for 4 chicken pies and 4 tuna pies. Each chicken pie cost $1.20 more than each tuna pie. How much did 1 tuna pie cost?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 4 chicken pies cost 4 × $1.20 = $4.80 more than the 4 tuna pies. Remove this extra: $30 − $4.80 = $25.20, which would be the cost of 8 tuna pies. So 1 tuna pie = $25.20 ÷ 8 = $3.15.


Mother gave Ming some money on Monday. She gave him $25 on Tuesday. Ming spent half of the total amount of money he received and had $28 left. How much money did Mother give to Ming on Monday?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

He had $28 left after spending half, so half the total = $28, meaning the total received = $28 × 2 = $56. Subtract Tuesday's $25: Monday's amount = $56 − $25 = $31.


Taylor, Umar and Victor went for a morning walk. Taylor walked a distance that was 6 times as much as Victor. Umar walked 1.12 km more than Taylor. Umar walked a total distance of 4.6 km. How many kilometres did Victor walk?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> km

Taylor's distance = Umar − 1.12 = 4.6 − 1.12 = 3.48 km. Taylor walked 6 times Victor, so Victor = 3.48 ÷ 6 = 0.58 km.


A grocer had 25 crates of tomatoes. Each crate contained 60 tomatoes. He threw away 303 rotten tomatoes and repacked the remaining into bags of 7 tomatoes each. How many bags of tomatoes did the grocer pack?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total tomatoes = 25 × 60 = 1500. After throwing away rotten ones: 1500 − 303 = 1197. Bags = 1197 ÷ 7 = 171 bags.


Rina bought 30 m of ribbon. After using the ribbon to tie a present and 4 identical parcels, she had 8.81 m of ribbon left. She used 4.75 m of ribbon to tie the present. How many metres of ribbon did she use to tie each parcel?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m

Ribbon used in total = 30 − 8.81 = 21.19 m. Subtract the present: 21.19 − 4.75 = 16.44 m used on the 4 parcels. Each parcel = 16.44 ÷ 4 = 4.11 m.


Daniel had 1980 stamps more than Eugene. After Daniel gave away 291 stamps, he had 4 times as many stamps as Eugene.
a) How many more stamps did Daniel have than Eugene in the end?
b) How many stamps did Daniel have at first?
(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) After giving away 291, Daniel's lead over Eugene = 1980 − 291 = 1689 stamps. (b) In the end Daniel = 4 times Eugene, so the 1689 difference = 3 units, 1 unit (Eugene) = 1689 ÷ 3 = 563. Daniel at first = Eugene + 1980 = 563 + 1980 = 2543 stamps.


There were 180 flowers at a florist. \(\dfrac{2}{3}\) of them were roses, \(\dfrac{2}{9}\) of them were sunflowers and the remaining were daisies.
a) What fraction of the flowers were daisies?
b) The daisies were sold at 5 for $21. How much was collected from the sale of all the daisies?
(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 baker sold donuts at $2 each. The customers received a free donut for every 4 donuts they bought.
a) What was the least amount of money a customer had to pay if he wanted exactly 15 donuts?
b) How many donuts did a customer receive in total when he paid $40?
(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) Buy 4, get 1 free = 5 donuts per group. For 15 donuts: 15 ÷ 5 = 3 groups, so he buys 4 × 3 = 12 donuts. Cost = 12 × $2 = $24. (b) $40 buys 40 ÷ 2 = 20 donuts. Free donuts = 20 ÷ 4 = 5. Total = 20 + 5 = 25 donuts.


Which of the following is a multiple of 6?

A multiple of 6 is a number in the 6 times table: 6, 12, 18, 24, 30, ... Among the options, 24 = 6 × 4 is a multiple of 6. (32, 3 and 16 are not.) Answer: 24.


Add by place value: 80 000 + 7000 + 300 + 0 tens + 2 = 87 302. The tens place is 0, so the answer is 87 302.


In the number 67.35, the digit ________ is in the tenths place.

In 67.35, the first digit after the decimal point is the tenths place. That digit is 3. (The 5 is hundredths.)


Arrange the following decimals from the smallest to the greatest.<br>4.8 , 0.48 , 4.08 , 0.84

Compare the whole-number parts first: 0.48 and 0.84 (whole part 0) are smaller than 4.08 and 4.8 (whole part 4). Among 0.48 and 0.84, 0.48 < 0.84. Among 4.08 and 4.8, 4.08 < 4.80. Order: 0.48, 0.84, 4.08, 4.8.


\(9\dfrac{3}{5}\) = \(\dfrac{ }{5}\)<br>What is the missing number in the box?

Convert the mixed number to an improper fraction with denominator 5: \(9\dfrac{3}{5}\) = \(\dfrac{9\times5+3}{5}\) = \(\dfrac{45+3}{5}\) = \(\dfrac{48}{5}\). The missing numerator is 48.


Kumar is 1.53 m tall. His father is 0.28 m taller than him. His mother is 0.13 m shorter than his father. What is his mother's height?


Write \(\dfrac{17}{6}\) as a mixed number.


Find the value of \(1 - \dfrac{1}{8} - \dfrac{3}{4}\).


Arrange the following numbers from the smallest to the greatest.
3907 , 3079 , 3790
<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="?" />

Compare by place value (all start with 3 thousands): 3079 (0 hundreds) < 3790 (7 hundreds) < 3907 (9 hundreds). Smallest to greatest: 3079, 3790, 3907.


A ribbon was 27.3 m long. Siti used 2.98 m of it for her project. She then cut the remaining ribbon equally into 8 pieces. What was the length of each piece of ribbon?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Muthu slept at 21 35 on Saturday night and woke up at 06 00 the next day. How long did he sleep?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> h <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> min

From 21 35 to 22 00 is 25 min. From 22 00 to 06 00 is 8 h. Total = 8 h 25 min.


Container X has 96 more balls than Container Y. How many balls must be transferred from Container Y to Container X so that it has 112 balls less than Container X?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The required new difference is 112. The difference grows by 2 for every ball moved from Y to X (X gains one, Y loses one). Extra difference needed = 112 − 96 = 16. Balls to transfer = 16 ÷ 2 = 8.


Factory A and Factory B produce 1508 boxes a day. Factory B produces 3 times as many boxes as Factory A. How many boxes does Factory B produce?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Factory B is 3 times Factory A, so together they are 3 + 1 = 4 equal units = 1508 boxes. One unit (Factory A) = 1508 ÷ 4 = 377. Factory B = 3 × 377 = 1131 boxes.


Mrs Choo bought a peach, 2 pears and 6 apples for $8.70. The cost of 1 pear and 3 apples was $2.60. What was the cost of the peach?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Ali bought 8 kg of flour. He used \(\dfrac{2}{5}\) kg of the flour to bake a cake and \(\dfrac{1}{4}\) kg of it to bake chocolate cookies.
a) What was the total mass of flour he used altogether?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) What was the mass of flour he had left?
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Mr Wong earned $0.25 for every newspaper he sold. He earned an additional $1.50 for every 10 copies of newspaper sold.
a) How much did Mr Wong earn in total for selling 10 copies of newspaper?
$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) He earned $48 one day. How many copies of newspaper did he sell that day?
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

a) 10 copies earn 10 × $0.25 = $2.50 plus the $1.50 bonus = $4.00. b) Every 10 copies earn $4, so $48 ÷ $4 = 12 sets of 10 copies = 12 × 10 = 120 copies.


The time in New Zealand is 4 hours ahead of the time in Singapore. When it is 10 00 in Singapore, it is 14 00 in New Zealand. Kathy went to New Zealand for a work trip. She would be taking a flight from New Zealand at 06 40 to come back to Singapore. The flight duration is 9 h 55 min. At what time would Kathy reach Singapore?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Flight leaves NZ at 06 40. Arrival in NZ time = 06 40 + 9 h 55 min = 16 35 (NZ time). Singapore is 4 h behind NZ, so subtract 4 h: 16 35 − 4 h = 12 35. Kathy reaches Singapore at 12 35.


Mr Lim had 344 fruits. \(\dfrac{3}{4}\) of the fruits sold were apples. Half of the remaining fruits sold were oranges and the rest were pears.
a) How many apples did he sell?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) Mr Lim wanted to sell as many oranges as apples. How many more oranges would he need?
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

1 unit = 344 ÷ 4 = 86. a) Apples = \(\dfrac{3}{4}\) = 3 units = 3 × 86 = 258. b) Remaining = 86; oranges = half = 86 ÷ 2 = 43. To match the apples (258), more oranges needed = 258 − 43 = 215.


In which of the following does the digit 5 stand for 500?

Method: the digit 5 stands for 500 when it is in the hundreds place. In 6573, the 5 is in the hundreds place, so it stands for 500. Answer: 6573.


Which of the following is a factor of both 24 and 30?

Method: find the common factors. Factors of 24: 1,2,3,4,6,8,12,24. Factors of 30: 1,2,3,5,6,10,15,30. 6 is a factor of both. Answer: 6.


Which number when rounded to the nearest ten becomes 53 200?

Method: rounding to the nearest ten gives 53 200 for numbers from 53 195 to 53 204. 53 196 rounds up to 53 200. Answer: 53 196.


How many one-fifths are there in 3 wholes?

Method: each whole has 5 one-fifths. 3 wholes = 3 x 5 = 15 one-fifths. Answer: 15.


The digit 6 in 23.16 stands for 6 ________

Method: in 23.16, the digit after the decimal point is tenths and the next is hundredths. The 6 is in the hundredths place, so it stands for 6 hundredths. Answer: hundredths.


45 069 = 40 000 + 5000 + <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> + 9


Write the missing number in the number pattern below.<br>11 000 , 10 600 , 10 200 , <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , 9400


Which two of the fractions below are smaller than \(\dfrac{1}{2}\)?
\(\dfrac{3}{4}\) , \(\dfrac{4}{9}\) , \(\dfrac{5}{10}\) , \(\dfrac{3}{7}\)
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


What is the value of \(\dfrac{2}{3}\) + \(\dfrac{5}{6}\)? Express your answer as a mixed number.


Method: 0.15 has 2 decimal places, so it is 15 hundredths = \(\dfrac{15}{100}\). Answer: \(\dfrac{15}{100}\).


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

Method: look at the tenths digit. 18.57 has 5 in the tenths place, which is 5 or more, so round up. 18.57 rounds to 19. Answer: 19.


7.3 − 0.92 = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: align the decimals. 7.30 - 0.92 = 6.38. Answer: 6.38.


Find the value of 5.79 × 6. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: 5.79 x 6 = 34.74 (since 579 x 6 = 3474, then place the decimal two places). Answer: 34.74.


The table shows the favourite fruits of a group of students.
Apple: 35, Mango: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, Orange: 32, Papaya: 54.
\(\dfrac{2}{5}\) of the students chose papaya as their favourite fruit. How many students chose mango as their favourite fruit?

Method: \(\dfrac{2}{5}\) of the total = 54 (papaya), so total = 54 ÷ 2 x 5 = 135 students. Mango = total - apple - orange - papaya = 135 - 35 - 32 - 54 = 14. Answer: 14.


Sally mixed 1.73 \(l\) of orange syrup with 4.55 \(l\) of water. She poured the mixture equally into 4 bottles. How many litres of the mixture were there in each bottle? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The mass of a watermelon is 3.4 kg. It is 5 times as heavy as a pear. What is the total mass of the pear and the watermelon? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: pear = 3.4 ÷ 5 = 0.68 kg. Total = watermelon + pear = 3.4 + 0.68 = 4.08 kg. Answer: 4.08 kg.


Mr and Mrs Tan took their children to watch a circus show on a Sunday. They bought 5 tickets in total. They had 3 children whose ages were 8, 13 and 14.
Circus Show Ticket Prices — Adult: Mon–Fri $33.50, Sat–Sun $38.50. Children (12 years and below): Mon–Fri $16, Sat–Sun $22.
How much did the 5 tickets cost altogether?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: it is Sunday, so use Sat–Sun prices. The two parents and the two older children (13 and 14, over 12) all pay adult: 4 adults x $38.50 = $154. The 8-year-old pays child: $22. Total = 154 + 22 = $176. Answer: $176.


The cost of 6 identical laptops is $7692. Find the cost of 5 such laptops. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: cost of 1 laptop = 7692 ÷ 6 = $1282. Cost of 5 laptops = 1282 x 5 = $6410. Answer: $6410.


Leon has \(\dfrac{2}{5}\) kg of flour in a container. He has \(\dfrac{1}{2}\) kg of flour less than Siti. How much flour do they have altogether? Express your answer as a mixed number in its simplest form.


Mrs Lee baked some cookies and ate \(\dfrac{2}{9}\) of the cookies. She gave 12 cookies to her friend and had 9 cookies left.
(a) How many cookies did she bake?
(b) What fraction of the cookies did she have left? Express your answer in its simplest form.
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Method: (a) she ate \(\dfrac{2}{9}\), so \(\dfrac{7}{9}\) remained. The 12 given away + 9 left = 21 cookies = \(\dfrac{7}{9}\) of the total. So \(\dfrac{1}{9}\) = 21 ÷ 7 = 3, and the total = 3 x 9 = 27 cookies. (b) cookies left = 9 out of 27 = \(\dfrac{9}{27}\) = \(\dfrac{1}{3}\). Answer: (a) 27; (b) \(\dfrac{1}{3}\).


Sharon and Leo had a total of 3260 stickers. Sharon had 3 times as many stickers as Leo. How many stickers must Sharon give to Leo so that Sharon has 270 more stickers than Leo? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: Sharon has 3 units and Leo 1 unit, total 4 units = 3260, so 1 unit = 815. Sharon = 2445, Leo = 815. For Sharon to have 270 more than Leo from a total of 3260: Leo's new amount = (3260 - 270) ÷ 2 = 2990 ÷ 2 = 1495, Sharon's new = 1495 + 270 = 1765. Sharon must give = 2445 - 1765 = 680 stickers. Answer: 680.


A bookshop sells pencils in packs of 4 and erasers in packs of 6. 4 pencils for $3. 6 erasers for $5.
(a) Henry bought an equal number of pencils and erasers. What is the least number of pencils he could have bought?
(b) Liling used all her money to buy 44 pencils. Using the same amount of money, what is the greatest number of erasers she could buy?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Method: (a) pencils come in 4s, erasers in 6s. The least equal number is the lowest common multiple of 4 and 6 = 12. (b) 44 pencils = 11 packs x $3 = $33. With $33, erasers cost $5 per 6: 33 ÷ 5 = 6 packs ($30) remainder $3, so 6 packs = 36 erasers (the $3 left is not enough for another pack). Answer: (a) 12; (b) 36.


Keith and Sam had the same amount of money. Keith bought 6 egg tarts and had $1.90 left. Sam wanted to buy 10 egg tarts but was short of $5.50.
(a) What was the cost of 1 egg tart?
(b) How much money did Sam have?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Method: (a) the difference between 10 and 6 egg tarts is 4 egg tarts. Keith had $1.90 left; Sam was short $5.50, so 4 egg tarts cost 1.90 + 5.50 = $7.40. 1 egg tart = 7.40 ÷ 4 = $1.85. (b) Sam (same money as Keith) = cost of 6 egg tarts + $1.90 = (1.85 x 6) + 1.90 = 11.10 + 1.90 = $13. Answer: (a) $1.85; (b) $13.


Arrange the following numbers from the smallest to the largest.
3.5 , 3.05 , \(3\dfrac{1}{100}\)
<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="?" />


In which of the following does the digit 8 stand for 800?

The digit 8 stands for 800 when it is in the hundreds place. In 7 862, the 8 is in the hundreds position, so it stands for 800. Answer: 7 862.


Add by place value: 10000 + 5000 + 600 + 4 = 15 604. Note there are no tens, so the tens digit is 0. Answer: 15 604.


A number must be divisible by both 2 and 3. 12 = 2 x 6 and 12 = 3 x 4, so both 2 and 3 are factors of 12. Answer: 12.


Which fraction is <b>not</b> in its simplest form?

A fraction is in simplest form when the numerator and denominator share no common factor other than 1. \(\dfrac{6}{9}\) can be simplified by dividing both by 3 to give \(\dfrac{2}{3}\), so it is NOT in simplest form. Answer: \(\dfrac{6}{9}\).


Arrange these decimals from the smallest to the greatest.<br>7.3 , 0.73 , 7.03 , 0.75

Compare whole-number parts first: 0.73 and 0.75 are less than 1; 7.03 and 7.3 are over 7. Order the small pair: 0.73 < 0.75. Order the large pair: 7.03 < 7.3. So smallest to greatest: 0.73 , 0.75 , 7.03 , 7.3. Answer: option 2.


The mass of a pail of sand is 2.5 kg. It is 30.14 kg lighter than a pile of bricks. What is the mass of the bricks?

The sand is 30.14 kg lighter than the bricks, so the bricks are 30.14 kg heavier than the sand. Mass of bricks = 2.5 + 30.14 = 32.64 kg. Answer: 32.64 kg.


Round off 12.329 \(l\) to the nearest tenth.

Rounding to the nearest tenth means keeping 1 decimal place. Look at the hundredths digit (2): since 2 is less than 5, round down. 12.329 rounds to 12.3 l. Answer: 12.3 l.


Round 8325 to the nearest ten. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To round to the nearest ten, look at the ones digit (5). Since 5 rounds up, the tens digit goes from 2 to 3. 8325 rounds to 8330. Answer: 8330.


How many one-elevenths are there in 1 whole? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

One whole = \(\dfrac{11}{11}\), which is eleven groups of \(\dfrac{1}{11}\). So there are 11 one-elevenths in 1 whole. Answer: 11.


Find the value of 6.73 x 8. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


4501 ÷ 7 = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Write \(2\dfrac{2}{3}\) as an improper fraction.

Multiply the whole number by the denominator and add the numerator: 2 x 3 + 2 = 8. Keep the denominator 3. So \(2\dfrac{2}{3}=\dfrac{8}{3}\). Answer: \(\dfrac{8}{3}\).


Find the sum of the first 2 common multiples of 4 and 6. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Common multiples of 4 and 6 are multiples of 12. The first two are 12 and 24. Their sum is 12 + 24 = 36. Answer: 36.


After spilling \(\dfrac{2}{3}\) \(l\) of water, John has \(1\dfrac{1}{2}\) \(l\) of water left. How much water does he have at first? Give your answer as a mixed number.

At first = water left + water spilled = \(1\dfrac{1}{2}+\dfrac{2}{3}\). Common denominator 6: \(1\dfrac{3}{6}+\dfrac{4}{6}=1\dfrac{7}{6}=2\dfrac{1}{6}\). Answer: \(2\dfrac{1}{6}\) l.


The perimeter of a square is 48 cm. Find the area of the square. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

A square has 4 equal sides, so each side = 48 ÷ 4 = 12 cm. Area = side x side = 12 x 12 = 144 cm^2. Answer: 144 cm^2.


In a party, the children are told to get into groups to play a game. If they form groups of 5, there will be 2 children left without a group. If they form groups of 6, there will be 4 children left without a group. What is the least number of children at the party? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number leaves remainder 2 when divided by 5 (so ends in 2 or 7) and remainder 4 when divided by 6. Check numbers ending in 2 or 7: 22 ÷ 6 = 3 r 4 and 22 ÷ 5 = 4 r 2. So the least number is 22. Answer: 22.


Mrs Tan had $188.70. She spent $39.90 on a blouse. She gave the rest of the money equally to her 3 children. How much did each child receive? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Money left after the blouse = 188.70 - 39.90 = 148.80. Shared among 3 children: 148.80 ÷ 3 = 49.60. Each child received $49.60. Answer: $49.60.


Katherine bought 10.25 \(l\) of fruit juice. She fills them into 9 bottles. Each bottle is filled with 0.45 \(l\) of fruit juice.
(a) How much fruit juice will be left?
(b) How much did Katherine pay for the fruit juice if it cost $4 per litre?
(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 mass of a bag containing 9 packets of milk is 23.5 kg. After taking out 4 packets, the mass of the bag and remaining packets of milk is 19.36 kg. Find the mass of the bag. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Tom earned $5670 a month. He spent \(\dfrac{2}{3}\) of his salary on food and \(\dfrac{1}{9}\) of it on transport. He saved the rest. How much did he save in a month? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


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

The total stays the same: 4730 + 1240 = 5970. In the end Timmy has twice Ahmad, so the total is 3 equal parts. Ahmad's final amount = 5970 ÷ 3 = 1990. Ahmad started with 1240, so he received 1990 - 1240 = 750 marbles. Answer: 750.


In which of the following does the digit 6 stand for 600?

The digit 6 stands for 600 when it is in the hundreds place. In 7603, the 6 is in the hundreds place (6 hundreds = 600). Answer: 7603.


Which of the following are common factors of 18 and 24?

Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common factors include 1, 2, 3, 6. Among the options, 3 and 6 are both common factors. Answer: 3 and 6.


How many one-quarters are there in 2 wholes?

Each whole has 4 one-quarters. 2 wholes = 2 × 4 = 8 one-quarters. Answer: 8.


\(7\dfrac{4}{9}\) = \(\dfrac{ }{9}\)<br>What is the missing number in the box?

Convert the mixed number to an improper fraction: 7 × 9 + 4 = 63 + 4 = 67. So \(7\dfrac{4}{9}=\dfrac{67}{9}\). Answer: 67.


What is the number when 223.74 is rounded to 1 decimal place?

To round 223.74 to 1 decimal place, look at the 2nd decimal digit (4). Since 4 < 5, round down: 223.7. Answer: 223.7.


Mary bought a table and 3 chairs. The table cost $180 more than each chair. She gave the cashier $1000 and received $40 change. What was the cost of each chair?


This number is a factor of 20 and a multiple of 5. It is between 6 and 19. What is this number?

Factors of 20: 1, 2, 4, 5, 10, 20. Multiples of 5: 5, 10, 15, 20. The number is in both lists and between 6 and 19: that is 10. Answer: 10.


Mrs Tan packed 40 plums into some bags. Each bag contained 7 plums. She sold each bag of plums at $6 and each remaining plum at $1 each. How much would she collect if she sold all the plums?

40 ÷ 7 = 5 bags with remainder 5 plums. 5 bags × $6 = $30, plus 5 plums × $1 = $5. Total = $30 + $5 = $35. Answer: $35.


Ann and David scored a total of 8060 points in a game show. Ann scored 4 times as many points as David. How many points did David score?

David = 1 unit, Ann = 4 units, total = 5 units = 8060. 1 unit = 8060 ÷ 5 = 1612. David scored 1612 points. Answer: 1612.


Ethan ate \(\dfrac{5}{12}\) of a pizza. His sister ate \(\dfrac{1}{3}\) of the same pizza. How much more of the pizza did Ethan eat than his sister?


Mr Tan is 1.6 m tall. He is taller than Mdm Siti by 0.02 m. How tall is Mdm Siti?

Mdm Siti is shorter, so subtract: 1.6 − 0.02 = 1.58 m. Answer: 1.58 m.


The total mass of 5 identical boxes is 11.25 kg. What is the mass of 9 such boxes?


The mass of a durian is 1.7 kg when rounded to 1 decimal place. Which of the following is the maximum possible mass of the durian?

Values from 1.65 up to just below 1.75 round to 1.7. The largest option that still rounds to 1.7 is 1.74. Wait — 1.84 rounds to 1.8, not 1.7. Re-check: the maximum value that rounds to 1.7 is just under 1.75, so 1.74 is the maximum among valid options. The answer key marks option (4) 1.84; however 1.84 rounds to 1.8. Mathematically the maximum that rounds to 1.7 is 1.74 (option 2).


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

Ninety thousand = 90 000. Sixteen = 16. Combine: 90 000 + 16 = 90 016. Answer: 90 016.


Write the missing number in the number pattern.<br>5624 , 5774 , 5924 , <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , 6224


What is the value of \(\dfrac{2}{3}\) + \(\dfrac{7}{9}\)? Express your answer as a mixed number.


Arrange these numbers from the greatest to the smallest.
0.065 , 0.605 , 0.506
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> (greatest) , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> (smallest)

Compare tenths first: 0.605 and 0.506 have 6 and 5 tenths; 0.065 has 0 tenths. So 0.605 > 0.506 > 0.065. Greatest to smallest: 0.605, 0.506, 0.065.


Find the value of 45 ÷ 7, correct to 2 decimal places.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

45 ÷ 7 = 6.428... The 3rd decimal digit is 8, so round up the 2nd decimal: 6.43. Answer: 6.43.


Mr Tay packed pens and pencils into boxes for sale. There are 698 boxes in total. Each box contains 11 pens and 6 pencils. How many pens and pencils are there altogether?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


2 similar spoons and 2 similar mugs cost $27. Each mug costs two times as much as each spoon. How much will 3 such spoons cost?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let 1 spoon = 1 unit, 1 mug = 2 units. 2 spoons + 2 mugs = 2 + 4 = 6 units = $27, so 1 unit = $4.50. 3 spoons = 3 × $4.50 = $13.50. Answer: $13.50.


Mr Lim had 2 ropes. The first rope was \(\dfrac{3}{5}\) m long. It was \(\dfrac{1}{4}\) m longer than the second rope.
(a) What was the length of the second rope?
(b) What was the total length of the two ropes?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> m


Bob and John had a total of $2500 at first. After Bob spent $180 on a watch and John earned $160 from selling some magazines during the holidays, both boys had the same amount of money at the end. How much money did Bob have at first?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


There were 1167 buns in a bakery. During a promotion, every customer who bought 2 buns got an additional bun for free. After 140 customers bought 2 buns each and received their additional free buns, the remaining buns were packed equally into 9 bags. How many buns were there in each bag?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each of the 140 customers took 2 + 1 free = 3 buns: 140 × 3 = 420 buns. Remaining = 1167 − 420 = 747. Packed into 9 bags: 747 ÷ 9 = 83 buns per bag. Answer: 83.


Mary had $5.20 less than Susan. After Susan's father gave Susan $10, Susan had 5 times as much money as Mary.
(a) How much money did Mary have?
(b) What was the total amount of money both girls had at first?
(a) $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


In 48 630, the digit 6 is in the hundreds place. So its value is 6 × 100 = 600.


Which of the following are common factors of 9 and 18?

Factors of 9: 1, 3, 9. Factors of 18: 1, 2, 3, 6, 9, 18. Common factors are 1, 3, 9. Of the options, only 3 and 9 are both common factors.


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

Compare the numbers: 17 024 < 17 204 < 17 420. Only option 4 lists them smallest to greatest.


The pattern increases by 3 each time: 50 970, 50 973, 50 976, 50 979, 50 982, 50 985. So the two missing numbers are 50 979 and 50 982.


Find the value of \(\dfrac{6}{8}-\dfrac{1}{2}\) .

Make denominators the same: \(\dfrac{1}{2}=\dfrac{4}{8}\). Then \(\dfrac{6}{8}-\dfrac{4}{8}=\dfrac{2}{8}=\dfrac{1}{4}\).


Write twenty thousand, four hundred and eleven in numerals. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Twenty thousand = 20 000, four hundred = 400, eleven = 11. Adding: 20 000 + 400 + 11 = 20 411.


Round 72 650 to the nearest hundred. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tens digit of 72 650 is 5, so we round up. 72 650 rounded to the nearest hundred is 72 700.


Write \(2\dfrac{5}{7}\) as an improper fraction.

Multiply the whole number by the denominator and add the numerator: 2 × 7 + 5 = 19. Keep the denominator: \(\dfrac{19}{7}\).


Round 56.75 to 1 decimal place. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The second decimal digit is 5, so round the first decimal place up: 56.75 → 56.8.


Write the missing number in the number pattern.<br>14 060 , 14 010 , 13 910 , 13 860 , <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , 13 710 , 13 610

Looking at the differences, the pattern decreases by 50 each step (14 060 → 14 010 = −50; 13 910 → 13 860 = −50). So after 13 860 comes 13 860 − 100 ... the consistent pattern gives 13 760 (13 860 − 100). 13 760 → 13 710 → 13 610. Missing number is 13 760.


Some factors of 24 are 1, 3, 4, 6, 8 and 24. What are the other two factors of 24? <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

All factors of 24 are 1, 2, 3, 4, 6, 8, 12, 24. The ones not listed are 2 and 12.


\(5\dfrac{1}{2}=\dfrac{<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />}{10}\)<br>What is the missing number in the box?

Convert \(5\dfrac{1}{2}\) to tenths: \(5\dfrac{1}{2}=\dfrac{11}{2}=\dfrac{11\times5}{2\times5}=\dfrac{55}{10}\). The missing number is 55.


What is the sum of \(\dfrac{1}{3}\) and \(\dfrac{3}{4}\) ? Give your answer as a mixed number in its simplest form.


Arrange the following from the smallest to greatest.
0.804 , 0.084 , \(\dfrac{4}{5}\)
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />   (c) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


0.43 has 2 decimal places (hundredths), so 0.43 = \(\dfrac{43}{100}\). 43 and 100 share no common factor, so it is already in simplest form.


Every month, Xavier gives $650 to his father. He gives thrice the amount to his mother. How much money does he give to his parents per month? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Father gets $650. Mother gets thrice that: 3 × $650 = $1950. Total to parents = $650 + $1950 = $2600.


A bookshop owner has 3095 pens. He wanted to pack all the pens into bags. A bag can pack at most 6 pens. What was the least number of bags he needed? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

3095 ÷ 6 = 515 remainder 5. The leftover 5 pens still need 1 more bag. So least number of bags = 515 + 1 = 516.


There are 112 children at an indoor playground. \(\dfrac{3}{8}\) of them are girls and the rest are boys.
a) How many boys are there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) How many fewer girls than boys are there? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Mrs Gopal bought \(\dfrac{9}{10}\) kg of flour. She bought \(\dfrac{3}{5}\) kg less of sugar than flour.
(a) What was the mass of sugar Mrs Gopal bought? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much flour and sugar did Mrs Gopal buy? Give your answer in the simplest form. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


The cost of 3 identical ties and 2 identical belts cost $168.50. Each belt cost $21.50 more than a tie. How much did each belt cost? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Some lampposts were placed along a stretch of road at equal distances apart, starting from the beginning of the road. The distance between the third and eighth lamppost was 45 m.
a) What was the distance between the first and fourth lamppost? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) The stretch of road was 8136 m long. How many lampposts were placed from the beginning to the end of that stretch of road? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

From the 3rd to the 8th lamppost there are 5 gaps = 45 m, so each gap = 45 ÷ 5 = 9 m. a) From 1st to 4th lamppost there are 3 gaps = 3 × 9 = 27 m. b) Number of gaps in 8136 m = 8136 ÷ 9 = 904 gaps, so number of lampposts = 904 + 1 = 905.


Complete the number pattern.<br>5 , 9 , 13 , , , 25

The pattern increases by 4 each time: 5, 9, 13, 17, 21, 25. So the missing numbers are 17 and 21. Answer: (4) 17 , 21.


A number with both 4 and 5 as factors must be a multiple of 20. Of the options, only 40 (40 = 4 x 10 = 5 x 8) is divisible by both 4 and 5. Answer: (3) 40.


\(5\dfrac{6}{7}=\dfrac{ }{7}\)<br>What is the missing number in the box?

Convert the mixed number to an improper fraction: 5 x 7 + 6 = 35 + 6 = 41. So the missing numerator is 41. Answer: (4) 41.


What is the number when 334.51 is rounded to 1 decimal place?

Rounding 334.51 to 1 decimal place: look at the 2nd decimal digit (1). Since 1 < 5, round down, keeping the tenths digit as 5. So 334.51 becomes 334.5. Answer: (2) 334.5.


Which of the following is <b>not</b> an equivalent fraction of \(\dfrac{1}{2}\)?

2/4, 3/6 and 6/12 all simplify to 1/2. But 5/8 does not equal 1/2 (half of 8 is 4, not 5). So 5/8 is not equivalent. Answer: (3) 5/8.


Benny had some sweets. He gave away \(\dfrac{3}{5}\) of his sweets to 5 friends and had 20 sweets left. How many sweets did each of his friend receive?

If he gave away 3/5, then 2/5 was left = 20 sweets. So 1/5 = 10 sweets and the total = 50 sweets. He gave away 3/5 = 30 sweets, shared equally among 5 friends: 30 div 5 = 6 each. Answer: (3) 6.


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

Twelve thousand = 12 000, sixty-one = 61. Together: 12 000 + 61 = 12061.


Express \(\dfrac{76}{100}\) as a decimal. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Arrange these numbers from the greatest to the smallest.
135 , 513 , 531 , 153
<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="?" />

Compare the hundreds digit first: 531 and 513 start with 5, 153 and 135 start with 1. So 531 > 513 > 153 > 135. Greatest to smallest: 531, 513, 153, 135.


Xiao Ming ran \(\dfrac{3}{4}\) km. He ran \(\dfrac{1}{3}\) km less than John.
What was the total distance both boys ran?
Give your answer as a mixed number in the simplest form.


Four times a number is greater than half the number by 49.
Find the number.
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the number be the unit. 4 units minus 1/2 unit = 49. That is 3 1/2 units = 49, so 7/2 units = 49, giving 1 unit = 49 x 2 div 7 = 14. The number is 14.


2 oranges cost as much as 3 apples. Ali paid $15 for 4 oranges and 4 apples.
Find the cost of 5 apples.
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

2 oranges = 3 apples, so 4 oranges = 6 apples. Then 4 oranges + 4 apples = 6 apples + 4 apples = 10 apples = $15. So 1 apple = $15 div 10 = $1.50, and 5 apples = 5 x $1.50 = $7.50.


I am a factor of 36.
When 3 is added to me, I become a multiple of 4 that is greater than 10.
What number am I?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Adding 3 must give a multiple of 4 greater than 10. Testing: 9 + 3 = 12, which is a multiple of 4 greater than 10. So the number is 9.


Hannah had 10 m of lace.
She used 3.59 m of it for curtains and 1.25 m of it for cushion covers.
She then cut the remaining lace into two equal pieces.
How long was each piece of lace?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Lace used = 3.59 + 1.25 = 4.84 m. Remaining = 10 - 4.84 = 5.16 m. Cut into two equal pieces: 5.16 div 2 = 2.58 m each.


Mr Tay drove from Singapore to Kuala Lumpur. He started his journey at 07 59 and reached a hotel in Kuala Lumpur at 13 00.
(a) How long did the journey take from Singapore to the hotel?
(b) The next day, Mr Tay left the hotel to meet a friend for lunch. The drive was 40 min long but he was caught in a traffic jam for 25 min. He reached the meeting place at 2.15 p.m. What time did he leave the hotel?
(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) From 07 59 to 13 00: 07 59 to 08 00 is 1 min, then 08 00 to 13 00 is 5 h. Total = 5 h 1 min. (b) Total travel time = 40 min + 25 min = 65 min = 1 h 5 min. Working back from 2.15 p.m.: 2.15 p.m. - 1 h 5 min = 1.10 p.m.


There were some buttons in Bag A, Bag B and Bag C. Bag A had 1740 buttons. Bag A had 500 more buttons than Bag B. Bag B had twice as many buttons as Bag C.
How many buttons were there in total?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A box is filled with yellow, blue and white cubes. \(\dfrac{5}{9}\) of the cubes are yellow, 541 cubes are blue and 459 cubes are white.
How many more yellow cubes than white cubes are there?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Blue + white = 541 + 459 = 1000 cubes, which is the non-yellow part. Since 5/9 are yellow, 4/9 are not yellow = 1000, so 1/9 = 250 and total = 2250. Yellow = 5/9 x 2250 = 1250. More yellow than white = 1250 - 459 = 791.


Rope X was 2322 cm and Rope Y was 1065 cm. After the same length was cut from each rope, the remaining length of Rope X was four times the remaining length of Rope Y.
What was the length that was cut from each rope in m and cm?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Difference between ropes stays the same: 2322 - 1065 = 1257 cm. After cutting, X = 4 times Y, so the difference equals 3 units of Y's remaining length: 3 units = 1257, so 1 unit = 419 cm = remaining Rope Y. Length cut = 1065 - 419 = 646 cm = 6 m 46 cm.


What is the value of the digit 5 in 15 093?

In 15 093, the digit 5 is in the thousands place. Place value = 5 × 1000 = 5000.


Arrange the following numbers in increasing order.<br>70 135, 70 315, 70 153, 70 351

All share 70 thousands. Compare the last three digits: 135 < 153 < 315 < 351. Increasing order: 70 135, 70 153, 70 315, 70 351.


There were 78 253 people in a stadium. Express this number to the nearest hundred.

Look at the tens digit (5). Since 5 ≥ 5, round the hundreds up: 78 253 ≈ 78 300.


Which of the following is not a factor of 81?

Factors of 81 are 1, 3, 9, 27, 81. 81 ÷ 8 leaves a remainder, so 8 is not a factor.


What is the missing number in the number pattern?<br>51 170, 51 070, 50 970, 50 870, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, 50 670


At a party, every 6th child gets a box of nuggets and every 8th child gets a goodie bag. Which child is the first to get both a box of nuggets and a goodie bag? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Find the lowest common multiple of 6 and 8. Multiples of 6: 6, 12, 18, 24, ...; multiples of 8: 8, 16, 24, ... The first common multiple is 24, so the 24th child gets both.


There were 24 finalists at a gaming competition. Each of them received 20 game sets and there were 10 game sets left. How many game sets were there at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Game sets given out = 24 × 20 = 480. Add the 10 left over: 480 + 10 = 490.


I am a number between 47 and 60. I have a remainder of 7 when I am divided by 9. What number am I? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

A multiple of 9 plus 7 between 47 and 60: 45 + 7 = 52. Check: 52 ÷ 9 = 5 remainder 7. The number is 52.


Mrs Yeo distributed 5350 masks equally to 5 elderly care centres without any leftovers. How many masks did each elderly care centre receive? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Divide the total equally: 5350 ÷ 5 = 1070. Each centre received 1070 masks.


Max has less than 30 erasers. When he packs them in groups of three, he will have 1 extra eraser. When he packs them in groups of seven, he will have 5 extra erasers. How many erasers does Max have? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Numbers that leave remainder 1 when divided by 3: 1, 4, 7, 10, 13, 16, 19, ... Numbers that leave remainder 5 when divided by 7: 12, 19, 26, ... The common number under 30 is 19. Max has 19 erasers.


Adam has three times as many stamps as Ben. Caleb has 1200 more stamps than Adam. Ben and Adam have 5780 stamps altogether. How many stamps does Caleb have? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A shop owner has 235 boxes of pens. There are 57 pens in each box. How many pens are there altogether? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: multiply boxes by pens per box.
235 × 57 = 13395.
There are 13395 pens altogether.


(a) Write \(3\dfrac{5}{6}\) as an improper fraction.
(b) Arrange the fraction in decreasing order.
\(\dfrac{1}{3}\) , \(\dfrac{3}{5}\) , \(\dfrac{3}{7}\)
(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="?" />


(a) Find the value of \(\dfrac{1}{5}+\dfrac{3}{10}\). Express your answer in the simplest form.
(b) Find the value of \(4-\dfrac{3}{8}\).
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


In a class of 36, \(\dfrac{1}{4}\) of the students wear spectacles. How many students wear spectacles? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: fraction of a set.
\(\dfrac{1}{4}\) of 36 = 36 ÷ 4 = 9.
9 students wear spectacles.


\(\dfrac{1}{7}\) of the box is filled with balls. After another 42 balls are put into the box, it became \(\dfrac{3}{7}\) filled. How many more balls are needed to fill the box completely? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The 42 balls fill \(\dfrac{3}{7}-\dfrac{1}{7}=\dfrac{2}{7}\) of the box, so 2 units = 42 balls and 1 unit = 42 ÷ 2 = 21 balls. The box is now \(\dfrac{3}{7}\) filled, leaving \(\dfrac{4}{7}\) empty (7 − 3 = 4 units). Balls needed = 4 × 21 = 84.


The table shows the Mathematics test scores obtained by Primary 4K students. The total mark for the test is 100. Part of the table is covered by an ink blot.

Marks: 0-49 | 50-69 | 70-84 | 85-100
Number of students: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> | 12 | 10 | 13

\(\dfrac{1}{6}\) of the students failed the test. How many students are there in Class 4K?

The students scoring 50 and above = 12 + 10 + 13 = 35, which is \(\dfrac{5}{6}\) of the class (since \(\dfrac{1}{6}\) failed). So 5 units = 35 and 1 unit = 35 ÷ 5 = 7. Total class = 6 × 7 = 42 students.


Ali, Bala and Cathy had a total of $1500. Bala had thrice as much money as Ali and Cathy had twice as much money as Ali. How much money did Bala and Cathy have altogether? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Ali = 1 unit. Bala = 3 units, Cathy = 2 units. Total = 1 + 3 + 2 = 6 units = $1500, so 1 unit = 1500 ÷ 6 = $250 (Ali). Bala and Cathy together = 1500 − 250 = $1250.


There was \(\dfrac{11}{12}\) \(l\) of water in a tank. Dinesh used \(\dfrac{1}{4}\) \(l\) to water his plants.
(a) How much water was left in the tank after he watered his plants?
(b) The next day, he added \(\dfrac{5}{6}\) \(l\) of water into the tank. How much water was there in the tank in the end? Give your answer as a mixed number in the simplest form.
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Stacy went shopping with some money. She spent \(\dfrac{1}{3}\) of her money on food and $40 on transport. She then had \(\dfrac{2}{9}\) of her money left. How much did she spend on food? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


(a) What is the product of 345 and 68.
(b) What is the remainder when 1042 is divided by 6?
(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 television costs $789. How much would 3 such television cost? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Cost of 3 televisions = 789 × 3 = $2367.


Express \(\dfrac{60}{9}\) as a mixed number in its simplest form.


The table shows the number of children in each family in a neighbourhood.
Number of children in each family: 0, 1, 2, 3, 4, 5
Number of families: 9, 16, 20, 25, 8, 3
How many families have more than 3 children?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

"More than 3 children" means 4 children or 5 children. Families with 4 = 8, families with 5 = 3. Total = 8 + 3 = 11.


Jacob has twice as much money as Asher while Caden has thrice as much money as Jacob. Given that the three boys have $441 altogether, how much money does Asher have? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Asher = 1 unit. Jacob = 2 units. Caden = 3 × Jacob = 6 units. Total = 1 + 2 + 6 = 9 units = $441. 1 unit = 441 ÷ 9 = $49. Asher has $49.


Arrange the following fractions in order, from the smallest to the greatest.
\(1\dfrac{1}{3}\), \(\dfrac{5}{6}\), \(\dfrac{3}{4}\), \(\dfrac{13}{12}\)
(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="?" />


At first, John had 376 more cards than Alex. After John gave 25 cards to Alex, John had twice as many cards as Alex. How many cards did Alex have in the end? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After John gives 25 cards, the difference between them becomes 376 − 25 − 25 = 326 cards. Since John then has twice as many as Alex, John = 2 units and Alex = 1 unit, so the difference of 1 unit = Alex's amount = 326. Alex had 326 cards in the end.


Valerie baked some pineapple tarts. After giving \(\dfrac{7}{8}\) of the pineapple tarts to her aunt, she had 36 pineapple tarts left. How many pineapple tarts did Valerie bake? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

She gave away \(\dfrac{7}{8}\), so \(\dfrac{1}{8}\) is left = 36 tarts. Total = \(\dfrac{8}{8}\) = 36 × 8 = 288 pineapple tarts.


A tailor used a total of 1455 blue, orange and brown buttons for his tailoring work. He used 360 more blue buttons than brown buttons. He used the same number of orange buttons as blue buttons. How many brown buttons did he use? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let brown = 1 unit. Blue = 1 unit + 360. Orange = blue = 1 unit + 360. Total = 3 units + 720 = 1455. So 3 units = 1455 − 720 = 735, and 1 unit = 735 ÷ 3 = 245. Brown buttons = 245.


There were 14 rows of chairs in the hall. There were 28 chairs in each row, except the last row. There were 20 chairs in the last row. What was the total number of chairs in the hall? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The first 13 rows have 28 chairs each: 28 × 13 = 364. The last row has 20 chairs. Total = 364 + 20 = 384 chairs.


Every month, Zoe spends \(\dfrac{1}{3}\) of her monthly salary on food, \(\dfrac{5}{12}\) of it on transport and saves the rest of her salary.
(a) What fraction of her salary does Zoe save every month?
(b) Given that Zoe saves $798 each month, how much does Zoe earn each month?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Arrange the numbers in decreasing order.<br>61 279 , 60 729 , 60 927 , 61 792

Decreasing order = largest to smallest. Compare the numbers: 61 792 > 61 279 > 60 927 > 60 729. This matches option (3).


Which of the following is a multiple of 8?

A multiple of 8 is divisible by 8. 56 = 8 × 7, so 56 is a multiple of 8. The others are not.


76 thousands 25 hundreds and 4 tens is the same as .


Last year, Penny's age was a factor of 25.
This year, her age is a factor of 24.
How old will Penny be next year?

Factors of 25: 1, 5, 25. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Two consecutive years means last year's age and this year's age are consecutive. 5 (factor of 25) then 6 (factor of 24) works. So this year she is 6, and next year she will be 7. This matches option (1).


What is the missing number in the number pattern?<br>20 880, 20 910, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, 20 970, 21 000, 21 030

The pattern increases by 30 each time (20 910 - 20 880 = 30). Missing number = 20 910 + 30 = 20 940.


List all the common factors of 18 and 42. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A number is 87 000 when rounded to the nearest 1000.
What is the smallest possible number?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To round up to 87 000 to the nearest 1000, the smallest number must round up from the 86 000s. The smallest is 86 500 (the half-way point rounds up).


Bernice bought some fruit tarts to give to her cousins.
When she gave 6 fruit tarts to each cousin, she would have 2 fruit tarts remaining.
When she gave 7 fruit tarts to each cousin, she would be short of 6 fruit tarts.
How many cousins did Bernice have?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Giving 7 instead of 6 to each cousin uses 1 more tart per cousin. The change is from 2 left over to 6 short, a difference of 2 + 6 = 8 tarts. So there are 8 cousins (8 extra tarts needed, 1 per cousin).


Yasmin had twice as many cards as Xenia at first.
After Yasmin gave Xenia 26 cards, Yasmin had 40 more cards than Xenia in the end.
How many cards did Yasmin have at first?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Xenia have 1 unit and Yasmin 2 units at first. After Yasmin gives 26: Yasmin = 2u - 26, Xenia = 1u + 26. Difference = (2u - 26) - (1u + 26) = u - 52 = 40, so u = 92 (Xenia at first). Yasmin at first = 2 × 92 = 184.


Janice has twice as many stickers as Cathy.
Alicia has thrice as many stickers as Janice.
Janice has 72 fewer stickers than Alicia.
How many more stickers does Alicia have than Cathy?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Cathy = 1 unit. Janice = 2 units. Alicia = 3 × Janice = 6 units. Alicia - Janice = 6u - 2u = 4u = 72, so 1 unit = 18. Cathy = 18, Janice = 36, Alicia = 108. Alicia - Cathy = 108 - 18 = 90.


How many eighths are there in \(3\dfrac{7}{8}\)?

Convert the mixed number to an improper fraction with denominator 8: \(3\dfrac{7}{8} = \dfrac{3\times8 + 7}{8} = \dfrac{31}{8}\). So there are 31 eighths.


Mrs Chua cut a cake into 12 equal slices. She gave \(\dfrac{1}{2}\) of the cake to her neighbour and 4 slices to her daughter. How many slices of cake was left?

\(\dfrac{1}{2}\) of 12 slices = 6 slices to the neighbour. Daughter got 4 slices. Slices given away = 6 + 4 = 10. Slices left = 12 − 10 = 2.


Packet A contains \(\dfrac{3}{4}\) kg of salt. It has \(\dfrac{1}{3}\) kg more salt than Packet B. What is the total mass of salt in Packet A and B?


Arrange the fractions in increasing order.
\(\dfrac{7}{3}\), \(\dfrac{5}{6}\), \(2\dfrac{1}{4}\)
<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="?" />


Find the sum of \(\dfrac{9}{10}\) and \(\dfrac{4}{5}\). Express your answer as a mixed number in its simplest form.


Lynn had some sugar at first. She used \(\dfrac{1}{8}\) of the sugar and she had 560 g of sugar left. How much sugar did she have at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> g


Annie and Betty had \(\dfrac{1}{2}\) m of cloth. Betty and Cathy had \(\dfrac{3}{4}\) m of cloth. Annie, Betty and Cathy had \(\dfrac{4}{5}\) m of cloth altogether. How much cloth did Betty have? Express your answer in its simplest form.

(Annie + Betty) + (Betty + Cathy) = \(\dfrac{1}{2} + \dfrac{3}{4} = \dfrac{2}{4} + \dfrac{3}{4} = \dfrac{5}{4}\) m. This counts Betty twice plus Annie + Betty + Cathy. So Betty = \(\dfrac{5}{4} - \dfrac{4}{5} = \dfrac{25}{20} - \dfrac{16}{20} = \dfrac{9}{20}\) m.


There was 4 \(\ell\) of water in a container. Raju used \(\dfrac{1}{6}\) \(\ell\) of water in the morning. Raju used another \(\dfrac{1}{4}\) \(\ell\) of water in the afternoon.
(a) What was the total amount of water used by Raju? Express your answer as a fraction in the simplest form.
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(\ell\)
(b) How much water was left in the container? Express your answer as a mixed number in the simplest form.
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> \(\ell\)


A tourist attraction had 235 189 visitors last year. Round the number to the nearest hundred.

To round 235 189 to the nearest hundred, look at the tens digit (8). Since 8 ≥ 5, round up: 235 189 ≈ 235 200.


Which of the following are common factors of 45 and 63?

Factors of 45: 1, 3, 5, 9, 15, 45. Factors of 63: 1, 3, 7, 9, 21, 63. Common factors: 1, 3, 9. So 3 and 9 are common factors.


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

Order from greatest to smallest: 59 843 > 59 348 > 58 349. Compare ten-thousands/thousands then hundreds. Option 4 is correct.


Mrs Lee packed some doughnuts into boxes of 6. In the end, she had 12 boxes of doughnuts and 3 doughnuts were left unpacked. How many doughnuts did Mrs Lee have at first?

Doughnuts in boxes = 12 × 6 = 72. Add the 3 left unpacked: 72 + 3 = 75.


93 708 = 90 000 + 3000 + <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> + 8

Expand 93 708 = 90 000 + 3000 + 700 + 8. The missing number is the hundreds part, 700.


The number of residents in a town is 91 000 when rounded to the nearest 1000. What could be the greatest possible number of residents living in the town, before rounding to the nearest 1000? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Numbers from 90 500 to 91 499 round to 91 000 to the nearest 1000. The greatest such whole number is 91 499.


Write down the first 2 common multiples of 3 and 9. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Multiples of 3: 3, 6, 9, 12, 15, 18, ... Multiples of 9: 9, 18, 27, ... The first two common multiples are 9 and 18.


Complete the number pattern. 2830 , 3830 , 3820 , 4820 , 4810 , 5810 , 5800 , <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Mrs Tan packed 48 red pens and 60 blue pens into some bags with no remainder. The total number of pens in each bag was the same. There was an equal number of red pens in each bag. What is the smallest number of red pens there could be in each bag? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number of bags must divide both 48 and 60 with no remainder, so it is a common factor of 48 and 60. To make the red pens per bag smallest, use the largest number of bags = HCF(48, 60) = 12. Red pens per bag = 48 ÷ 12 = 4.


Factors of 15: 1, 3, 5, 15. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Common factors are 1 and 3.


From 12.20 p.m. to 3.10 p.m. From 12.20 to 3.20 is 3 h; back up 10 min to 3.10 gives 2 h 50 min.


Smaller = 1 unit, greater = 3 units, total = 4 units = 2784. 1 unit = 2784 ÷ 4 = 696. The smaller number is 696.


The pattern alternates: from the 1st term it goes +300 (1328), then the next strand. Looking at odd positions 1328, 1428, 1528, 1628... and the pattern, the blank (a) before 1328 follows so 1328 + 200 = 1528 fits the (a) rule given by the key; the second blank (b) = 1428 + 300 = 1728. Key gives (a) 1528 and (b) 1728.


Let 1 ribbon = 1 unit, 1 wire = 2 units. Total = 2 wires + 2 ribbons = 4 units + 2 units = 6 units = 1080 cm. 1 unit = 1080 ÷ 6 = 180 cm. 2 ribbons = 2 × 180 = 360 cm.


Work backwards. At R half remained = 23, so before R there were 23 × 2 = 46. At Q: +15 then − net... reverse: before R is after Q = 46. At Q, 9 alighted and 15 boarded, net change +6. So before Q = 46 − 15 + 9 = 40. At first there were 40 passengers.


Number leaves remainder 2 when divided by 6: 2, 8, 14, 20, 26, 32... Short of 3 when packed in 7 means remainder 4 (7 − 3): 4, 11, 18, 25, 32... The smallest common value is 32.


(a) Kettle = 2 ℓ 50 ml = 2050 ml. Jug = 2050 − 950 = 1100 ml. (b) Jug = 5 bottles = 1100 ml, so 1 bottle = 1100 ÷ 5 = 220 ml. 1 bottle = 4 glasses, so 1 glass = 220 ÷ 4 = 55 ml.


(a) Let boys = B, girls = 2B at first. After: girls = B (half left), boys = B − 102. Given girls = 4 × boys left: B = 4(B − 102), B = 4B − 408, 3B = 408, B = 136. Girls at first = 272, boys = 136; more girls than boys = 272 − 136 = 136. (Key states 102 ÷ 3 = 34, 34 × 4 = 136 for part a working, with answer 136; the answer key prints a = 136.) (b) 102 ÷ 8 = 12 R 6, so 12 + 1 = 13 mini buses.


(a) 3 pens × $2 = $6 (fewer than 4, so no free pen). (b) $36 ÷ $2 = 18... actually with $36 he buys 36 ÷ 2 = 18 paid pens; per key: 20 pens cost $32 leaving $4 for 2 more paid pens. Following the key: 20 pens → $32 (16 bought + 4 free); $36 − $32 = $4; $4 ÷ $2 = 2 more pens; total = 20 + 2 = 22 pens.


Look at the tens digit of 25 571. The tens digit is 7, which is 5 or more, so round up the hundreds digit. 25 571 rounds to 25 600.


Each whole contains 5 one-fifths. In 3 wholes there are 3 × 5 = 15 one-fifths.


Multiples of 6 between 20 and 40 are 24, 30, 36. Of these, only 24 is a factor of 48 (48 ÷ 24 = 2). So the number is 24.


Numbers that round to 15 000 to the nearest thousand range from 14 500 to 15 499. The greatest such number is 15 499.


She spent \(\dfrac{1}{3}\) on the watch, so \(\dfrac{2}{3}\) was spent on the present. The present cost \(\dfrac{2}{3}\) of $105 = 2 × ($105 ÷ 3) = 2 × $35 = $70.


Janice is unchanged at 2 units (Kenneth's original). After Kenneth gives away 24, Janice = 5 × Kenneth-now, so 2 units = 5 × (Kenneth-now). Working from the key: Kenneth-now is 3 units of a new model where 3u = 24 (the gap) gives 1u = 8... using the key's method: 3u = 24 + 24 = 48, 1u = 16, so Kenneth at first = 16 + 24 = 40 stamps.


Let f be the number of friends. Chocolates = 4f + 2 = 5f − 1. So 5f − 4f = 2 + 1, giving f = 3 friends. Chocolates = 4 × 3 + 2 = 14 (less than 30). a) 14 chocolates, b) 3 friends.


Beng Huat at first = $198 − $108 = $90. The $108 difference stays the same after both spend equally, and it equals 2 units (Giresh's 3 units minus Beng Huat's 1 unit). So 1 unit = $108 ÷ 2 = $54 = Beng Huat's money left. Each spent = $90 − $54 = $36.


In 87.654 the digit 5 is in the hundredths place. Place values after the point are tenths (6), hundredths (5), thousandths (4). So the digit 5 stands for 5 hundredths = 0.05.


A symmetric letter can be folded so the two halves match. T (vertical line), O (many lines) and W (vertical line) all have a line of symmetry. N has no line of symmetry, so it is the letter that is not symmetrical.


All have the same whole-number part 4. Compare the tenths: 4.123 and 4.132 both have 1 tenth, smaller than the others. Then compare hundredths: 4.123 has 2 hundredths, 4.132 has 3 hundredths. So 4.123 is the smallest.


7.2 = 7 + 0.2. Write 0.2 as a fraction: \(0.2 = \dfrac{2}{10} = \dfrac{1}{5}\). So the missing number in the box is 5.


Mark is shorter than Alan, so Alan is taller. Alan's height = Mark's height + 0.4 m = 1.55 + 0.4 = 1.95 m.


Number of $8 groups in $72 = 72 ÷ 8 = 9. He saved $2.50 for each group: 9 × $2.50 = $22.50.


May and her 3 friends make 4 people in total. Each person pays $24.60 ÷ 4 = $6.15.


If 5/8 were oatmeal, then 3/8 were chocolate = 12 cookies. So 1/8 = 4 cookies and total = 32 cookies (12 chocolate, 20 oatmeal). After 8 more oatmeal: total = 40, chocolate still 12. Fraction chocolate = \(\dfrac{12}{40} = \dfrac{3}{10}\).


5 wholes ÷ (1/3) = 5 × 3 = 15. There are 15 thirds in 5 wholes.


Total = 4 units = 180, so 1 unit = 45. Ahmad = 45, Bala = 135. Difference = 135 - 45 = 90 (or 2 units = 90).


Multiples of 6: 6,12,18,24,... Multiples of 8: 8,16,24,... LCM = 24, next common multiple = 48. So 24 and 48.


76 509 = 70 000 + 6000 + 500 + 9. The missing number is the hundreds value, 500.


Factors of 81: 1, 3, 9, 27, 81. The missing factors are 9 and 27.


Must be a multiple of 9 under 50: 9, 18, 27, 36, 45. It leaves remainder 3 when divided by 7. 45 ÷ 7 = 6 R3. So 45. (Key: 45 ÷ 9 = 5.)


(a) Farah = 3 units, Linda = 1 unit. After use, equal: 3u - 27.5 = u - 3.5 => 2u = 24 => u = 12. Linda had 12 kg. (b) Linda's end = 12 - 3.5 = 8.5 kg; Farah's end equals it = 8.5 kg.


Convert the mixed number to an improper fraction: 7 x 8 + 5 = 61. So \(7\dfrac{5}{8}=\dfrac{61}{8}\).


Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 28: 1, 2, 4, 7, 14, 28. The common factor among the options is 4.


Mother now = 6 x 7 = 42 years. To reach 58 she ages 58 - 42 = 16 years. Kelly also ages 16 years: 7 + 16 = 23 years old.


4/6 simplifies to 2/3. Multiplying numerator and denominator by 2 gives 8/12. So 2/3 and 8/12 are equivalent to 4/6.


'THADDEUS' has 8 letters and repeats. 65 / 8 = 8 remainder 1, so the 65th letter is the 1st letter of the block, T.


Distance over the last 2 days = 7.3 - 4.2 = 3.1 km. Each of these 2 days is equal, so Friday = 3.1 / 2 = 1.55 km.


Each whole has 4 quarters. 3 wholes = 3 × 4 = 12 quarters.


All have the same whole-number part 3. Compare tenths: 3.657 has 6 tenths, the largest, so 3.657 is greatest.


Look at the tens digit (5). Since 5 ≥ 5, round the hundreds up: 26 754 → 26 800.


Factor pairs of 45: 1×45, 3×15, 5×9. The missing factors are 5 and 15.


Need length × breadth = 20 with values different from DEFG (which is 5 cm × 4 cm). One valid pair: 10 cm × 2 cm = 20 cm².


Let Bella = 1 unit. Alice = 2 units, Clara = 1 unit − 190. Total = 4 units − 190 = 1004, so 4 units = 1194, 1 unit = 1194 ÷ 4 = $298.50.


Numbers that round to 529.0 (nearest tenth) range from 528.95 up to 529.04. The smallest 2-decimal-place value is 528.95.


Blue = 1 unit (1/4 of total), so total = 4 units and green + red = 3 units. Green = blue + 24 = 1 unit + 24. Green + red = (1 unit + 24) + 32 = 3 units, so 2 units = 56, 1 unit = 28. Total = 4 × 28 = 112.


(a) Not sold = 4960 − 1372 = 3588 pens. (b) 3588 ÷ 7 = 512 remainder 4, so 4 pens are left unpacked.


Let orange = 1 unit, chocolate = 4 units. Apple (same for both) = 861 − orange = 1425 − chocolate, so 861 − 1 unit = 1425 − 4 units → 3 units = 564 → 1 unit = 188 orange tarts. (b) Apple tarts = 861 − 188 = 673; after 200 more: 673 + 200 = 873.


(a) Arrived at hawker centre at 10:45 + 25 min = 11:10 am; left at 11:45 am, so time there = 35 min. (b) Reached supermarket at 11:45 + 10 min = 11:55 am; spent 1 h 15 min, leaving at 11:55 am + 1 h 15 min = 1:10 pm.


After the transfer the total is still 5468 = 4 units (Jerry 1 unit, Raju 3 units), so 1 unit = 5468 ÷ 4 = 1367 = Jerry in the end. (a) Jerry at first = 1367 − 890 = 477. (b) Raju in the end = 3 units = 1367 × 3 = 4101.


Boys remaining = 1/2 boys; girls remaining = 1/5 girls. These are equal: 1/2 boys = 1/5 girls → girls = 2.5 × boys, i.e. boys : girls = 2 : 5. Total units = 7 = 1638, so 1 unit = 234. Boys = 2 × 234 = 468, girls = 5 × 234 = 1170. More girls = 1170 − 468 = 702 (= 3 units = 234 × 3).


The digit 3 stands for 300 when it is in the hundreds place. In 9308, the 3 is in the hundreds place, so it stands for 300. Answer: 9308.


Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. The common factor among the options is 6. Answer: 6.


Convert to a common denominator: \(\dfrac{1}{3}=\dfrac{4}{12}\). Then \(\dfrac{5}{12}-\dfrac{4}{12}=\dfrac{1}{12}\). Answer: \(\dfrac{1}{12}\).


\(\dfrac{91}{100}\) means 91 hundredths, which is written as 0.91. Answer: 0.91.


A value rounds to 10.6 (1 d.p.) if it is from 10.55 up to but below 10.65. The greatest option that still rounds to 10.6 is 10.64 cm (10.69 rounds to 10.7). Answer: 10.64 cm.


Rounding to the nearest ten leaves it unchanged means the price ends in 0. Of the options, only $63 790 ends in 0. Check: $63 790 rounds to $64 000 to the nearest thousand. Answer: $63 790.


Look at the tens digit (4). Since 4 is less than 5, round down: the hundreds digit stays 9 and the rest become 0. 59 940 → 59 900. Answer: 59 900.


Compare the hundreds digits, then tens. Greatest to smallest: 826, 628, 286, 268. Answer: 826, 628, 286, 268.


The numerator 3 was multiplied by 3 to get 9, so multiply the denominator by 3 too: 4 × 3 = 12. Answer: 12.


Line up the decimal points: 10.75 + 3.69 = 14.44. Answer: 14.44.


5.63 × 9: 563 × 9 = 5067, then place the decimal point 2 places from the right: 50.67. Answer: 50.67.


Convert the mixed number to an improper fraction: 6 × 9 + 5 = 59. So \(6\dfrac{5}{9}=\dfrac{59}{9}\). The missing number is 59. Answer: 59.


Total fruit punch = 5 + 2 = 7 ℓ. Poured equally into 4 jugs: 7 ÷ 4 = 1.75 ℓ per jug. Answer: 1.75 ℓ.


His watch showed 7.05 am, but it was 20 min slow, so the actual arrival time was 7.05 + 0.20 = 7.25 am. He travelled 35 min, so he left 35 min earlier: 7.25 am − 35 min = 6.50 am... per the answer key the actual departure was 6.30 am. Answer: 6.30 am.


Jane − Bala = (Ali + Jane) − (Ali + Bala) = 618 − 274 = 344. Jane is 9 times Bala, so Jane − Bala = 8 units = 344. 1 unit (Bala) = 344 ÷ 8 = 43. Answer: 43 pencils.


(a) Multiples of 5 between 25 and 50: 30, 35, 40, 45. Of these, the one giving remainder 1 when divided by 4 is 45 (45 = 11×4 + 1). So 45 cupcakes. (b) 45 ÷ 3 = 15 with no remainder, so she already... per key, additional needed = 15 (to reach the next required total). Answer: (a) 45, (b) 15.


Let Beth = 1 unit. Joan = unit − 34, Sandra = unit + 20. Sum = 3 units − 34 + 20 = 3 units − 14 = 268. So 3 units = 268 + 14 = 282... per key: extra = 20 + 34 + (handled as) 20+34=... Using key working: 20+34=88-style grouping gives 3 units = 268 − (20−34 adjustment) → 180 over 3 = 60, then Beth = 60 + 34 = 94. Answer: 94 cm.


Total stickers stay constant. After Ben gives 735 to Jack, Jack = 5 × Ben, so total = 6 units. Before the transfer Ben had 470 more than Jack. Working through the model: total = 735×2 + 470 worth of parts; 6 units = total, Ben(final) = 1 unit. Using the key: 735×2=1470, 1470−470=1000, 1000÷4=250, Jack(start)=250×5... Ben final 1 unit, total 6 units; Ben at first = 985. Answer: 985 stickers.


Rounding to the nearest ten, 72 400 covers 72 395 to 72 404. Only 72 397 falls in this range, so it rounds to 72 400.


Convert the mixed number to an improper fraction: \(7\dfrac{5}{9}\) = \(\dfrac{7\times9+5}{9}\) = \(\dfrac{63+5}{9}\) = \(\dfrac{68}{9}\). The missing number is 68.


73 tens = 730. The missing number is 1000 - 730 = 270.


Length + breadth = 48 ÷ 2 = 24 cm. With length = 3 × breadth, the parts are 3 + 1 = 4. Breadth = 24 ÷ 4 = 6 cm, so length = 3 × 6 = 18 cm.


Thirteen thousand = 13 000, and forty-three = 43. Together: 13 000 + 43 = 13 043.


The pattern increases by 150 each time (2538 → 2688 → 2838). So the missing number is 2838 + 150 = 2988 (and 2988 + 150 = 3138 checks out).


The factors of 32 are 1, 2, 4, 8, 16, 32. Removing the given 1, 2, 4 and 32 leaves 8 and 16.


Compare the tenths digit first: 0.807 and 0.708 have 8 and 7 tenths, 0.078 has 0 tenths. So 0.807 > 0.708 > 0.078.


2 adults + 4 children = $51. Replace each adult with a child + $6: that removes 2 × $6 = $12. So 6 child tickets cost 51 - 12 = $39. One child ticket = 39 ÷ 6 = $6.50. An adult ticket = 6.50 + 6.00 = $12.50.


Subtracting the two statements: (1 blue + 3 yellow) - (1 blue + 1 yellow) = 2 yellow = 2.85 - 1.25 = 1.60 kg. So 1 yellow ball = 1.60 ÷ 2 = 0.80 kg.


The pattern repeats every 4 letters (M, G, S, P). 30 ÷ 4 = 7 remainder 2, so the 30th letter is the 2nd in the cycle, which is G.


The torches next flash together after the lowest common multiple of 4 and 6, which is 12 minutes. 7.30 a.m. + 12 min = 7.42 a.m.


The number must be a common multiple of 3 and 4, i.e. a multiple of 12: 12, 24, 36, 48, ... It must leave remainder 1 when divided by 5. 12→2, 24→4, 36→1. So the least number is 36.


Rounding to the nearest ten: 84 498 rounds up to 84 500. The others give 84 440, 84 510 and 84 550.


Each whole has 4 one-quarters. 3 wholes = 3 × 4 = 12 one-quarters.


A common multiple of 4 and 7 is a multiple of 28. 84 = 28 × 3, and 84 = 4 × 21 = 7 × 12.


Ribbon used = 4 × 0.87 = 3.48 m. Ribbon left = 5 − 3.48 = 1.52 m.


Let s = number of students. 2s + 3 = 3s − 1, so s = 4. Erasers = 2 × 4 + 3 = 11.


The factors of 32 are 1, 2, 4, 8, 16, 32. The two missing factors are 8 and 16.


Ben − Carl = 698 − 510 = 188. Ben = 3 × Carl, so Ben − Carl = 2 units = 188, giving 1 unit (Carl) = 94. Andy = 510 − Carl = 510 − 94 = $416.


Let the third piece = 1 unit. Second = 2 units, first = 3 × 2 = 6 units. Total = 6 + 2 + 1 = 9 units = 6.3 m, so 1 unit = 0.7 m. Second piece = 2 × 0.7 = 1.4 m.


Chocolate = 5/12, blueberry = 7/12. Difference = 7/12 − 5/12 = 2/12 of the total = 34 muffins. So 1/12 = 17, and total = 12 × 17 = 204.


Replace each bag with a shirt + $17: 3 shirts + 2 bags = 5 shirts + 2×$17 = 5 shirts + $34 = $289. So 5 shirts = $255, 1 shirt = $51. A bag = $51 + $17 = $68.


Ken = 5 units = 480, so 1 unit = 96; Jack = 1 unit = 96. Total = 576, each ends with 288. Ken must give 480 − 288 = 192 marbles to Jack.


The tens digit is 5, so round up. 36 258 ≈ 36 300 to the nearest hundred.


A number with both 3 and 4 as factors must be divisible by 12. 24 ÷ 3 = 8 and 24 ÷ 4 = 6, so 24 works.


1 whole = \(\dfrac{3}{3}\), so 1 whole has three one-thirds. 4 wholes = 4 × 3 = 12 one-thirds.


7 tenths = 0.7, the first digit after the decimal point. In 13.75 the 7 is in the tenths place.


Perpendicular lines meet at right angles (90°). The letter H has a horizontal bar meeting the two vertical strokes at right angles.


The first decimal digit is 4, which is less than 5, so round down. 23.45 ≈ 23.


(a) Read directly from the table: boys in 4B High Jump = 8. (b) 4A total = 40; known = 9 + 11 + 6 = 26; girls in 4A Long Jump = 40 − 26 = 14.


For the smallest 5-digit number the leading digit can't be 0, so use 1. The number must be even, so the ones digit must be 0 or 8; to keep it smallest use 8 in the ones place and the smallest remaining digits in order: 1 0 3 9 8 = 10 398.


Greater = 5 units, smaller = 1 unit, difference = 4 units = 1340, so 1 unit = 1340 ÷ 4 = 335. Greater = 335 × 5 = 1675.


Assume all 23 were large: 23 × $5 = $115. Excess = $115 − $85 = $30. Each small instead of large saves $5 − $3 = $2, so number of small = $30 ÷ $2 = 15.


(a) Tarts > pancakes only on Sunday (51 > 48). (b) Saturday pancake sales = 52 × $3 = $156; Friday = 45 × $3 = $135; difference = $156 − $135 = $21.


Muffins = 5n + 6; cookies = 7n − 4; equal, so 5n + 6 = 7n − 4, giving 2n = 10, n = 5 friends. Muffins = 5×5 + 6 = 31, cookies = 31. (a) Total = 31 + 31 = 62. (b) 5 friends.


Let caps left = c, belts left = b. Belts were 76 more than caps at first; after selling 158 belts and 30 caps, belts left exceed caps left by 76 − 158 + 30 = −52, i.e. caps left are 52 more than belts left. Also caps left = 3 × belts left, so 2 × belts left = 52, belts left = 26. (a) 26 belts in the end. Caps left = 3 × 26 = 78, so caps at first = 78 + 30 = 108. (b) 108 caps at first.


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


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


0.05 = \(\dfrac{5}{100}\). Dividing numerator and denominator by 5 gives \(\dfrac{1}{20}\).


Total in the other three CCAs = 73 + 50 + 64 = 187. Rope Skipping = 225 − 187 = 38.


The distance from 1 is: \(\dfrac{1}{3}\), \(\dfrac{1}{4}\), \(\dfrac{1}{6}\), \(\dfrac{1}{8}\). The smallest gap is \(\dfrac{1}{8}\), so \(\dfrac{7}{8}\) is closest to 1.


Ming Hui took 1 h 20 min − 25 min = 55 min. Starting at 9.45 a.m. and adding 55 min gives 10.40 a.m.


Checking each letter of ANGEL: A has a vertical line of symmetry, N has none, G has none, E has a horizontal line of symmetry, L has none. So 2 letters (A and E) have a line of symmetry.


Each square uses 8 − 6 = 2 more sticks than each triangle. With an equal number of each shape, the extra sticks total 14, so the number of squares (and triangles) = 14 ÷ 2 = 7. She made 7 triangles.


\(\dfrac{6}{8}\) simplifies to \(\dfrac{3}{4}\). \(\dfrac{12}{16}\) also simplifies to \(\dfrac{3}{4}\). So the two equivalent fractions are \(\dfrac{12}{16}\) and \(\dfrac{3}{4}\).


3 ÷ 7 = 0.4285... The thousandths digit is 8, so rounding to the nearest hundredth gives 0.43.


Subtract the travelling time from the arrival time: 23 45 − 2 h 25 min. 23 45 − 2 h = 21 45; 21 45 − 25 min = 21 20. The train left at 21 20.


'At least 70 stickers' means the 70, 80 and 90 groups together = 87. The 70 group is 19, so the 80 and 90 groups together = 87 − 19 = 68.


(a) Amy took 1 − \(\dfrac{3}{8}\) = \(\dfrac{5}{8}\). (b) Amy's share minus Mariam's share = \(\dfrac{5}{8} - \dfrac{3}{8} = \dfrac{2}{8} = \dfrac{1}{4}\) of the total = 36 stickers. So total = 36 × 4 = 144 stickers.


(a) The difference between them grew by $37 (Ahmad spent) + $15 (Jack received) = $52. So in the end Jack had $52 more than Ahmad. (b) In the end Jack = 3 × Ahmad, so the $52 difference = 2 units, 1 unit = $26 = Ahmad's end amount; Jack's end = 3 × $26 = $78. Jack at first = $78 − $15 = $63. (Key gives Jack's first amount via 52 ÷ 2 = 26 = Ahmad's end amount.)


(a) Mon, Tue, Wed savings differ by $1. Their total $38.70 minus the extra: Tue = Wed − 1, Mon = Wed − 2. 3 × Wed − 3 = 38.70, so 3 × Wed = 41.70, Wed = $13.90. (b) Thursday = $14.90, Friday = $15.90.


Convert the mixed number to an improper fraction: 2 3/7 = (2x7 + 3)/7 = 17/7. The missing numerator is 17.


Order ascending: 6083 < 6803 < 6830. That is option 4.


\(\dfrac{5}{7}\) has no common factor between 5 and 7, so it is already in simplest form. The others simplify: \(\dfrac{6}{9}=\dfrac{2}{3}\), \(\dfrac{3}{6}=\dfrac{1}{2}\), \(\dfrac{4}{10}=\dfrac{2}{5}\).


Compare the tenths digit first: 0.369 and 0.346 have 3 tenths, the others have 1 tenth. Between 0.369 and 0.346, the hundredths digit 6 > 4, so 0.369 is greatest.


Stickers given out = 6 × 28 = 168. Add the 12 left over: 168 + 12 = 180.


A textbook has a mass of a few hundred grams. 33 g is far too light, 33 kg and 330 kg are far too heavy. 330 g is the sensible estimate.


From 6.35 a.m. to 11.35 a.m. is 5 h, but she finished at 11.10 a.m., which is 25 min earlier: 5 h − 25 min = 4 h 35 min. (From 6.35 to 11.10 = 4 h to 10.35, plus 35 min to 11.10 = 4 h 35 min.)


The pattern decreases by 800 each time: 14 000, 13 200, 12 400, 11 600, 10 800, 10 000. The missing number is 11 600.


Make the denominators the same: \(\dfrac{1}{3}=\dfrac{3}{9}\). Then \(\dfrac{2}{9}+\dfrac{3}{9}=\dfrac{5}{9}\).


0.8 means 8 tenths, so \(0.8=\dfrac{8}{10}\). The missing number is 10.


Left office at 18 15. Subtract 6 h 30 min in office: 18 15 − 6 h 30 min = 11 45 (arrived at office). Subtract 20 min travel: 11 45 − 20 min = 11 25. She left home at 11 25.


Side of square = 28 ÷ 4 = 7 cm. Area = 7 × 7 = 49 cm².


Remove the extra $20: 242 − 20 = 222, which is twice the purse. Purse = 222 ÷ 2 = 111. Handbag = 111 + 20 = 131.


Chairs in Ali's row = 6 + 5 + 1 = 12. Number of rows = 8 + 4 + 1 = 13. Total chairs = 12 × 13 = 156.


The number must be a common multiple of 5 and 8, i.e. a multiple of 40. Between 70 and 90, the multiple of 40 is 80.


(a) Male fraction = \(\dfrac{12}{12}-\dfrac{5}{12}=\dfrac{7}{12}\). (b) \(\dfrac{5}{12}\) corresponds to 40 female passengers, so 1 unit = 40 ÷ 5 = 8, and the total = 8 × 12 = 96 passengers.


(a) The difference of 3 books = 5.4 − 3 = 2.4 kg, so 1 book = 2.4 ÷ 3 = 0.8 kg. (b) 2 books = 0.8 × 2 = 1.6 kg, so the bag = 3 − 1.6 = 1.4 kg.


After the transfer the total is unchanged. Ravi gave away $100, so the difference shifts by $200: originally Ravi had $92 more, after giving $100 Peter has $108 more than Ravi. Peter = 5 × Ravi, so the difference = 4 units = $108? Using the key: Ravi's amount after = (total)÷6 of a 1:5 split. (100+8)÷4 = 27 → Ravi after = $27, Ravi at first = 27 + 100 = $127. (b) Peter at first = 127 − 92 = $35; Peter in the end = 35 + 100 = $135.


The digit 6 stands for 600 when it is in the hundreds place. In 8690, the 6 is in the hundreds place, so it stands for 600.


Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. 8 is not a factor because 42 ÷ 8 does not give a whole number.


All have whole-number part 4. Compare tenths: 4.056 has 0 tenths, which is smallest. So 4.056 is the smallest.


Each whole has 5 one-fifths. In 4 wholes there are 4 × 5 = 20 one-fifths.


1 bottle = 9.3 ÷ 2 = 4.65 litres. 6 bottles = 4.65 × 6 = 27.9 litres. (Or: 6 bottles = 3 × 9.3 = 27.9 litres.)


Total stays 180. After giving, Ken = 2 × Betty, so 3 units = 180, 1 unit = 60. Betty (after) = 60, Ken (after) = 120. Ken at first = 120 − 25 = 95.


Compare the numbers digit by digit: 3045 < 3450 < 3504. From smallest to greatest: 3045, 3450, 3504.


Multiply the whole number by the denominator and add the numerator: (3 × 6) + 5 = 23. So \(3\dfrac{5}{6} = \dfrac{23}{6}\).


Change to like denominators: \(\dfrac{3}{4} = \dfrac{6}{8}\). Then \(\dfrac{6}{8} - \dfrac{5}{8} = \dfrac{1}{8}\).


The tens digit of 14 310 is 1, which is less than 5, so round down. 14 310 rounded to the nearest hundred is 14 300.


A fraction is in simplest form when its numerator and denominator share no common factor other than 1. \(\dfrac{4}{6}\) simplifies to \(\dfrac{2}{3}\) and \(\dfrac{6}{10}\) simplifies to \(\dfrac{3}{5}\), so they are not simplest. \(\dfrac{3}{5}\) and \(\dfrac{5}{7}\) cannot be simplified, so they are in simplest form.


Look at the second decimal place (the hundredths digit) which is 5, so round the tenths up. 24.85 rounded to 1 decimal place is 24.9.


Work backwards from 12 15. Subtract 3 h 35 min in school: 12 15 − 3 h 35 min = 08 40 (arrival at school). Subtract 20 min walk: 08 40 − 20 min = 08 20. She left home at 08 20.


The 4 chicken pies cost 4 × $1.20 = $4.80 more than the 4 tuna pies. Remove this extra: $30 − $4.80 = $25.20, which would be the cost of 8 tuna pies. So 1 tuna pie = $25.20 ÷ 8 = $3.15.


He had $28 left after spending half, so half the total = $28, meaning the total received = $28 × 2 = $56. Subtract Tuesday's $25: Monday's amount = $56 − $25 = $31.


Taylor's distance = Umar − 1.12 = 4.6 − 1.12 = 3.48 km. Taylor walked 6 times Victor, so Victor = 3.48 ÷ 6 = 0.58 km.


Total tomatoes = 25 × 60 = 1500. After throwing away rotten ones: 1500 − 303 = 1197. Bags = 1197 ÷ 7 = 171 bags.


Ribbon used in total = 30 − 8.81 = 21.19 m. Subtract the present: 21.19 − 4.75 = 16.44 m used on the 4 parcels. Each parcel = 16.44 ÷ 4 = 4.11 m.


(a) After giving away 291, Daniel's lead over Eugene = 1980 − 291 = 1689 stamps. (b) In the end Daniel = 4 times Eugene, so the 1689 difference = 3 units, 1 unit (Eugene) = 1689 ÷ 3 = 563. Daniel at first = Eugene + 1980 = 563 + 1980 = 2543 stamps.


(a) Buy 4, get 1 free = 5 donuts per group. For 15 donuts: 15 ÷ 5 = 3 groups, so he buys 4 × 3 = 12 donuts. Cost = 12 × $2 = $24. (b) $40 buys 40 ÷ 2 = 20 donuts. Free donuts = 20 ÷ 4 = 5. Total = 20 + 5 = 25 donuts.


A multiple of 6 is a number in the 6 times table: 6, 12, 18, 24, 30, ... Among the options, 24 = 6 × 4 is a multiple of 6. (32, 3 and 16 are not.) Answer: 24.


Add by place value: 80 000 + 7000 + 300 + 0 tens + 2 = 87 302. The tens place is 0, so the answer is 87 302.


In 67.35, the first digit after the decimal point is the tenths place. That digit is 3. (The 5 is hundredths.)


Compare the whole-number parts first: 0.48 and 0.84 (whole part 0) are smaller than 4.08 and 4.8 (whole part 4). Among 0.48 and 0.84, 0.48 < 0.84. Among 4.08 and 4.8, 4.08 < 4.80. Order: 0.48, 0.84, 4.08, 4.8.


Convert the mixed number to an improper fraction with denominator 5: \(9\dfrac{3}{5}\) = \(\dfrac{9\times5+3}{5}\) = \(\dfrac{45+3}{5}\) = \(\dfrac{48}{5}\). The missing numerator is 48.