At first, Dan had the same amount of money as Evan. After Dan spent $480, Evan had three times as much money as Dan.
a) How much did Dan have in the end?
$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
b) How much did Dan have at first?
$<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Let Dan's amount at the end be 1 unit; then Evan (unchanged) is 3 units. The difference between Evan and Dan-now is the $480 Dan spent, which equals \(3u - 1u = 2u\). So \(2u = \$480\), giving \(1u = \$240\) (Dan in the end). Dan at first = Evan = \(3u = 3 \times \$240 = \$720\).


Mr Lee bought \(\dfrac{1}{4}\) kg of rice. He bought \(\dfrac{2}{5}\) kg more flour than rice. How many kilograms of rice and flour did Mr Lee buy altogether? Express your answer in its simplest form.


On a farm, \(\dfrac{1}{6}\) of the animals are sheep, \(\dfrac{1}{3}\) of them are ducks and \(\dfrac{1}{4}\) of them are horses. The remaining 90 animals are rabbits. How many animals are there in the farm altogether?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Fraction that are sheep, ducks and horses \(= \dfrac{1}{6} + \dfrac{1}{3} + \dfrac{1}{4} = \dfrac{2}{12} + \dfrac{4}{12} + \dfrac{3}{12} = \dfrac{9}{12} = \dfrac{3}{4}\). So rabbits are \(1 - \dfrac{3}{4} = \dfrac{1}{4}\), i.e. 3 of 12 equal units = 90. Per key: take 12 units total, rabbits = 3 units = 90, so 1 unit = 30, total = 12 units = \(30 \times 12 = 360\) animals.


Ninety-four thousand, eight hundred and seven, written in numeral is

Ninety-four thousand = 94 000; eight hundred = 800; and seven = 7. So \(94000 + 800 + 7 = 94807\). The numeral is 94 807.


Which of the following is a common factor of 4 and 8?

Factors of 4: 1, 2, 4. Factors of 8: 1, 2, 4, 8. A common factor must divide BOTH numbers. Among the options, only 4 divides both 4 and 8. So the answer is 4.


There were 40 children queuing to enter a room. Every 4th child in the queue received a toy and every 5th child received a sweet. How many children received both a toy and a sweet?

A child gets both if their position is a common multiple of 4 and 5, i.e. a multiple of 20. Within 40, these are positions 20 and 40. So 2 children received both.


If you add 1 to a certain number and round it to the nearest ten, the answer is 1950. If you add 2 to the number and round it to the nearest ten, the answer is 1960. What is the number?

Try 1953: \(1953 + 1 = 1954\), which rounds to 1950. \(1953 + 2 = 1955\), which rounds to 1960. Both conditions are satisfied, so the number is 1953.


What is the largest number that can be formed using the digits 4, 7, 6, and 1? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To make the largest number, arrange the digits from greatest to smallest: 7, 6, 4, 1. So the largest number is 7641.


What is the sum of the first two multiples of 5? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The first two multiples of 5 are 5 and 10. Their sum is \(5 + 10 = 15\).


When rounded to the nearest hundred, the number of audience at a theatre was 2600. Write down the largest possible number of audience at the theatre. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Numbers from 2550 to 2649 round to 2600 (to the nearest hundred). The largest of these is 2649.


Sarah sold a total of 20 bowls and plates for $86. Each bowl was sold at $5 and each plate was sold at $3. How many bowls did Sarah sell? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

If all 20 were plates: \(20 \times 3 = 60\) dollars. The actual total is $86, which is \(86 - 60 = 26\) more. Each bowl is \(5 - 3 = 2\) dollars more than a plate, so number of bowls = \(26 \div 2 = 13\). Sarah sold 13 bowls.


Ethan had twice as many beads as Sophie. After Ethan used 36 beads for a bracelet, Sophie had twice as many beads as Ethan. How many beads did Sophie have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Sophie have 1 unit at first, so Ethan had 2 units. After using 36, Ethan had \(2\text{ units} - 36\), and this equals half of Sophie's, i.e. Sophie's 1 unit = \(2 \times (2\text{ units} - 36)\). So \(1\text{ unit} = 4\text{ units} - 72\), giving \(3\text{ units} = 72\), so 1 unit = 24. Sophie had 24 beads at first.


Siti spent a total of $1400 on a bookshelf, a table and a chair. The bookshelf cost $630. The table cost $500 more than the chair.
(a) How much did she spend on the table and the chair altogether?
(b) How much did she spend on the chair? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Table + chair = total - bookshelf = \(1400 - 630 = 770\) dollars. (b) Table = chair + 500, so chair + chair + 500 = 770, giving \(2 \times \text{chair} = 770 - 500 = 270\), so chair = \(270 \div 2 = 135\) dollars.


Which of the following is forty-five thousand, nine hundred and six in numerals?

Forty-five thousand = 45 000, nine hundred = 900, and six = 6. Adding these gives 45 000 + 900 + 6 = 45 906. The answer is option (3), 45 906.


Arrange these numbers in decreasing order.<br>86 372, 85 327, 86 237

Decreasing order means largest to smallest. Compare the thousands: 86 372 and 86 237 both have 86 thousands, and 85 327 has 85 thousands so it is smallest. Between 86 372 and 86 237, the hundreds 3 > 2, so 86 372 > 86 237. Order: 86 372, 86 237, 85 327. The answer is option (2).


Each term increases by 100: 62 831 + 100 = 62 931, then 62 931 + 100 = 63 031. Checking forward, 63 031 + 100 = 63 131 which matches. The missing number is 63 031, option (3).


Which of the following numbers when rounded to the nearest hundred becomes 84 000?

Rounding to the nearest hundred: 83 875 rounds to 83 900; 83 953 rounds to 84 000; 84 092 rounds to 84 100; 84 234 rounds to 84 200. Only 83 953 rounds to 84 000. The answer is option (2).


Which of the following has both 4 and 7 as factors?

A number with both 4 and 7 as factors must be a multiple of \(4 \times 7 = 28\). Checking: 11 (no), 21 = 3 x 7 (only 7), 64 = 4 x 16 (only 4), 84 = 28 x 3 (both 4 and 7). The answer is option (4), 84.


At a party, every 6th guest gets a lollipop and every 8th guest gets a packet of juice. Which guest is the first to get both a lollipop and a packet of juice?

The first guest to get both is the lowest common multiple of 6 and 8. Multiples of 6: 6, 12, 18, 24; multiples of 8: 8, 16, 24. The smallest common multiple is 24, so the 24th guest is first to get both. The answer is option (3).


a) What is the value of the digit 7 in 58 701?
b) Round 19 572 to the nearest thousand.
(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) In 58 701 the digit 7 is in the hundreds place, so its value is \(7 \times 100 = 700\). b) To round 19 572 to the nearest thousand, look at the hundreds digit 5; since 5 rounds up, 19 572 becomes 20 000.


a) Write 7 ten thousands, 64 tens and 3 ones in numerals.
b) Find the value of \(4308 \times 9\).
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Read the statements made by these 2 students carefully. Ariel says 4 is a factor of 96. Tom says 4 is a factor of 76. One of the following statements is correct.

Check whether 4 divides each number. 96 divided by 4 is 24 with no remainder, so 4 is a factor of 96 (Ariel is correct). 76 divided by 4 is 19 with no remainder, so 4 is a factor of 76 (Tom is correct). Both are correct, so the correct statement is 'Both Ariel and Tom are correct.'


Alvin, Simon and Tina shared $6726 equally among themselves. Simon spent $1045 of his money. How much money did Simon have in the end? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mike has 75 packets of stamps. Each packet has 26 stamps. He packs all his stamps into bags of 5. How many bags of 5 stamps are there? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total stamps: \(75 \times 26 = 1950\). Each bag holds 5 stamps, so number of bags: \(1950 \div 5 = 390\). There are 390 bags.


A desk cost twice as much as a chair. Daniel spent $2264 on 2 identical desks and 4 identical chairs. What was the total cost of a desk and a chair? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let a chair be 1 unit; a desk is then 2 units. 2 desks = 4 units and 4 chairs = 4 units, giving \(4 + 4 = 8\) units. So 8 units = $2264 and 1 unit = \(2264 \div 8 = 283\). A desk and a chair together = 2 units + 1 unit = 3 units = \(283 \times 3 = 849\). The total cost is $849.


Sandy had some sweets to give her friends. If she gave each friend 4 sweets, she would have 22 sweets left. If she gave each friend 6 sweets, she would have 8 sweets left. How many sweets did Sandy have? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each friend gets 2 more sweets in the second case (\(6 - 4 = 2\)), and the leftover drops by \(22 - 8 = 14\) sweets. So those 14 extra sweets cover the 2-per-friend increase: number of friends = \(14 \div 2 = 7\). Total sweets = (4 sweets x 7 friends) + 22 left over = \(28 + 22 = 50\). Sandy had 50 sweets.


Forty-six thousand and sixteen in figures is .

Forty-six thousand = 46 000, and sixteen = 16. 46 000 + 16 = 46 016. Option (3).


In which of the following numbers does the digit 8 stands for 80?

The 8 must be in the tens place to stand for 80. In 3082 the 8 is in the tens place (80). Option (2).


13 429 rounded to the nearest hundred is .

Look at the tens digit (2). Since 2 < 5, round down: 13 429 to the nearest hundred is 13 400. Option (3).


Make denominators the same: \(\dfrac{1}{3}=\dfrac{3}{9}\). Then \(\dfrac{3}{9}+\dfrac{1}{9}=\dfrac{4}{9}\). Option (4).


What is the number when 17.54 is rounded to 1 decimal place?

To round to 1 decimal place, look at the hundredths digit (4). Since 4 < 5, keep the tenths digit: 17.54 to 1 d.p. is 17.5. Option (2).


Abby started cleaning her room at 13 30. She took 1 h 30 min to clean her room. What time did she finish cleaning her room?


Jason spent $55 on 2 identical shirts and a pair of pants. A pair of pants cost $25 more than a shirt. How much did he spend on 1 shirt?

$55 - $25 = $30 is the cost of 3 shirts' worth (2 shirts + 1 shirt-equivalent of pants). 3 units = $30, so 1 shirt = $10. Option (1).


\(83\,905 = 80\,000 + 3000 +\) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(+ 5\)<br>What is the missing number?

83 905 = 80 000 + 3000 + 900 + 5. The missing number is 900 (the hundreds value).


Write the missing number in the number pattern below.<br>13 000 , 12 600 , 12 200 , 11 800 , <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , 11 000


Write 5 thousandths as a decimal. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Write \(\dfrac{85}{100}\) as a decimal. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Arrange the following numbers in order from the greatest to the smallest.
3.909, 3.093, 3.099
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />   (c) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Compare tenths first: 3.909 has 9 tenths (largest). Then 3.099 vs 3.093 — hundredths equal (9), thousandths 9 > 3, so 3.099 > 3.093. Order greatest to smallest: 3.909, 3.099, 3.093.


Mrs Wong wants to pack 36 blueberry cupcakes and 54 chocolate cupcakes into boxes with no remainder. The total number of cupcakes packed into each box is the same. The number of blueberry cupcakes in each box is the same. What is the greatest number of boxes that Mrs Wong can pack? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Find the common factors of 36 and 54: 1, 2, 3, 6, 9, 18. The greatest common factor is 18, so the greatest number of boxes is 18.


Aini prepared 6 \(\ell\) of fruit punch for a party. She poured them equally into 4 bottles. What is the volume of the fruit punch in each bottle? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

6 \(\ell\) ÷ 4 = 1.5 \(\ell\) in each bottle.


Kelvin is 1.81 m tall. He is 0.35 m taller than Jonathan. Jonathan is 0.29 m shorter than Elson. What is Elson's height? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Jonathan = 1.81 - 0.35 = 1.46 m. Elson is 0.29 m taller than Jonathan: 1.46 + 0.29 = 1.75 m.


Leela's watch is 15 minutes slower. The time shown on her watch is 1.35 p.m. Find the actual time using the 24-hour clock. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The watch is 15 min slow, so the actual time is 15 min later: 1.35 p.m. + 15 min = 1.50 p.m. = 13 50 in the 24-hour clock.


When I open my storybook, two pages face me. The sum of these two page numbers is 667. What is the page number of the smaller number? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Two facing pages are consecutive numbers. Sum = 667, so the smaller page = (667 - 1) ÷ 2 = 666 ÷ 2 = 333.


Mark bought some sweets. He gave his friends \(\dfrac{1}{7}\) of the sweets and gave his brother \(\dfrac{3}{4}\) of the sweets. All the remaining sweets were eaten by him. What fraction of the sweets did Mark eat?


Nicole had baked five times as many cookies as Joey at first. After Nicole gave away 235 cookies and Joey gave away 19 cookies, they had the same number of cookies left.
(a) How many cookies did Nicole bake at first?
(b) How many cookies did each of them 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="?" />

Let Joey = 1 unit, Nicole = 5 units. After giving away: 5u - 235 = 1u - 19, so 4u = 235 - 19 = 216, 1u = 54. (a) Nicole baked 5u = 5 × 54 = 270. (b) Each had 1u - 19 = 54 - 19 = 35 in the end.


Mrs Devi and Mdm Tan baked an equal number of muffins for sale. Mrs Devi sold 49 muffins and had \(\dfrac{2}{9}\) of the muffins left.
(a) How many muffins did Mrs Devi have left?
(b) How many muffins did Mrs Devi and Mdm Tan bake in all?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Mrs Devi sold \(\dfrac{7}{9}\) of her muffins (since \(\dfrac{2}{9}\) are left) = 49, so 7 units = 49, 1 unit = 7. (a) Left = 2 units = 2 × 7 = 14. (b) Each baked 9 units = 9 × 7 = 63; total for both = 63 × 2 = 126.


Charlie had twice as marbles as Sally. After Sally lost 45 marbles, Charlie had 5 times as many marbles as Sally. How many marbles did Charlie have? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Charlie's marbles never change. At first Charlie = 2 × Sally. After Sally loses 45, Charlie = 5 × (new Sally). Let new Sally = 1 unit, Charlie = 5 units; original Sally = 5u ÷ 2. Since Sally lost 45: 5u/2 - 45 = u, giving 3u/2 = 45, u = 30. Charlie = 5u... using the key: 3u = 45 + 45 = 90, 1u = 30, Charlie = 5 × 30 = 150.


Three children shared some money. Alice and Benny received $100 altogether. Benny and Catherine received $450 in all. Catherine received five times as much money as Alice. How much money did Alice receive? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Catherine - Alice = (Benny+Catherine) - (Alice+Benny) = 450 - 100 = 350. Catherine is 5 times Alice, so Catherine - Alice = 4 units = 350, 1 unit = 350 ÷ 4 = $87.50. Alice (1 unit) received $87.50.


77 thousands and 3 tens is the same as ____________.


Which of the following is not a factor of 56?

Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. 56 ÷ 6 = 9 remainder 2, so 6 is not a factor.


Which of the following fractions is in its simplest form?

4/9: no common factor of 4 and 9 except 1, so it is in simplest form. 2/8 = 1/4, 3/12 = 1/4, 6/10 = 3/5.


Arrange these distances from the longest to the shortest.<br>\(1340m\) , \(1km\ 304m\) , \(1\dfrac{3}{4}km\)


The table shows the number of Pokémon cards five boys have.
Ali: 84, Brian: 48, Cheng: 112, Dinesh: 56, Ethan: 102
Which two boys have a total of 150 Pokémon cards?


A baker bought 5.44 kg of flour. He repacked it equally into 8 packets. How much flour was there in each packet?


Ken started painting his bedroom at 9 a.m. He stopped for lunch at 12 p.m. and continued painting at 1.30 p.m. He finished painting his room at 4.30 p.m. How long did he take to paint his room?

Morning: 9 a.m. to 12 p.m. = 3 h. Afternoon: 1.30 p.m. to 4.30 p.m. = 3 h. Total painting time = 3 h + 3 h... wait, 3 h + 3 h would be 6 h, but lunch (12 to 1.30) is excluded. Total = 3 h + 3 h = 6 h? Actual painting: 3 h + 3 h = 6 h. Key gives option 1 (5 h 30 min); morning 9 to 12 = 3 h, afternoon 1.30 to 4.30 = 3 h, total painting 6 h. See notes.


The figure shows the flight departure details to Hong Kong.
Sunshine Airlines — Hong Kong, Flight Departure Time: 15 05.
Amber needs to reach the boarding gate at least 30 min before the flight departure time. She takes 20 min to walk to the boarding gate. What is the latest time she should start walking to the boarding gate?

Must reach gate by 30 min before 15 05 = 14 35. She walks 20 min, so she must start by 14 35 - 20 min = 14 15.


The table shows the number of children and adults who visited the library on a weekday. Part of the table is covered by an ink blot.
Male — Children 119, Adults [hidden], Total 246.
Female — Children 123, Adults 230, Total 353.
What is the total number of adults who went to the library on that weekday?

Male adults = total 246 − children 119 = 127. Total adults = male adults 127 + female adults 230 = 357.


The first 18 letters of a pattern are given.
C, A, B, C, D, E, C, A, B, C, D, E, C, A, B, C, D, E, ...?
What is the letter in the 50th position?

The pattern repeats every 6 letters: C, A, B, C, D, E. 50 ÷ 6 = 8 remainder 2, so the 50th letter is the 2nd letter of the block, which is A.


Tyra paid $9.60 for 4 similar rulers and 4 similar files. Each file cost $0.70 more than each ruler. How much did each ruler cost?

4 files cost 4 × $0.70 = $2.80 more than 4 rulers. Remove this: $9.60 − $2.80 = $6.80 for 8 rulers' worth. $6.80 ÷ 8 = $0.85 per ruler.


A player has to play a total of four games in Round 1 of a competition. The scores for Malik's first three games are: 1st 9.3, 2nd 10.1, 3rd 9.5, 4th ?.<br>Malik will qualify for Round 2 if the total score for three out of the four games is 30 or more. What is the lowest score Malik must get in the 4th game to qualify for Round 2?

Best three of four must total ≥ 30. The two highest existing scores are 10.1 + 9.5 = 19.6. The 4th game must make the best three reach 30: 30 − 19.6 = 10.4. So the lowest 4th-game score is 10.4.


Round 29 540 to the nearest hundred. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tens digit is 4 (less than 5), so round down: 29 540 rounds to 29 500.


Arrange these fractions from the smallest to the greatest.
\(\dfrac{4}{7}\) , \(\dfrac{1}{2}\) , \(\dfrac{6}{7}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


Write 64 thousandths as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


0.39 = 39 hundredths = 39/100. 39 and 100 share no common factor, so it is already in simplest form.


Write the missing number in the number pattern.<br>11 005 , 10 205 , 9405 , 8605 , <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , 7005


Mdm Tan had $7360. She saved $4825 and divided the rest equally among her 3 children. How much did each child receive? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Remaining after saving: $7360 − $4825 = $2535. Each child: $2535 ÷ 3 = $845.


Sally bought 18 donuts at 3 for $3.95. How much did she pay for the donuts? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Raju had $50. A bar of chocolate cost $5.50. At a sale (Buy 2 Get 1 Free), Raju took home 6 bars of chocolate. How much change did he receive? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Buy 2 get 1 free: for 6 bars taken home, Raju pays for only 4 bars. 4 × $5.50 = $22. Change = $50 − $22 = $28.


Uncle Lee had three times as many apples as Aunt Mei. After he sold 75 apples, Aunt Mei had twice as many apples as him. How many apples did Aunt Mei have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Aunt Mei have M. Uncle Lee had 3M. After selling 75: 3M − 75. Aunt Mei is now twice his: M = 2(3M − 75) → M = 6M − 150 → 150 = 5M → M = 30. (Per key working: 75 ÷ 5 = 15; total parts give Aunt Mei 30.)


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

The digit 8 stands for 800 when it sits in the hundreds place. In 5840, the 8 is in the hundreds place, so it stands for 800. In 4058 it is 8, in 5084 it is 80, in 8504 it is 8000.


45 879 rounded to the nearest hundred is ____________.

To round 45 879 to the nearest hundred, look at the tens digit (7). Since 7 is 5 or more, round the hundreds up: 45 879 rounds to 45 900.


Arrange these fractions from the smallest to the greatest.<br>\(\dfrac{1}{2}\) , \(\dfrac{4}{9}\) , \(\dfrac{8}{9}\)

Compare the fractions: 4/9 is just under a half (4.5/9 = 1/2), so 4/9 < 1/2. And 8/9 is the largest. Ordered smallest to greatest: 4/9, 1/2, 8/9.


Compare the decimals by place value. 3.038 has 0 tenths and 3 hundredths, the smallest of all. 3.07 = 3.070, 3.15, 3.304 are all larger. So 3.038 is smallest.


Convert 7/20 to a decimal: multiply numerator and denominator by 5 to get 35/100 = 0.35. So 4 7/20 = 4.35.


Adam is below 10 years old. His age is a factor of 28 and a multiple of 4. How old is he?

Factors of 28 below 10: 1, 2, 4, 7. Of these, the multiples of 4 are: 4. So Adam is 4 years old. (8 is a multiple of 4 but not a factor of 28.)


In a library, there were 2580 fiction books. The number of non-fiction books was 3 times the number of fiction books. How many books were there altogether?


Mrs Lim had some money. After buying 48 toy planes at $367 each, she had $10 left. How much money did she have at first?


Azri and Liying had the same number of stamps at first. After Azri gave away 60 stamps, Liying had 5 times as many stamps as Azri. How many stamps did Azri have at first?

Let Azri's amount after giving away be 1 unit; Liying = 5 units. They started equal, so the 60 given away is the difference: 5 units - 1 unit = 4 units = 60, so 1 unit = 15. Azri started with the same as Liying = 5 units = 75 stamps.


Mrs Lee used \(\dfrac{3}{8}\) kg of flour to bake cookies. The amount of flour used to bake a cake was \(\dfrac{1}{5}\) kg more than the amount used to bake cookies. How much flour did she use altogether?


A rope of length 20 m is cut into 8 equal pieces. How long is each piece?

Length of each piece = 20 div 8 = 2.5 m.


A decimal when rounded to the nearest whole number is 175. Which of the following is the smallest possible decimal?

To round to 175, the decimal must be at least 174.5 (rounds up) and below 175.5. 174.49 rounds to 174 (too small). 174.50 rounds up to 175 and is the smallest of the options that rounds to 175.


Arrange these numbers from the smallest to the greatest.
5604 , 5064 , 5640
<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 by place value. 5064 (thousands 5, hundreds 0), 5604 (hundreds 6), 5640 (hundreds 6, tens 4). Smallest to greatest: 5064, 5604, 5640.


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

The factors of 18 are 1, 2, 3, 6, 9, 18. The ones not listed are 6 and 9.


Write \(3\dfrac{4}{5}\) as an improper fraction.

Multiply the whole number by the denominator and add the numerator: 3 x 5 + 4 = 19. So 3 4/5 = 19/5.


Make the denominators the same: 1/4 = 2/8. Then 2/8 + 5/8 = 7/8.


There are 872 pears and peaches in a box. \(\dfrac{3}{8}\) of them are pears. How many peaches are there?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Peaches are the remaining fraction: 1 - 3/8 = 5/8. Number of peaches = 5/8 x 872 = 5 x 109 = 545.


Mrs Tay bought a dress and 2 skirts for $250. The dress cost $65.50 more than a skirt. What was the cost of 1 skirt?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let 1 skirt = 1 unit. Dress = 1 unit + $65.50. Total = 3 units + $65.50 = $250, so 3 units = $184.50, 1 unit = $61.50. One skirt costs $61.50.


Johnson and Steven have 1200 sweets altogether. Johnson has 5 times as many sweets as Steven. How many sweets must Johnson give to Steven so that they have the same number of sweets?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total = 6 units = 1200, so 1 unit = 200. Steven = 200, Johnson = 1000. To be equal each must have 600. Johnson must give Steven 1000 - 600 = 400 sweets. (Equivalently, give 2 units = 400.)


In a clothing donation drive, Classes 4A, 4B and 4C collected 3445 kg of clothes in total. Class 4A collected 123 kg less than the combined collection of classes 4B and 4C. Class 4C collected 3 times the amount collected by class 4B. What was the amount of clothes collected by class 4B?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let 4B = 1 unit, 4C = 3 units, so 4B+4C = 4 units. 4A = 4 units - 123. Total = (4 units) + (4 units - 123) = 8 units - 123 = 3445. So 8 units = 3568, 1 unit = 446. Class 4B collected 446 kg.


Joan had some money. She spent \(\dfrac{2}{3}\) of it on a dress and \(\dfrac{1}{4}\) of it on a doll. She had $27 left. How much more money did she spend on the dress than on the doll?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Lisa had 10 kg of grapes more than Zara. When Lisa gave away 1.5 kg of grapes and Zara gave away 0.5 kg of grapes, Lisa still had 4 times as much grapes as Zara. How many kilograms of grapes did Zara have at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After giving away, the difference between Lisa and Zara = 10 - 1.5 + 0.5 = 9 kg. This difference is 4 units - 1 unit = 3 units = 9 kg, so 1 unit = 3 kg (Zara's amount after giving away). Zara at first = 3 + 0.5 = 3.5 kg.


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


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

Rounding to the nearest hundred: 59 951 rounds to 60 000 (the tens digit 5 rounds up). 59 599 rounds to 59 600; 60 070 rounds to 60 100; 60 140 rounds to 60 100.


What is the second common multiple of 4 and 6?

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


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

\(\dfrac{4}{6} = \dfrac{2}{3}\). Checking: \(\dfrac{12}{18} = \dfrac{2}{3}\), so it is equivalent.


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

In 41.32, the first decimal place (tenths) is 3 and the second (hundredths) is 2. So the digit in the hundredths place is 2.


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


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


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


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

The pattern decreases by 30 each time: \(875 - 845 = 30\). So the missing term is \(815 - 30 = 785\) (and \(785 - 30 = 755\) checks).


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


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


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

\(\dfrac{3}{6} = \dfrac{1}{2}\) and \(\dfrac{6}{8} = \dfrac{3}{4}\) can be simplified. \(\dfrac{2}{5}\) and \(\dfrac{5}{7}\) cannot, so they are already in simplest form.


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


Arrange the following numbers from the smallest to the greatest.
\(0.801\) , \(0.081\) , \(\dfrac{4}{5}\)
<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="?" />


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


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

\(52 = 1 \times 52 = 2 \times 26 = 4 \times 13\). So all factors are 1, 2, 4, 13, 26, 52. The other two are 13 and 26.


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

The number must be a common multiple of 3 and 8, i.e. a multiple of 24, and fewer than 50. Multiples of 24 below 50 are 24 and 48; the greatest is 48.


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


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


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

(a) Let Priscilla = P. Victor = P − 180, William = P + 20. Total: \(P + (P-180) + (P+20) = 680 \Rightarrow 3P - 160 = 680 \Rightarrow 3P = 840 \Rightarrow P = 280\). (b) Victor at first = \(280 - 180 = 100\). Priscilla (280) is twice Victor's final amount, so Victor's final = \(280 \div 2 = 140\). Victor bought \(140 - 100 = 40\).


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

After Aqil gives away 60, the gap between Riley and Aqil becomes \(60 - 24 = 36\) (Riley now leads). Riley = 4 × Aqil(now), so the gap = 3 units = 36, giving 1 unit = \(36 \div 3 = 12\) = Aqil now. Aqil at first = \(12 + 60 = 72\).


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

Place value: the digit 8 stands for 800 only when 8 is in the hundreds place. In 4823, the 8 is in the hundreds place, so it stands for 800.


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

A common multiple of 4 and 6 is a multiple of 12. Among the options, 36 = 12 × 3 is a multiple of both 4 (4×9) and 6 (6×6). The others are not.


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

2/3 = 4/6 = 6/9 = 12/18 (multiply numerator and denominator by the same number). 18/24 simplifies to 3/4, which is not equal to 2/3, so it is not equivalent.


Joyce has 40 marbles. 10 marbles are red, 18 marbles are green and the rest are purple. What fraction of the marbles are purple?

Purple = 40 − 10 − 18 = 12 marbles. Fraction purple = 12/40 = 3/10.


Arrange these numbers from the greatest to the smallest.
489 , 948 , 984 , 498
<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 by place value. Greatest to smallest: 984, 948, 498, 489.


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

Forty thousand = 40 000; thirty-seven = 37. Together: 40 000 + 37 = 40037.


Which two of the fractions below are smaller than \(\dfrac{1}{2}\)?
\(\dfrac{2}{3}\) , \(\dfrac{4}{9}\) , \(\dfrac{5}{11}\) , \(\dfrac{6}{12}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


What is the value of \(\dfrac{5}{6} + \dfrac{7}{12}\)? Express your answer as a mixed number.


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

7 thousandths = 7/1000 = 0.007 (7 in the thousandths place).


How many minutes are there in 4 hours and 27 minutes? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


John drank 0.84 \(\ell\) of orange juice. He drank 0.44 \(\ell\) of orange juice less than Sam. How much orange juice did the two boys drink altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Bobby had $54. He spent \(\dfrac{1}{6}\) of it on some books. How much money did he have left? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Ali and Devi had a total of 842 stamps. After Ali gave 79 stamps to Devi, they had the same number of stamps. Find the number of stamps Ali had at first. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After giving, each has 842 ÷ 2 = 421 stamps. Ali had 79 more before giving, so Ali at first = 421 + 79 = 500 stamps.


Amanda had $1240 and Sophie had $1304 in savings at first. Then, Amanda saved $20 each day while Sophie saved $12 each day. After how many days did the 2 girls have the same amount of money? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Sophie starts $1304 − $1240 = $64 ahead. Amanda gains $20 − $12 = $8 more each day. Days to catch up = 64 ÷ 8 = 8 days.


Tom bought 4 erasers and 3 pencils from the bookshop for $6.10. Jane bought 7 erasers and 3 pencils for $7.30. What is the price of 1 pencil? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The difference between the two purchases is 3 erasers = $7.30 − $6.10 = $1.20, so 1 eraser = $0.40. Then 4 erasers = $1.60, so 3 pencils = $6.10 − $1.60 = $4.50, and 1 pencil = $4.50 ÷ 3 = $1.50.


A shop sells doughnuts: 1 doughnut for $2; buy 5 doughnuts and get 1 free. Suki wants to buy 15 doughnuts. What is the least amount she has to pay? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Buying 5 and getting 1 free gives 6 doughnuts for $10. Two such sets give 12 doughnuts for $20. She still needs 3 more at $2 each = $6. Total = $20 + $6 = $26.


A shopkeeper had 9 bags of potatoes. Each bag contained 12.25 kg of potatoes. What was the total mass of potatoes in the 9 bags? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A shopkeeper had 9 bags of potatoes, each containing 12.25 kg, a total of 110.25 kg. The shopkeeper bought another 24.75 kg of potatoes. He then packed all the potatoes into bags of 3 kg each. He sold all the bags at a cost of $6 for each bag. How much did he receive from the sale of the potatoes? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total potatoes = 110.25 + 24.75 = 135 kg. Number of 3 kg bags = 135 ÷ 3 = 45. Money received = 45 × $6 = $270.


Mdm Nura baked some apple, blueberry and chocolate tarts. She baked 4 apple tarts and twice as many blueberry tarts as apple tarts. She baked 3 more chocolate tarts than blueberry tarts. How many tarts did she bake altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Apple = 4. Blueberry = 2 × 4 = 8. Chocolate = 8 + 3 = 11. Total = 4 + 8 + 11 = 23 tarts.


In March there were 312 students choosing a favourite sport, with 40 choosing tennis. In April, 8 new students chose badminton as their favourite sport. The number of students who chose tennis remained unchanged. What fraction of the students chose tennis as their favourite sport in April? Give your answer in the simplest form.

New total in April = 312 + 8 = 320. Tennis is still 40. Fraction = 40/320 = 1/8.


Mr Lee had red, yellow and purple files. \(\dfrac{1}{4}\) of the files were red and \(\dfrac{3}{5}\) of the files were yellow. The rest of the files were purple. What fraction of the files were purple?


Mr Lee had red, yellow and purple files. \(\dfrac{1}{4}\) were red, \(\dfrac{3}{5}\) were yellow and \(\dfrac{3}{20}\) were purple. Mr Lee had 40 red files. What was the difference between the number of yellow files and the number of purple files? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Red is 1/4 = 5/20 of the files and equals 40, so 5 units = 40, 1 unit = 8 (where 1 unit = 1/20). Yellow = 12 units = 96; purple = 3 units = 24. Difference = 96 − 24 = 72.


At a mall, a watch cost 6 times as much as a bag. The bag cost $91.25 less than the watch. Mrs Tan bought a watch and 3 bags. How much did Mrs Tan spend? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the bag be 1 unit; the watch is 6 units. The difference 6 − 1 = 5 units = $91.25, so 1 unit (bag) = $18.25. Watch + 3 bags = 6 + 3 = 9 units = 9 × $18.25 = $164.25.


At a mall, a watch cost 6 times as much as a bag, and the bag cost $91.25 less than the watch. Mrs Tan bought a watch and 3 bags for $164.25. Mrs Tan paid the cashier with two $100 notes. How much change did she get? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A bookstore had an equal number of pens and rulers. After 1852 pens and 547 rulers were sold, there were 4 times as many rulers as pens left. How many pens were there at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the starting number of each be N. Pens left = N − 1852; rulers left = N − 547. Rulers left = 4 × pens left, so the extra rulers (1852 − 547 = 1305) equal 3 times the pens left: 3 units = 1305, 1 unit = 435 (pens left). Pens at first = 435 + 1852 = 2287.


A bookstore had 2287 pens and 2287 rulers at first. After 1852 pens and 547 rulers were sold, the cost of each pen was $2 and the cost of each ruler was 70¢. How much was collected from the sale of pens and rulers? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The sum of two numbers is 29. One of the numbers is a factor of 45. The other number is a multiple of 5. What is the difference between the two numbers? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The two numbers add to 29. A factor of 45 (1,3,5,9,15,45) plus a multiple of 5 (5,10,15,20,25,...) = 29: 9 + 20 = 29 works (9 is a factor of 45, 20 is a multiple of 5). Difference = 20 − 9 = 11.


The sum of two numbers is 561. One of the numbers is a 2-digit number. The other number is a 3-digit number. What is the smallest possible difference between the two numbers? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To make the difference smallest, make the 2-digit number as large as possible: the largest 2-digit number is 99, so the 3-digit number is 561 − 99 = 462. Difference = 462 − 99 = 363.


In 125.34, which digit is in the tenths place?

In a decimal, the first digit after the decimal point is the tenths place. In \(125.34\) the digit after the point is 3, so the tenths digit is 3.


Arrange the numbers from the smallest to the greatest.<br>\(6.7\), \(0.67\), \(6.07\), \(0.76\)

Compare whole-number parts first: \(0.67\) and \(0.76\) are less than 1; \(6.07\) and \(6.7\) are more than 6. Within each pair compare tenths: \(0.67 < 0.76\) and \(6.07 < 6.70\). Order: 0.67, 0.76, 6.07, 6.7.


(a) Express \(5\dfrac{73}{100}\) as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Round \(45.999\) to the nearest 1 decimal place. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) \(\dfrac{73}{100}\) means 73 hundredths \(= 0.73\), so \(5\dfrac{73}{100} = 5.73\). (b) Look at the hundredths digit of \(45.999\), which is 9 (≥5), so round the tenths up: \(45.999 \approx 46.0\).


The total length of two ropes, Rope P and Rope Q, is \(23.06\) m.
The length of Rope Q is \(14.78\) m.
What is the difference in length between Rope P and Rope Q?
Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m

First find Rope P: \(23.06 - 14.78 = 8.28\) m. The difference between Rope P and Rope Q is \(14.78 - 8.28 = 6.5\) m.


Bala had \(10.5\) kg of sugar.
He used \(3.5\) kg of it and repacked the rest equally into 5 boxes.
What was the mass of sugar in each box?
Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

Sugar left after using some: \(10.5 - 3.5 = 7\) kg. Repacked equally into 5 boxes: \(7 \div 5 = 1.4\) kg per box.


Siti paid $10.40 for a chocolate cake and 4 curry puffs.
Sumei paid $13.60 for a chocolate cake and 8 curry puffs.
Shanti bought 5 chocolate cakes.
(a) What was the cost of 1 curry puff? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much did Shanti pay for the 5 chocolate cakes? $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Janice had \(6\) \(\ell\) of orange juice.
She poured \(3.85\) \(\ell\) of orange juice equally into 7 identical cups.
(a) How much orange juice was left? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(\ell\)
(b) How much orange juice was there in each cup? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> \(\ell\)

(a) Juice poured out is 3.85 ℓ, so juice left \(= 6 - 3.85 = 2.15\) ℓ. (b) The 3.85 ℓ poured out is shared equally into 7 cups: \(3.85 \div 7 = 0.55\) ℓ in each cup.


Which digit in \(17.48\) is in the tenths place?

In \(17.48\) the digit right after the decimal point is the tenths place. That digit is \(4\). (The \(8\) is in the hundredths place.) Answer: \(4\).


Express \(6\dfrac{7}{25}\) as a decimal.


Round \(39.95\) to 1 decimal place. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To round to 1 decimal place, look at the hundredths digit. \(39.95\) has hundredths digit \(5\), so round the tenths up: \(39.9\to40.0\). Answer: \(40.0\).


Complete the number pattern.<br>\(7.38, 7.48, 7.47, 7.57, 7.56, 7.66,\) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(, 7.75, 7.74, 7.84\)


A water bottle contained \(1.2\) \(l\) of water. It contained \(2.5\) \(l\) less water than a kettle. How much water was there in 4 such kettles? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

One kettle holds \(1.2+2.5=3.7\) \(l\) (the bottle has 2.5 l less than a kettle). For 4 kettles: \(3.7\times4=14.8\) \(l\). Answer: \(14.8\) \(l\).


Mrs Tan had \(7.86\) \(kg\) of flour less than Mrs Siva. After Mrs Siva used \(10\) \(kg\) of flour, Mrs Tan had 3 times as much flour as Mrs Siva had left.
(a) How many more kilograms of flour did Mrs Tan have than Mrs Siva in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many kilograms of flour did Mrs Siva have left? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Mrs Tan's amount is unchanged. At the start Mrs Siva had \(7.86\) kg more than Mrs Tan; after using \(10\) kg, Mrs Siva is now \(10-7.86=2.14\) kg less than Mrs Tan. So Mrs Tan has \(2.14\) kg more than Mrs Siva in the end. (b) In the end Tan = 3 × Siva, so the difference (Tan − Siva) = 2 units = \(2.14\) kg, giving 1 unit = Siva = \(2.14\div2=1.07\) kg. Answers: (a) \(2.14\) kg, (b) \(1.07\) kg.


The value of the digit 3 in 57.43 is ____________.

The digit 3 in 57.43 is in the hundredths place. Its value is \(3 \times 0.01 = 0.03\).


The hundredths digit is 8; the thousandths digit is 6 (≥5), so round up. \(32.786 \approx 32.79\).


Arrange the following decimals in increasing order.<br>2.186   2.816   2.168   2.681

Compare digit by digit after the units: 2.168 < 2.186 < 2.681 < 2.816. Increasing order is 2.168, 2.186, 2.681, 2.816.


Mary bought 3 m of ribbon. She used 1.65 m of it to tie a present. How many metres of ribbon had she left?


A bag costs four times as much as a purse. Jamie paid $33 for a bag and 2 purses. How much did a bag cost?

Let a purse be 1 unit; a bag is 4 units. Bag + 2 purses = 4 + 2 = 6 units = $33, so 1 unit = $5.50. A bag = 4 units = \(4 \times 5.50 = 22\).


Divide 6 by 7. Correct your answer to 1 decimal place. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

\(6 \div 7 = 0.857...\). The second decimal digit is 5, so round up the first decimal place: \(0.857... \approx 0.9\).


Pearly had \(5.4\ell\) of watermelon juice. Pearly had twice as much watermelon juice as May. May had three times as much watermelon juice as Amy. How much more watermelon juice does Pearly have than Amy? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Tan had 2.53 kg more flour than Mrs Sim. After Mrs Tan used 4.09 kg of flour, Mrs Sim had four times as much flour as Mrs Tan had left. How many kilograms of flour did Mrs Tan have at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After using 4.09 kg, Mrs Tan's amount is (Tan first − 4.09). Mrs Sim = Tan first − 2.53. Sim = 4 × Tan's remaining: \(T - 2.53 = 4(T - 4.09)\). So \(T - 2.53 = 4T - 16.36\), giving \(3T = 13.83\) and \(T = 4.61\) kg. (Equivalently the difference 4.09 − 2.53 = 1.56 kg equals 3 units of Tan's remainder; 1 unit = 0.52 kg; Tan first = 0.52 + 4.09 = 4.61 kg.)


Mr Tan placed 8 flags around the border of a square field. The distance between each flag and the next was equal for all the flags. The distance between the 1st flag and the 6th flag was 27 m. What was the total distance of the border around the square field? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

From the 1st flag to the 6th flag there are 5 gaps: \(27 \div 5 = 5.4\) m per gap. With 8 flags around a closed border there are 8 equal gaps: \(5.4 \times 8 = 43.2\) m.


All factors of 32 are 1, 2, 4, 8, 16, 32. Andy listed 1, 2, 8, 32, so the missing factors are 4 and 16.


Let Ada = 1 unit. Ben = 2 units, Chris = 1 unit − 40. Total = 4 units − 40 = 720, so 4 units = 760 and 1 unit = 190. Ben = 2 units = 380.


(a) One T-shirt = $120 ÷ 5 = $24. (b) The pants cost 3 times one T-shirt = 3 × $24 = $72.


Add by place value: 50 000 + 900 + 8 = 50 908. There are 5 ten-thousands, 0 thousands, 9 hundreds, 0 tens and 8 ones. Answer: 50 908.


Compare from the largest place value. All have 9 thousands. Hundreds: 9605 and 9506 have 6 and 5 hundreds; 9065 has 0 hundreds. So 9605 > 9506 > 9065. Greatest to smallest: 9605, 9506, 9065. Answer: option 4.


A number with both 3 and 4 as factors must be a multiple of 12. Check: 15 (no), 18 (4 is not a factor), 20 (3 is not a factor), 24 = 3 x 8 = 4 x 6. So 24 has both 3 and 4 as factors. Answer: option 4.


a) Seventy-eight thousand and twenty = 78 000 + 20 = 78 020. b) 39 500 is exactly halfway between 39 000 and 40 000; rounding to the nearest thousand rounds the half up to 40 000.


Divide 853 by 9 and find the remainder. 9 x 94 = 846, and 853 - 846 = 7. So 94 full boxes are packed and 7 books are left unpacked. Answer: 7 books.


When Betty gives $35 to Andy, Andy gains $35 and Betty loses $35, so the gap between them widens by 2 x $35 = $70. New difference = $450 + $70 = $520. Answer: $520.


For an equal number of pens and pencils, the count must be a common multiple of 6 and 8. The least common multiple of 6 and 8 is 24, so the least number of pens is 24 and the least number of pencils is 24. Total = 24 + 24 = 48.


Let watermelons = 1 unit, durians = 4 units. After selling 114 durians, durians left = watermelons = 1 unit, so 114 durians = 4 units - 1 unit = 3 units. 1 unit = 114 / 3 = 38. Watermelons = 38 and durians left = 38, so fruits left = 38 + 38 = 76.


Assume all 35 notes are $2: value = 35 x $2 = $70. The actual total is $118, which is $48 more. Each $2 note swapped for a $5 note adds $3. So number of $5 notes = $48 / $3 = 16.


Factors of 16: 1, 2, 4, 8, 16. Factors of 28: 1, 2, 4, 7, 14, 28. The factors common to both are 1, 2 and 4.


Numbers from 51 500 to 52 499 round to 52 000. The greatest of these is 52 499.


Rounds to 800, so the number is 750-849; the hundreds digit is 8, tens digit < 5. Hundreds = twice tens means tens = 4 (8 = 2 x 4). Digits sum to 15: 8 + 4 + ones = 15, so ones = 3. The number is 843.


The number of each colour must be a common multiple of 5 and 3. The least common multiple is 15, so there are 15 red and 15 blue marbles. Altogether 15 + 15 = 30 marbles.


After receiving erasers, total 84 is split as Dan : Elijah = 2 : 1, i.e. 3 units = 84, so 1 unit = 84 ÷ 6... working: 84 ÷ 3 units gives Dan 56 and Elijah 28 after. The equal amount added is x, so Elijah-first = 28 - x and Dan-first = 56 - x = 3(28 - x). Solving: 56 - x = 84 - 3x, 2x = 28, x = 14. Dan at first = 56 - 14 = 42 erasers. (Key working: 84 ÷ 6 = 14, 14 x 3 = 42.)


The 4 other charities received 4 x $60 = $240, which is the rest of the savings. Fraction left = 1 - \(\dfrac{3}{8}\) - \(\dfrac{1}{4}\) = 1 - \(\dfrac{3}{8}\) - \(\dfrac{2}{8}\) = \(\dfrac{3}{8}\). So \(\dfrac{3}{8}\) of savings = $240, meaning \(\dfrac{1}{8}\) = $80 and total savings = $80 x 8 = $640. All 6 charities together received the whole savings, $640.


Fifty thousand = 50 000, eight hundred = 800, three = 3. So the number is 50 000 + 800 + 3 = 50 803.


Compare from the largest place value. 39 039 and 39 309 are in the 39-thousands; 39 039 < 39 309. 40 309 and 40 390 are in the 40-thousands; 40 309 < 40 390. Increasing order: 39 039, 39 309, 40 309, 40 390.


Nearest ten: the ones digit is 5, so round up the tens: 74 945 ≈ 74 950. Nearest hundred: the tens digit is 4 (less than 5), so round down: 74 945 ≈ 74 900.


Multiples of 7: 49, 56, 63, ... The only one between 50 and 60 is 56 (7 × 8 = 56).


Make the denominators the same: \(\dfrac{1}{4}=\dfrac{3}{12}\). Then \(\dfrac{11}{12}-\dfrac{3}{12}=\dfrac{8}{12}\). Simplify by dividing by 4: \(\dfrac{8}{12}=\dfrac{2}{3}\).


(a) Total mangoes = 162 × 36 = 5832. (b) Mangoes left after selling = 5832 - 738 = 5094. Bags = 5094 ÷ 9 = 566.


Work backwards from the end. Before receiving 648: 1330 - 648 = 682. Before giving away 238: 682 + 238 = 920. So Sam had 920 cards at first.


School B = 3064 × 4 = 12 256 books. (a) More books in B than A = 12 256 - 3064 = 9192. (b) To make both equal, move half the difference: 9192 ÷ 2 = 4596 books.


(a) The red bulb blinks every 6 minutes, so in 48 minutes it blinks 48 ÷ 6 = 8 times. (b) The bulbs blink together at multiples of the LCM of 4 and 6, which is 12 minutes. After 8.00 p.m., the next time they blink together is 12 minutes later, at 8.12 p.m.


In 38.479, the digit 7 is in the hundredths place. Its value is 7 hundredths = 0.07.


Convert \(1\dfrac{3}{5}\) to an improper fraction: \(1\dfrac{3}{5}=\dfrac{8}{5}\). So there are 8 one-fifths.


Look at the tenths digit (5). Since 5 \(\geq\) 5, round up: 13.592 rounds to 14.


21.73 + 4.98 = 26.71. Line up the decimal points and add: 73 + 98 hundredths = 171 hundredths (carry), giving 26.71.


Stickers left = \(1-\dfrac{2}{5}=\dfrac{3}{5}\) of the total = 27. So \(\dfrac{1}{5}=27\div3=9\), and the total \(=9\times5=45\) stickers.


\(\dfrac{3}{7}\): multiply numerator and denominator by 2 to get a denominator of 14, so the numerator is 6 (\(\dfrac{6}{14}\)). For \(\dfrac{9}{[?]}\), 9 = 3 x 3, so multiply 7 by 3 to get 21 (\(\dfrac{9}{21}\)).


The sequence increases by 100 each time: 67 852, 67 952, 68 052, 68 152, ... So the missing number is 68 052.


Remove the bag's extra cost: 285 - 57 = 228, which is the cost of 6 purses (1 bag now equals 1 purse). Each purse = 228 / 6 = $38.


She used 720 - 320 = 400 g more flour than sugar, so the sugar left is 400 g more than the flour left. Since sugar left is 6 times the flour left, the 5 extra units = 400 g, so 1 unit (flour left) = 400 / 5 = 80 g. Original flour = flour left + flour used = 80 + 720 = 800 g.


8974 ÷ 8: 8 into 89 is 11 r1; bring down 7 → 17, 8 into 17 is 2 r1; bring down 4 → 14, 8 into 14 is 1 r6. Quotient = 1121 remainder 6.


Convert the mixed number to an improper fraction: \(1\dfrac{5}{8}=\dfrac{1\times8+5}{8}=\dfrac{13}{8}\). So the missing value is 13.


7 units = 56, so 1 unit = 56 ÷ 7 = 8. Roses = 2 units = 8 × 2 = 16.


The remaining part of the journey is \(1-\dfrac{7}{10}=\dfrac{3}{10}\), which equals 480 m. So 3 units = 480 m, 1 unit = 480 ÷ 3 = 160 m. Whole journey = 10 units = 160 × 10 = 1600 m.


(a) Arthur and Ben started equal. After Arthur gives away 72, Ben = 4 × Arthur. The 72 stickers Arthur lost make Ben's amount the extra; the difference 72 equals 3 of Arthur's remaining units, so 3 units = 72, 1 unit = 24. Arthur had 24 stickers left. (b) Caleb received 72 stickers. He gave \(\dfrac{4}{9}\) away and kept \(\dfrac{5}{9}\): 1 unit = 72 ÷ 9 = 8, kept = 5 units = 8 × 5 = 40 stickers.


The tenths digit is 2 and the hundredths digit is 6. Since 6 ≥ 5, round the tenths digit up: 43.26 → 43.3.


16 ÷ 7 = 2.2857... To 2 decimal places, look at the 3rd decimal (5), round up: 2.29.


(a) Transport in 5 days = $2.70 × 5 = $13.50. (b) Money left after transport = $30 − $13.50 = $16.50. Food = remaining − savings = $16.50 − $1.80 = $14.70.


Remaining sugar = 5 − 0.32 = 4.68 kg. Each packet = 4.68 ÷ 6 = 0.78 kg.


After moving 4.55 kg, the difference between the bags becomes 26.5 + 2 × 4.55 = 35.6 kg. Bag A is now 5 times Bag B, so the difference is 4 units = 35.6 kg, giving 1 unit (Bag B now) = 35.6 ÷ 4 = 8.90 kg. Bag B at first = 8.90 + 4.55 = 13.45 kg.


Compare from the highest place value. Ten-thousands all 4; thousands: 46 327 and 46 825 have 6, 47 209 has 7, so 47 209 is largest. Between 46 327 and 46 825, hundreds 3 < 8, so 46 327 < 46 825. Smallest to greatest: 46 327, 46 825, 47 209.


The hundreds digit is 5, so round up. 39 565 rounds up to 40 000 to the nearest thousand.


A number with both 3 and 4 as factors must be divisible by both. 24 = 3 × 8 = 4 × 6, so both 3 and 4 divide 24. (15 not divisible by 4; 32 not by 3; 38 not by 3 or 4.)


A common multiple of 6 and 9 must be in both times tables. 36 = 6 × 6 = 9 × 4, so 36 is a multiple of both. (16 is neither; 42 = 6×7 but not a multiple of 9; 63 = 9×7 but not a multiple of 6.)


Erasers given away: 3986 - 2013 = 1973. Then 1973 - 750 = 1223. Mary had 1223 erasers left.


Multiply the monthly amount by the number of months: 346 × 7 = 2422. He spends $2422 in seven months.


(a) 1028 ÷ 4 = 257. (b) Product means multiply: 45 × 12 = 540.


Total oranges = 126 × 36 = 4536. Number of bags = 4536 ÷ 8 = 567. There were 567 bags.


Let 1 bag be 1 unit. Watch = 4 units. Watch + 3 bags = 4 + 3 = 7 units = $728. So 1 unit (1 bag) = 728 ÷ 7 = $104. Watch = 4 × 104 = $416.


Method: rename 7 as a fraction with denominator 5. \(7=\dfrac{35}{5}\). Then \(\dfrac{35}{5}-\dfrac{3}{5}=\dfrac{32}{5}=6\dfrac{2}{5}\).


Method: Tom jogged less than Siti, so subtract. \(\dfrac{4}{5}=\dfrac{8}{10}\). Tom = \(\dfrac{8}{10}-\dfrac{3}{10}=\dfrac{5}{10}=\dfrac{1}{2}\) km.


Method: \(\dfrac{2}{9}\) of the roses are red = 16, so 1 unit (\(\dfrac{1}{9}\)) = 16 \(\div\) 2 = 8 roses. Yellow is the rest: \(\dfrac{9}{9}-\dfrac{2}{9}=\dfrac{7}{9}\) = 7 units. Yellow roses = 8 \(\times\) 7 = 56.


Method: spent = \(\dfrac{2}{11}\) (2 units), saved = \(\dfrac{9}{11}\) (9 units). Saved is $749 more than spent: 9 units - 2 units = 7 units = $749. So 1 unit = 749 \(\div\) 7 = $107. Spent = 2 units = 2 \(\times\) 107 = $214.


The digit in the tens place is 3 (less than 5), so we round down. 47 832 rounds to 47 800.


Factors of 18 are 1, 2, 3, 6, 9, 18. 12 is not a factor of 18 (it is a factor of 36 only), so 12 is not a common factor.


To get from denominator 4 to 20, multiply by 5. So the numerator is 3 × 5 = 15. \(\dfrac{3}{4} = \dfrac{15}{20}\).


Let the start amount be n. Amelie: n − 35. Devna: n + 7 = 4(n − 35). So n + 7 = 4n − 140, giving 147 = 3n, n = 49. Amelie at the end = 49 − 35 = 14. (Check: Devna = 49 + 7 = 56 = 4 × 14.)


(a) The number is 18 (its largest factor). Factors of 18 are 1, 2, 3, 6, 9, 18; excluding 1 and 18 the others are 2, 3, 6, 9. (b) Multiples of 7 between 40 and 70: 42, 49, 56, 63. Adding 2 gives 44, 51, 58, 65; only 65 is a multiple of 5, so the number is 63.


Total stamps = 345 + 126 = 471 (unchanged when transferred). Current difference = 345 − 126 = 219. We want Benny to have 37 more than Caius, so the difference must drop from 219 to 37, a reduction of 219 − 37 = 182. Each stamp given reduces the gap by 2, so Benny gives 182 ÷ 2 = 91 stamps.


Fifty-eight thousand = 58 000; thirty-nine = 39. So 58 000 + 39 = 58 039.


Rounding to the nearest hundred gives 72 000 for any number from 71 950 to 72 049. 71 952 rounds to 72 000. (71 839 to 71 800; 72 050 to 72 100; 72 499 to 72 500.)


5 tenths = 0.5, the first digit after the decimal point. In 27.53 the 5 is in the tenths place, so it stands for 5 tenths.


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


The number must be a common multiple of 3 and 8, i.e. a multiple of 24, and fewer than 60. 48 is divisible by both 3 and 8 (48 = 3 x 16 = 8 x 6).


Perimeter = 2 x (length + breadth). 42 = 2 x (length + 6), so length + 6 = 21, length = 15 m.


The letter T has a vertical line of symmetry (left and right halves are mirror images). F, N and S have no line of symmetry.


Numbers from 2895 to 2904 round to 2900 to the nearest ten. The smallest is 2895.


Subtract the difference from the sum: 203 - 27 = 176. This is twice the smaller number, so smaller = 176 ÷ 2 = 88.


8 units = 624, so 1 unit = 624 ÷ 8 = 78. Blue = 5 units, pink = 3 units, difference = 2 units = 78 x 2 = 156.


(a) Every group of 3 bought + 1 free = 4 items. 72 ÷ 4 = 18 groups, so 18 x 1 = 18 free items. (b) Bala's $145 buys 145 ÷ 5 = 29 sets of 3 items. Each set gives 3 bought + 1 free = 4 items, so 29 x 4 = 116 items in total.


3 pens + 3 highlighters = 3 x $4.20 = $12.60. 3 pens + 5 highlighters = $17.40. Difference: 2 highlighters = $17.40 - $12.60 = $4.80, so 1 highlighter = $4.80 ÷ 2 = $2.40.


Reading 56 780 from the right: 0 is ones, 8 is tens, 7 is hundreds, 6 is thousands, 5 is ten thousands. The digit in the tens place is 8.


Order the three numbers from smallest to greatest. Comparing the tens/ones: 1035 < 1053 < 1305. So the correct arrangement is 1035, 1053, 1305.


A multiple of both 4 and 7 is a multiple of 28. 56 = 28 x 2, and 56 = 4 x 14 = 7 x 8. So 56 is a multiple of both 4 and 7.


Pens = 4 units, rulers = 1 unit. Difference = 3 units = 480, so 1 unit = 160. Rulers = 160, pens = 640. Total pens and rulers = 160 + 640 = 800.


Total = 2350. Remove the extra 80: 2350 - 80 = 2270, halve to get Zachary's share = 1135. Timothy = 1135 + 80 = 1215.


She used half plus a quarter of a pizza: 1/2 + 1/4 = 3/4 of a pizza gone. Left = 3 - 3/4 = 2 and 1/4 pizzas.


Cows are 7/9 of the animals, so sheep are 2/9. 126 / 9 = 14 per ninth. Sheep = 2 x 14 = 28.


Perimeter = 2 x (length + breadth). 96 / 2 = 48 = length + breadth. Length = 48 - 8 = 40 cm.


Giving 14 books to Ben reduces Alice's lead by 2 x 14 = 28. After giving, the lead is 29, so originally the lead was 29 + 28 = 57.


1 ring file = 2 notepads. So 1 ring file + 2 notepads = 2 + 2 = 4 notepad-units = $10.80. One notepad = 10.80 / 4 = $2.70.


Total girls = 12 + 15 + 7 = 34. Boys equal girls, so total boys = 34. Boys who liked burger = 34 - 20 - 6 = 8.


Forty thousand = 40 000; eleven = 11. Combined: 40 000 + 11 = 40011.


The thousandths place is the 3rd place after the decimal point. 8 thousandths = 0.008.


Multiply the whole number by the denominator and add the numerator: 3 x 7 + 3 = 24. Keep the denominator 7: 24/7.


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


To round to 4.0 (nearest tenth), the number must be from 3.95 up to 4.04 (since 4.05 rounds to 4.1). With 2 decimal places, the greatest value is 4.04.


(a) Ethan + Fedrick = 3/8 + 1/3 = 9/24 + 8/24 = 17/24. Germaine took the rest = 1 - 17/24 = 7/24. (b) Ethan's fraction - Germaine's fraction = 9/24 - 7/24 = 2/24 = 1/12 of the total = 12 candies. So total = 12 x 12 = 144 candies.


The digit 6 stands for 600 when 6 is in the hundreds place. In 7690, the 6 is in the hundreds place, so it stands for 600.


Compare the numbers: 4089 < 4809 < 4890. Only option 4 lists them from smallest to greatest.


Area of square = side × side. Side × side = 64, so side = 8 cm (since 8 × 8 = 64).


To round 39 520 to the nearest hundred, look at the tens digit (2). Since 2 < 5, round down: 39 520 ≈ 39 500.


The numerator 3 becomes 12, multiplied by 4. So the denominator 5 must also be multiplied by 4: 5 × 4 = 20.


Tank = 3 units, 2 buckets = 2 units, total = 5 units = 8.15 l. 1 unit (one bucket) = 8.15 ÷ 5 = 1.63 l.


Money left for butter cookies = 33.60 − 7.80 = 25.80. One packet = 25.80 ÷ 4 = $6.45.


Kelvin's duration = 1 h 10 min + 30 min = 1 h 40 min. Starting at 1145: 1145 + 1 h = 1245, + 40 min = 1325. Kelvin completed his run at 1325.


Find the highest common factor of 24 and 32. Factors of 24: 1,2,3,4,6,8,12,24. Factors of 32: 1,2,4,8,16,32. The greatest common factor is 8, so 8 gift bags.


Chocolate = \(\dfrac{4}{5}\) (4 units), vanilla = \(\dfrac{1}{5}\) (1 unit). Difference = 4 − 1 = 3 units = 240. 1 unit = 240 ÷ 3 = 80. Vanilla = 1 unit = 80 muffins.


(a) 455 × 12 = 5460 pens. (b) 5460 ÷ 8 = 682 remainder 4, so 4 pens are left unpacked.


(a) After giving, total is still 828, split as Fatimah:Ben = 1:3 = 4 units. 1 unit = 828 ÷ 4 = 207. Fatimah had 207 stamps in the end. (b) Ben in the end = 3 × 207 = 621. Ben at first = 621 − 68 (the stamps he received) = 553.


Belt = 1 unit, wallet = 2 units, shirt = 1 unit − $6. Total = 4 units − 6 = 90.80, so 4 units = 96.80, 1 unit = 96.80 ÷ 4 = $24.20 (belt). (b) Wallet = 2 units = 2 × 24.20 = $48.40.


(a) Samantha finished homework at 1535 + 1 h 5 min = 1640. She swam from 1640 to 1810 = 1 h 30 min. (b) Ken started 50 min before 1535 = 1445. He finished at 1445 + 1 h 25 min = 1610 = 4.10 pm.


Mobile phone = \(\dfrac{4}{7}\) (4 units), so remaining money = \(\dfrac{3}{7}\) (3 units). The 3 units = $65 + $190 = $255. 1 unit = 255 ÷ 3 = $85. Mobile phone = 4 units = 4 × 85 = $340.


In 20 561, the digit 5 is in the hundreds place. Its value is 5 hundreds = 500.


A number with both 3 and 5 as factors must be divisible by 3 and by 5. 15 = 3 × 5, so both 3 and 5 are factors of 15.


Compare whole-number parts first: 0.67 and 0.76 are less than 1; 7.06 and 7.6 are over 7. Order: 0.67, 0.76, 7.06, 7.6.


\(\dfrac{3}{5}\) of the class = 24 girls, so 1 unit (\(\dfrac{1}{5}\)) = 24 ÷ 3 = 8. Total class = 5 units = 8 × 5 = 40 students.


109 ÷ 7 = 15.57... ≈ 15.6 kg (correct to 1 decimal place).


Subtract 2 h 30 min from 01 25. 01 25 − 30 min = 00 55; 00 55 − 2 h = 22 55 (the previous day). Start time = 2255.


Giving 8 instead of 7 needs 1 more per friend; being short of 12 means there are 12 friends. Sweets = 7 × 12 = 84 (between 50 and 100).


(a) Walked = 6 km − 4 km 80 m = 1 km 920 m. (b) Difference = 4 km 80 m − 1 km 920 m = 2 km 160 m.


After the changes the total = 993 − 96 + 48 = 945. Each ended with 945 ÷ 3 = 315. Betty ended with 315 after buying 48, so Betty had 315 − 48 = 267 at first.


Thirty-two thousand = 32 000; forty-six = 46. Together: 32 046.


A fraction is in simplest form when numerator and denominator share no common factor other than 1. \(\dfrac{4}{10}=\dfrac{2}{5}\), \(\dfrac{2}{8}=\dfrac{1}{4}\), \(\dfrac{3}{6}=\dfrac{1}{2}\); only \(\dfrac{4}{9}\) cannot be reduced.


Compare digit by digit from the hundreds place. Greatest to smallest: 973, 937, 397, 379.


Make like denominators: 1/4 = 2/8. Then 2/8 + 5/8 = 7/8.


He arrived 10 min before 07 30, i.e. at 07 20. From 06 00 to 07 20 is 1 h 20 min.


Side = square root of 81 = 9 cm. Perimeter = 9 x 4 = 36 cm.


After the transfer the total stays the same and Noah = 4 x Liam, so the total is 5 units. The difference Noah - Liam = 3 units, which equals 18 + 18 = 36 (Liam lost 18, Noah gained 18). So 3 units = 36, 1 unit = 12. Liam had 1 unit = 12 marbles in the end.


Total lemonade = 13.59 + 3.75 = 17.34 l. 17.34 / 3 = 5 remainder 2.34, so 5 full bottles plus 1 more for the leftover = 6 bottles.


Let Wednesday = 1 unit, Tuesday = 3 units, Monday = 3 units + 1220. Total = 7 units + 1220 = 4398, so 7 units = 3178 and 1 unit = 454. Tuesday = 3 units = 3 x 454 = 1362 worksheets.


Assume all 12 are vans: 12 x 9 = 108. That is 108 - 88 = 20 too many. Each car instead of a van loses 9 - 5 = 4. So cars = 20 / 4 = 5 cars.


Jayden = 5/8, Linda = 3/8, so the total is 8 units, Jayden 5 units, Linda 3 units. The difference 5 - 3 = 2 units = 36, so 1 unit = 18. (a) Linda = 3 units = 54 apples. (b) Total = 8 units = 144 apples. 6 apples = $4, so 144 apples cost (144/6) x 4 = $96.


The pattern increases by 6 each time: 8, 14, 20, 26, 32, 38. The two missing numbers are 26 and 32.


Look at the tens digit (6). Since 6 is 5 or more, round the hundreds up: 34 762 rounds to 34 800.


The first digit after the decimal point is the tenths place. In 56.87 that digit is 8.


The number must be divisible by 4, by 7, and have 8 as a factor. 56 is divisible by 4 (56÷4=14), by 7 (56÷7=8) and by 8 (56÷8=7). So Mr Tan has 56 pencils.


Let each start with x. Alan now = x + 36, Brian now = x - 24. x + 36 = 4(x - 24) → x + 36 = 4x - 96 → 132 = 3x → x = 44. Each had 44 marbles at first.


4 m = 400 cm. Ribbon used for 5 pieces = 400 - 75 = 325 cm. Each piece = 325 ÷ 5 = 65 cm.


Fifteen thousand = 15 000; twenty-five = 25. Together: 15 025.


Multiply numerator and denominator of \(\dfrac{5}{6}\) by 2: \(\dfrac{5 \times 2}{6 \times 2} = \dfrac{10}{12}\). The missing number is 10.


Work backwards from 1125. Subtract 1 h to get 1025, then subtract 45 min to get 0940. Nadim started at 0940.


Let Ethan = 1 unit. David = 4 units. Fiona = 4 units - 60. Total = 1 + 4 + 4 units - 60 = 9 units - 60 = 1380, so 9 units = 1440, 1 unit = 160. David = 4 units = 4 × 160 = 640 stamps.


Total = 7 units = 1785, so 1 unit = 255. Non-fiction = 2 units, fiction = 5 units. Difference = 5 - 2 = 3 units = 3 × 255 = 765 more fiction books.


Compare the numbers: 4189 < 4819 < 4891. Option 4 lists them smallest to greatest.


A square has 4 equal sides. Length = perimeter ÷ 4 = 64 ÷ 4 = 16 m.


Highlighters are $3.50 − $2.80 = $0.70 cheaper each in July; pens are $2.60 − $1.70 = $0.90 cheaper each. Meiling (June) spends more by 6 × $0.70 + 4 × $0.90 = $4.20 + $3.60 = $7.80.


1 whole = \(\dfrac{6}{6}\), which is 6 sixths. So there are 6 one-sixths in 1 whole.


Compare tenths first: 0.807 (8 tenths) > 0.708 (7 tenths) > 0.078 (0 tenths). Greatest to smallest: 0.807, 0.708, 0.078.


0.4 means 4 tenths = \(\dfrac{4}{10}\). The missing denominator is 10.


(a) Boys in hall = total boys − boys in field = 315 − 127 = 188. (b) Total girls = 208 + 50 = 258.


Numbers rounding to 1200 to the nearest hundred lie from 1150 up to 1249. (a) Smallest = 1150. (b) Greatest = 1249.


1504 ÷ 5 = 300 remainder 4. The 4 leftover apples still need 1 more box, so 300 + 1 = 301 boxes.


Suppose all 30 are squares: 30 × 4 = 120 sides. Actual sides = 108, a shortfall of 120 − 108 = 12. Each triangle has 1 fewer side than a square (4 − 3 = 1), so number of triangles = 12 ÷ 1 = 12.


Each duck = 2 chickens, so 2 ducks = 4 chickens. Total = 5 + 4 = 9 chicken-units = 12.6 kg, so 1 chicken = 12.6 ÷ 9 = 1.4 kg. (b) 1 duck = 1.4 × 2 = 2.8 kg; 1 chicken + 1 duck = 1.4 + 2.8 = 4.2 kg.


Fiction = 7 units = 3528, so 1 unit (non-fiction) = 3528 ÷ 7 = 504. (a) More fiction than non-fiction = 6 units = 504 × 6 = 3024. (b) Altogether = 8 units = 504 × 8 = 4032.


Let boys = 2 units (so half remain = 1 unit) and girls = 4 units (so a quarter remain = 1 unit) to make the remainders equal. Girls − boys = 4u − 2u = 2u = 540, so 1 unit = 270. Boys = 540, girls = 1080. (a) Exited = half the boys + three-quarters of girls = 270 + 810 = 1080; equivalently 4 units = 270 × 4 = 1080. (b) Total at first = 6 units = 270 × 6 = 1620.


Lily is unchanged. In the end Lily = 6 units and Jasmine = 1 unit. Lily − Jasmine (end) = 5 units. The gap grew by the 1125 Jasmine sold: 2425 + 1125 = 3550 = 5 units, so 1 unit = 710. (a) Jasmine in the end = 1 unit = 710. (b) Lily = 6 units = 710 × 6 = 4260.


In 57.92 the first digit after the decimal point is the tenths place. That digit is 9.


\(\dfrac{1}{4}\) equals 3/12, 4/16 and 6/24 (each numerator is one-quarter of the denominator). \(\dfrac{7}{32}\) is not, since 7 × 4 = 28 ≠ 32. So \(\dfrac{7}{32}\) is not equivalent.


A number with both 2 and 3 as factors must be divisible by 6. Among the options, 18 = 6 × 3 is divisible by both 2 and 3.


Convert the mixed number to an improper fraction: \(6\dfrac{3}{8}\) = (6 × 8 + 3)/8 = (48 + 3)/8 = \(\dfrac{51}{8}\). The missing number is 51.


Total juice = 17.82 + 5.18 = 23 l. Each jug = 23 ÷ 8 = 2.875 l. Rounded to the nearest tenth = 2.9 l.


The letter C has a horizontal line of symmetry (top and bottom halves mirror each other). G, N and K have no line of symmetry.


Need a number 20–50 that leaves remainder 4 when divided by 6 and remainder 2 when divided by 8. Check 34: 34 ÷ 6 = 5 r4 ✓ and 34 ÷ 8 = 4 r2 ✓. So Bala has 34 stickers.


Twenty thousand = 20 000, and forty-one = 41. Combine: 20 000 + 41 = 20 041.


Look at the tens digit of 18 430, which is 3. Since 3 < 5, round down: 18 430 → 18 400.


Each piece = 3 ÷ 7 = 0.428... m. Rounded to the nearest hundredth (2 decimal places) = 0.43 m.


(a) Total bought = 24 × 32 = 768 sweets. (b) Sweets given away = 12 × 40 = 480. Sweets left = 768 − 480 = 288.


Let red = 1 unit. Blue = 2 units, green = 3 × blue = 6 units. Blue + green = 2 + 6 = 8 units = 1728, so 1 unit = 1728 ÷ 8 = 216. (a) Green = 6 units = 6 × 216 = 1296. (b) Red = 1 unit = 216, so green − red = 1296 − 216 = 1080.


(a) 3 tables + 5 stools = 173.1; 1 table + 3 stools = 65.3. Tripling the second: 3 tables + 9 stools = 195.9. Subtract the first: 4 stools = 195.9 − 173.1 = 22.8 kg, so 1 stool = 5.7 kg. From the second: 1 table = 65.3 − 3 × 5.7 = 65.3 − 17.1 = 48.2 kg. Table + stool = 48.2 + 5.7 = 53.9 kg. (b) 4 stools = 4 × 5.7 = 22.8 kg.


Let Dan's amount at the end be 1 unit; then Evan (unchanged) is 3 units. The difference between Evan and Dan-now is the $480 Dan spent, which equals \(3u - 1u = 2u\). So \(2u = \$480\), giving \(1u = \$240\) (Dan in the end). Dan at first = Evan = \(3u = 3 \times \$240 = \$720\).


Fraction that are sheep, ducks and horses \(= \dfrac{1}{6} + \dfrac{1}{3} + \dfrac{1}{4} = \dfrac{2}{12} + \dfrac{4}{12} + \dfrac{3}{12} = \dfrac{9}{12} = \dfrac{3}{4}\). So rabbits are \(1 - \dfrac{3}{4} = \dfrac{1}{4}\), i.e. 3 of 12 equal units = 90. Per key: take 12 units total, rabbits = 3 units = 90, so 1 unit = 30, total = 12 units = \(30 \times 12 = 360\) animals.


Ninety-four thousand = 94 000; eight hundred = 800; and seven = 7. So \(94000 + 800 + 7 = 94807\). The numeral is 94 807.


Factors of 4: 1, 2, 4. Factors of 8: 1, 2, 4, 8. A common factor must divide BOTH numbers. Among the options, only 4 divides both 4 and 8. So the answer is 4.


A child gets both if their position is a common multiple of 4 and 5, i.e. a multiple of 20. Within 40, these are positions 20 and 40. So 2 children received both.


Try 1953: \(1953 + 1 = 1954\), which rounds to 1950. \(1953 + 2 = 1955\), which rounds to 1960. Both conditions are satisfied, so the number is 1953.


To make the largest number, arrange the digits from greatest to smallest: 7, 6, 4, 1. So the largest number is 7641.


The first two multiples of 5 are 5 and 10. Their sum is \(5 + 10 = 15\).


Numbers from 2550 to 2649 round to 2600 (to the nearest hundred). The largest of these is 2649.


If all 20 were plates: \(20 \times 3 = 60\) dollars. The actual total is $86, which is \(86 - 60 = 26\) more. Each bowl is \(5 - 3 = 2\) dollars more than a plate, so number of bowls = \(26 \div 2 = 13\). Sarah sold 13 bowls.


Let Sophie have 1 unit at first, so Ethan had 2 units. After using 36, Ethan had \(2\text{ units} - 36\), and this equals half of Sophie's, i.e. Sophie's 1 unit = \(2 \times (2\text{ units} - 36)\). So \(1\text{ unit} = 4\text{ units} - 72\), giving \(3\text{ units} = 72\), so 1 unit = 24. Sophie had 24 beads at first.


(a) Table + chair = total - bookshelf = \(1400 - 630 = 770\) dollars. (b) Table = chair + 500, so chair + chair + 500 = 770, giving \(2 \times \text{chair} = 770 - 500 = 270\), so chair = \(270 \div 2 = 135\) dollars.


Forty-five thousand = 45 000, nine hundred = 900, and six = 6. Adding these gives 45 000 + 900 + 6 = 45 906. The answer is option (3), 45 906.


Decreasing order means largest to smallest. Compare the thousands: 86 372 and 86 237 both have 86 thousands, and 85 327 has 85 thousands so it is smallest. Between 86 372 and 86 237, the hundreds 3 > 2, so 86 372 > 86 237. Order: 86 372, 86 237, 85 327. The answer is option (2).


Each term increases by 100: 62 831 + 100 = 62 931, then 62 931 + 100 = 63 031. Checking forward, 63 031 + 100 = 63 131 which matches. The missing number is 63 031, option (3).


Rounding to the nearest hundred: 83 875 rounds to 83 900; 83 953 rounds to 84 000; 84 092 rounds to 84 100; 84 234 rounds to 84 200. Only 83 953 rounds to 84 000. The answer is option (2).


A number with both 4 and 7 as factors must be a multiple of \(4 \times 7 = 28\). Checking: 11 (no), 21 = 3 x 7 (only 7), 64 = 4 x 16 (only 4), 84 = 28 x 3 (both 4 and 7). The answer is option (4), 84.


The first guest to get both is the lowest common multiple of 6 and 8. Multiples of 6: 6, 12, 18, 24; multiples of 8: 8, 16, 24. The smallest common multiple is 24, so the 24th guest is first to get both. The answer is option (3).


a) In 58 701 the digit 7 is in the hundreds place, so its value is \(7 \times 100 = 700\). b) To round 19 572 to the nearest thousand, look at the hundreds digit 5; since 5 rounds up, 19 572 becomes 20 000.


Check whether 4 divides each number. 96 divided by 4 is 24 with no remainder, so 4 is a factor of 96 (Ariel is correct). 76 divided by 4 is 19 with no remainder, so 4 is a factor of 76 (Tom is correct). Both are correct, so the correct statement is 'Both Ariel and Tom are correct.'


Total stamps: \(75 \times 26 = 1950\). Each bag holds 5 stamps, so number of bags: \(1950 \div 5 = 390\). There are 390 bags.


Let a chair be 1 unit; a desk is then 2 units. 2 desks = 4 units and 4 chairs = 4 units, giving \(4 + 4 = 8\) units. So 8 units = $2264 and 1 unit = \(2264 \div 8 = 283\). A desk and a chair together = 2 units + 1 unit = 3 units = \(283 \times 3 = 849\). The total cost is $849.


Each friend gets 2 more sweets in the second case (\(6 - 4 = 2\)), and the leftover drops by \(22 - 8 = 14\) sweets. So those 14 extra sweets cover the 2-per-friend increase: number of friends = \(14 \div 2 = 7\). Total sweets = (4 sweets x 7 friends) + 22 left over = \(28 + 22 = 50\). Sandy had 50 sweets.


Forty-six thousand = 46 000, and sixteen = 16. 46 000 + 16 = 46 016. Option (3).


The 8 must be in the tens place to stand for 80. In 3082 the 8 is in the tens place (80). Option (2).


Look at the tens digit (2). Since 2 < 5, round down: 13 429 to the nearest hundred is 13 400. Option (3).


Make denominators the same: \(\dfrac{1}{3}=\dfrac{3}{9}\). Then \(\dfrac{3}{9}+\dfrac{1}{9}=\dfrac{4}{9}\). Option (4).


To round to 1 decimal place, look at the hundredths digit (4). Since 4 < 5, keep the tenths digit: 17.54 to 1 d.p. is 17.5. Option (2).


$55 - $25 = $30 is the cost of 3 shirts' worth (2 shirts + 1 shirt-equivalent of pants). 3 units = $30, so 1 shirt = $10. Option (1).


83 905 = 80 000 + 3000 + 900 + 5. The missing number is 900 (the hundreds value).


Compare tenths first: 3.909 has 9 tenths (largest). Then 3.099 vs 3.093 — hundredths equal (9), thousandths 9 > 3, so 3.099 > 3.093. Order greatest to smallest: 3.909, 3.099, 3.093.


Find the common factors of 36 and 54: 1, 2, 3, 6, 9, 18. The greatest common factor is 18, so the greatest number of boxes is 18.


Jonathan = 1.81 - 0.35 = 1.46 m. Elson is 0.29 m taller than Jonathan: 1.46 + 0.29 = 1.75 m.


The watch is 15 min slow, so the actual time is 15 min later: 1.35 p.m. + 15 min = 1.50 p.m. = 13 50 in the 24-hour clock.


Two facing pages are consecutive numbers. Sum = 667, so the smaller page = (667 - 1) ÷ 2 = 666 ÷ 2 = 333.


Let Joey = 1 unit, Nicole = 5 units. After giving away: 5u - 235 = 1u - 19, so 4u = 235 - 19 = 216, 1u = 54. (a) Nicole baked 5u = 5 × 54 = 270. (b) Each had 1u - 19 = 54 - 19 = 35 in the end.


Mrs Devi sold \(\dfrac{7}{9}\) of her muffins (since \(\dfrac{2}{9}\) are left) = 49, so 7 units = 49, 1 unit = 7. (a) Left = 2 units = 2 × 7 = 14. (b) Each baked 9 units = 9 × 7 = 63; total for both = 63 × 2 = 126.


Charlie's marbles never change. At first Charlie = 2 × Sally. After Sally loses 45, Charlie = 5 × (new Sally). Let new Sally = 1 unit, Charlie = 5 units; original Sally = 5u ÷ 2. Since Sally lost 45: 5u/2 - 45 = u, giving 3u/2 = 45, u = 30. Charlie = 5u... using the key: 3u = 45 + 45 = 90, 1u = 30, Charlie = 5 × 30 = 150.


Catherine - Alice = (Benny+Catherine) - (Alice+Benny) = 450 - 100 = 350. Catherine is 5 times Alice, so Catherine - Alice = 4 units = 350, 1 unit = 350 ÷ 4 = $87.50. Alice (1 unit) received $87.50.


Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. 56 ÷ 6 = 9 remainder 2, so 6 is not a factor.


4/9: no common factor of 4 and 9 except 1, so it is in simplest form. 2/8 = 1/4, 3/12 = 1/4, 6/10 = 3/5.


Morning: 9 a.m. to 12 p.m. = 3 h. Afternoon: 1.30 p.m. to 4.30 p.m. = 3 h. Total painting time = 3 h + 3 h... wait, 3 h + 3 h would be 6 h, but lunch (12 to 1.30) is excluded. Total = 3 h + 3 h = 6 h? Actual painting: 3 h + 3 h = 6 h. Key gives option 1 (5 h 30 min); morning 9 to 12 = 3 h, afternoon 1.30 to 4.30 = 3 h, total painting 6 h. See notes.


Must reach gate by 30 min before 15 05 = 14 35. She walks 20 min, so she must start by 14 35 - 20 min = 14 15.


Male adults = total 246 − children 119 = 127. Total adults = male adults 127 + female adults 230 = 357.


The pattern repeats every 6 letters: C, A, B, C, D, E. 50 ÷ 6 = 8 remainder 2, so the 50th letter is the 2nd letter of the block, which is A.


4 files cost 4 × $0.70 = $2.80 more than 4 rulers. Remove this: $9.60 − $2.80 = $6.80 for 8 rulers' worth. $6.80 ÷ 8 = $0.85 per ruler.


Best three of four must total ≥ 30. The two highest existing scores are 10.1 + 9.5 = 19.6. The 4th game must make the best three reach 30: 30 − 19.6 = 10.4. So the lowest 4th-game score is 10.4.


0.39 = 39 hundredths = 39/100. 39 and 100 share no common factor, so it is already in simplest form.


Buy 2 get 1 free: for 6 bars taken home, Raju pays for only 4 bars. 4 × $5.50 = $22. Change = $50 − $22 = $28.


Let Aunt Mei have M. Uncle Lee had 3M. After selling 75: 3M − 75. Aunt Mei is now twice his: M = 2(3M − 75) → M = 6M − 150 → 150 = 5M → M = 30. (Per key working: 75 ÷ 5 = 15; total parts give Aunt Mei 30.)


The digit 8 stands for 800 when it sits in the hundreds place. In 5840, the 8 is in the hundreds place, so it stands for 800. In 4058 it is 8, in 5084 it is 80, in 8504 it is 8000.


To round 45 879 to the nearest hundred, look at the tens digit (7). Since 7 is 5 or more, round the hundreds up: 45 879 rounds to 45 900.


Compare the fractions: 4/9 is just under a half (4.5/9 = 1/2), so 4/9 < 1/2. And 8/9 is the largest. Ordered smallest to greatest: 4/9, 1/2, 8/9.


Compare the decimals by place value. 3.038 has 0 tenths and 3 hundredths, the smallest of all. 3.07 = 3.070, 3.15, 3.304 are all larger. So 3.038 is smallest.


Convert 7/20 to a decimal: multiply numerator and denominator by 5 to get 35/100 = 0.35. So 4 7/20 = 4.35.


Factors of 28 below 10: 1, 2, 4, 7. Of these, the multiples of 4 are: 4. So Adam is 4 years old. (8 is a multiple of 4 but not a factor of 28.)


Let Azri's amount after giving away be 1 unit; Liying = 5 units. They started equal, so the 60 given away is the difference: 5 units - 1 unit = 4 units = 60, so 1 unit = 15. Azri started with the same as Liying = 5 units = 75 stamps.


To round to 175, the decimal must be at least 174.5 (rounds up) and below 175.5. 174.49 rounds to 174 (too small). 174.50 rounds up to 175 and is the smallest of the options that rounds to 175.


Compare the numbers by place value. 5064 (thousands 5, hundreds 0), 5604 (hundreds 6), 5640 (hundreds 6, tens 4). Smallest to greatest: 5064, 5604, 5640.


The factors of 18 are 1, 2, 3, 6, 9, 18. The ones not listed are 6 and 9.


Multiply the whole number by the denominator and add the numerator: 3 x 5 + 4 = 19. So 3 4/5 = 19/5.


Make the denominators the same: 1/4 = 2/8. Then 2/8 + 5/8 = 7/8.


Peaches are the remaining fraction: 1 - 3/8 = 5/8. Number of peaches = 5/8 x 872 = 5 x 109 = 545.


Let 1 skirt = 1 unit. Dress = 1 unit + $65.50. Total = 3 units + $65.50 = $250, so 3 units = $184.50, 1 unit = $61.50. One skirt costs $61.50.


Total = 6 units = 1200, so 1 unit = 200. Steven = 200, Johnson = 1000. To be equal each must have 600. Johnson must give Steven 1000 - 600 = 400 sweets. (Equivalently, give 2 units = 400.)


Let 4B = 1 unit, 4C = 3 units, so 4B+4C = 4 units. 4A = 4 units - 123. Total = (4 units) + (4 units - 123) = 8 units - 123 = 3445. So 8 units = 3568, 1 unit = 446. Class 4B collected 446 kg.


After giving away, the difference between Lisa and Zara = 10 - 1.5 + 0.5 = 9 kg. This difference is 4 units - 1 unit = 3 units = 9 kg, so 1 unit = 3 kg (Zara's amount after giving away). Zara at first = 3 + 0.5 = 3.5 kg.


Rounding to the nearest hundred: 59 951 rounds to 60 000 (the tens digit 5 rounds up). 59 599 rounds to 59 600; 60 070 rounds to 60 100; 60 140 rounds to 60 100.


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


\(\dfrac{4}{6} = \dfrac{2}{3}\). Checking: \(\dfrac{12}{18} = \dfrac{2}{3}\), so it is equivalent.


In 41.32, the first decimal place (tenths) is 3 and the second (hundredths) is 2. So the digit in the hundredths place is 2.


The pattern decreases by 30 each time: \(875 - 845 = 30\). So the missing term is \(815 - 30 = 785\) (and \(785 - 30 = 755\) checks).


\(\dfrac{3}{6} = \dfrac{1}{2}\) and \(\dfrac{6}{8} = \dfrac{3}{4}\) can be simplified. \(\dfrac{2}{5}\) and \(\dfrac{5}{7}\) cannot, so they are already in simplest form.


\(52 = 1 \times 52 = 2 \times 26 = 4 \times 13\). So all factors are 1, 2, 4, 13, 26, 52. The other two are 13 and 26.


The number must be a common multiple of 3 and 8, i.e. a multiple of 24, and fewer than 50. Multiples of 24 below 50 are 24 and 48; the greatest is 48.


(a) Let Priscilla = P. Victor = P − 180, William = P + 20. Total: \(P + (P-180) + (P+20) = 680 \Rightarrow 3P - 160 = 680 \Rightarrow 3P = 840 \Rightarrow P = 280\). (b) Victor at first = \(280 - 180 = 100\). Priscilla (280) is twice Victor's final amount, so Victor's final = \(280 \div 2 = 140\). Victor bought \(140 - 100 = 40\).


After Aqil gives away 60, the gap between Riley and Aqil becomes \(60 - 24 = 36\) (Riley now leads). Riley = 4 × Aqil(now), so the gap = 3 units = 36, giving 1 unit = \(36 \div 3 = 12\) = Aqil now. Aqil at first = \(12 + 60 = 72\).


Place value: the digit 8 stands for 800 only when 8 is in the hundreds place. In 4823, the 8 is in the hundreds place, so it stands for 800.


A common multiple of 4 and 6 is a multiple of 12. Among the options, 36 = 12 × 3 is a multiple of both 4 (4×9) and 6 (6×6). The others are not.


2/3 = 4/6 = 6/9 = 12/18 (multiply numerator and denominator by the same number). 18/24 simplifies to 3/4, which is not equal to 2/3, so it is not equivalent.


Purple = 40 − 10 − 18 = 12 marbles. Fraction purple = 12/40 = 3/10.


Compare by place value. Greatest to smallest: 984, 948, 498, 489.


Forty thousand = 40 000; thirty-seven = 37. Together: 40 000 + 37 = 40037.


After giving, each has 842 ÷ 2 = 421 stamps. Ali had 79 more before giving, so Ali at first = 421 + 79 = 500 stamps.


Sophie starts $1304 − $1240 = $64 ahead. Amanda gains $20 − $12 = $8 more each day. Days to catch up = 64 ÷ 8 = 8 days.


The difference between the two purchases is 3 erasers = $7.30 − $6.10 = $1.20, so 1 eraser = $0.40. Then 4 erasers = $1.60, so 3 pencils = $6.10 − $1.60 = $4.50, and 1 pencil = $4.50 ÷ 3 = $1.50.


Buying 5 and getting 1 free gives 6 doughnuts for $10. Two such sets give 12 doughnuts for $20. She still needs 3 more at $2 each = $6. Total = $20 + $6 = $26.


Total potatoes = 110.25 + 24.75 = 135 kg. Number of 3 kg bags = 135 ÷ 3 = 45. Money received = 45 × $6 = $270.


Apple = 4. Blueberry = 2 × 4 = 8. Chocolate = 8 + 3 = 11. Total = 4 + 8 + 11 = 23 tarts.


New total in April = 312 + 8 = 320. Tennis is still 40. Fraction = 40/320 = 1/8.


Red is 1/4 = 5/20 of the files and equals 40, so 5 units = 40, 1 unit = 8 (where 1 unit = 1/20). Yellow = 12 units = 96; purple = 3 units = 24. Difference = 96 − 24 = 72.


Let the bag be 1 unit; the watch is 6 units. The difference 6 − 1 = 5 units = $91.25, so 1 unit (bag) = $18.25. Watch + 3 bags = 6 + 3 = 9 units = 9 × $18.25 = $164.25.


Let the starting number of each be N. Pens left = N − 1852; rulers left = N − 547. Rulers left = 4 × pens left, so the extra rulers (1852 − 547 = 1305) equal 3 times the pens left: 3 units = 1305, 1 unit = 435 (pens left). Pens at first = 435 + 1852 = 2287.


The two numbers add to 29. A factor of 45 (1,3,5,9,15,45) plus a multiple of 5 (5,10,15,20,25,...) = 29: 9 + 20 = 29 works (9 is a factor of 45, 20 is a multiple of 5). Difference = 20 − 9 = 11.


To make the difference smallest, make the 2-digit number as large as possible: the largest 2-digit number is 99, so the 3-digit number is 561 − 99 = 462. Difference = 462 − 99 = 363.


In a decimal, the first digit after the decimal point is the tenths place. In \(125.34\) the digit after the point is 3, so the tenths digit is 3.


Compare whole-number parts first: \(0.67\) and \(0.76\) are less than 1; \(6.07\) and \(6.7\) are more than 6. Within each pair compare tenths: \(0.67 < 0.76\) and \(6.07 < 6.70\). Order: 0.67, 0.76, 6.07, 6.7.


(a) \(\dfrac{73}{100}\) means 73 hundredths \(= 0.73\), so \(5\dfrac{73}{100} = 5.73\). (b) Look at the hundredths digit of \(45.999\), which is 9 (≥5), so round the tenths up: \(45.999 \approx 46.0\).


First find Rope P: \(23.06 - 14.78 = 8.28\) m. The difference between Rope P and Rope Q is \(14.78 - 8.28 = 6.5\) m.


Sugar left after using some: \(10.5 - 3.5 = 7\) kg. Repacked equally into 5 boxes: \(7 \div 5 = 1.4\) kg per box.


(a) Juice poured out is 3.85 ℓ, so juice left \(= 6 - 3.85 = 2.15\) ℓ. (b) The 3.85 ℓ poured out is shared equally into 7 cups: \(3.85 \div 7 = 0.55\) ℓ in each cup.


In \(17.48\) the digit right after the decimal point is the tenths place. That digit is \(4\). (The \(8\) is in the hundredths place.) Answer: \(4\).


To round to 1 decimal place, look at the hundredths digit. \(39.95\) has hundredths digit \(5\), so round the tenths up: \(39.9\to40.0\). Answer: \(40.0\).


One kettle holds \(1.2+2.5=3.7\) \(l\) (the bottle has 2.5 l less than a kettle). For 4 kettles: \(3.7\times4=14.8\) \(l\). Answer: \(14.8\) \(l\).


(a) Mrs Tan's amount is unchanged. At the start Mrs Siva had \(7.86\) kg more than Mrs Tan; after using \(10\) kg, Mrs Siva is now \(10-7.86=2.14\) kg less than Mrs Tan. So Mrs Tan has \(2.14\) kg more than Mrs Siva in the end. (b) In the end Tan = 3 × Siva, so the difference (Tan − Siva) = 2 units = \(2.14\) kg, giving 1 unit = Siva = \(2.14\div2=1.07\) kg. Answers: (a) \(2.14\) kg, (b) \(1.07\) kg.


The digit 3 in 57.43 is in the hundredths place. Its value is \(3 \times 0.01 = 0.03\).


The hundredths digit is 8; the thousandths digit is 6 (≥5), so round up. \(32.786 \approx 32.79\).


Compare digit by digit after the units: 2.168 < 2.186 < 2.681 < 2.816. Increasing order is 2.168, 2.186, 2.681, 2.816.


Let a purse be 1 unit; a bag is 4 units. Bag + 2 purses = 4 + 2 = 6 units = $33, so 1 unit = $5.50. A bag = 4 units = \(4 \times 5.50 = 22\).


\(6 \div 7 = 0.857...\). The second decimal digit is 5, so round up the first decimal place: \(0.857... \approx 0.9\).


After using 4.09 kg, Mrs Tan's amount is (Tan first − 4.09). Mrs Sim = Tan first − 2.53. Sim = 4 × Tan's remaining: \(T - 2.53 = 4(T - 4.09)\). So \(T - 2.53 = 4T - 16.36\), giving \(3T = 13.83\) and \(T = 4.61\) kg. (Equivalently the difference 4.09 − 2.53 = 1.56 kg equals 3 units of Tan's remainder; 1 unit = 0.52 kg; Tan first = 0.52 + 4.09 = 4.61 kg.)


From the 1st flag to the 6th flag there are 5 gaps: \(27 \div 5 = 5.4\) m per gap. With 8 flags around a closed border there are 8 equal gaps: \(5.4 \times 8 = 43.2\) m.


The number of beads Mrs Tan bought when rounded to the nearest hundred is 4500. What is the greatest possible number of beads that she bought?

A number rounds to 4500 to the nearest hundred when it is from 4450 to 4549. The greatest such number is 4549, since 4550 would round up to 4600.


Look at the number sequence carefully.
24, 28, 32, 36, 40, … …
What is the 20th number?

The sequence increases by 4 each time, starting at 24. The number of 4s added is 1 less than the position, so the 20th term adds \(19 \times 4 = 76\). Then \(76 + 24 = 100\).


What is the remainder when 5729 is divided by 9? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


List down all the common factors of 15 and 42. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Factors of 15: 1, 3, 5, 15. Factors of 42: 1, 2, 3, 6, 7, 14, 21, 42. The common factors are 1 and 3.


(a) Find the 7th multiple of 4.
(b) List down the second common multiple of 6 and 9.
(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 7th multiple of 4 is \(7 \times 4 = 28\). (b) Multiples of 6: 6, 12, 18, 24, 30, 36, …; multiples of 9: 9, 18, 27, 36, …. Common multiples are 18 (1st) and 36 (2nd), so the second common multiple is 36.


Denise has some stamps and pens. She has as many stamps as pens. When she gives each friend 3 pens, she will have 9 pens left. When each friend gets 4 stamps from Denise, she will have 6 extra stamps. How many friends does Denise have? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the number of friends be a value. Pens = \(3 \times \text{friends} + 9\) and stamps = \(4 \times \text{friends} + 6\). Since stamps equal pens, \(3 \times \text{friends} + 9 = 4 \times \text{friends} + 6\), so \(9 - 6 = 4 \times \text{friends} - 3 \times \text{friends}\), giving friends = 3. (Check: 3 friends → pens = \(3 \times 3 + 9 = 18\), stamps = \(4 \times 3 + 6 = 18\).)


Devi baked 675 cookies on Saturday. She baked 4 times as many cookies on Sunday as on Saturday.
(a) How many cookies did she bake on Sunday?
(b) Devi packed all the cookies that she baked on Saturday into boxes. Each box had 5 cookies. How many boxes of cookies did she pack? Round your answer to the nearest ten.
(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) Sunday = 4 times Saturday = \(675 \times 4 = 2700\) cookies. (b) Boxes = \(675 \div 5 = 135\) boxes; rounded to the nearest ten this is 140.


\(12\,608 = 10\,000 + 2000 + + 8\)<br>What is the missing number in the box?

Method: subtract the known parts from the total. \(12\,608 - 10\,000 - 2000 - 8 = 600\). The missing number is 600 (the hundreds place value of 12 608).


What is the missing numerator in the box?<br>\(4\dfrac{1}{3} = \dfrac{ }{3}\)

Method: convert the mixed number to an improper fraction. \(4\dfrac{1}{3} = \dfrac{4 \times 3 + 1}{3} = \dfrac{13}{3}\). The missing numerator is 13.


Method: test divisibility by 4. \(16 = 4 \times 4\), \(32 = 4 \times 8\), \(60 = 4 \times 15\) — all divisible. \(27 \div 4 = 6\,R3\), so 4 is not a factor of 27.


(a) What is the first common multiple of 3 and 7? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Round 18 067 to the nearest hundred. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) List multiples: 3, 6, 9, 12, 15, 18, 21... and 7, 14, 21... The first common multiple is 21 (\(3 \times 7\)). (b) The tens digit of 18 067 is 6, which is 5 or more, so round up: 18 067 rounds to 18 100.


Harry bought some brownies. He packed them into boxes of 6. Then, he had 48 boxes of brownies and 5 brownies were left unpacked. How many brownies did Harry buy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: brownies in full boxes \(= 48 \times 6 = 288\). Add the 5 unpacked: \(288 + 5 = 293\). Harry bought 293 brownies.


Jenny bought 2 tables and 3 chairs. Each table cost twice as much as a chair. Jenny spent a total of $378.
(a) Find the cost of a chair. \(\\)<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Find the cost of the 2 tables. \(\\)<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Method (units): a table = 2 chair-units. 2 tables = 4 units, 3 chairs = 3 units, total = 7 units = $378. (a) 1 chair = \(378 \div 7 = \$54\). (b) 2 tables = 4 units = \(54 \times 4 = \$216\).


Which of the following is thirteen thousand, nine hundred and twenty in numerals?

Thirteen thousand = 13 000, nine hundred = 900, twenty = 20. Combine: 13 000 + 900 + 20 = 13 920. Answer: 13 920.


In 72 140, which digit is in the tens place?

In 72 140, reading from the right: 0 is ones, 4 is tens, 1 is hundreds, 2 is thousands, 7 is ten thousands. The tens digit is 4.


In which of the following numbers does the digit 3 have the greatest value?


Which of the following numbers when rounded off to the nearest ten becomes 72 500?


Peter drew a repeated pattern using some letters on his drawing paper. The first 21 letters are A B C D C B A A B C D C B A A B C D C B A. What is the 80th letter?

The pattern repeats in blocks of 7 letters: A B C D C B A. 80 divided by 7 = 11 remainder 3. The remainder 3 points to the 3rd letter of the block, which is C.


(a) Arrange the following numbers from the greatest to the smallest.
3899, 9938, 9983, 3998
<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="?" />
(b) Write the missing number in the number pattern.
4549, 4699, 4849, <input type="text" id="input_4" class="fill-blank-input" placeholder="?" /> , 5149, 5299

(a) Compare the numbers: the two starting with 9 are larger. 9983 > 9938; then 3998 > 3899. Greatest to smallest: 9983, 9938, 3998, 3899. (b) The pattern increases by 150 each step (4549, 4699, 4849, ...). 4849 + 150 = 4999.


(a) Some factors of 28 are 1, 2, 4 and 28. What are the other two factors of 28?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
(b) Find the first common multiple of 4 and 6.
<input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

(a) The factors of 28 are 1, 2, 4, 7, 14, 28. The two not listed are 7 and 14. (b) Multiples of 4: 4, 8, 12, ...; multiples of 6: 6, 12, ... The first common multiple is 12.


(a) What is the product of 207 and 86?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What is the quotient when 8017 is divided by 9?
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Ali bought a packet of sweets. When he put the sweets into bags of 6, he would have no sweets left. When he put them into bags of 8, he would have 4 sweets left. The packet contained more than 40 but less than 70 sweets. How many sweets were there in the packet?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

A multiple of 6 between 40 and 70: 42, 48, 54, 60, 66. Numbers that leave remainder 4 when divided by 8 (i.e. 4 more than a multiple of 8: 44, 52, 60, 68). The number in both lists is 60.