Which two fractions are in the simplest form?
\(\dfrac{3}{9}\), \(\dfrac{2}{5}\), \(\dfrac{2}{6}\), \(\dfrac{3}{8}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

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


Use all the digits given to form the greatest odd number.
2, 9, 4, 8, 5
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

For the greatest odd number, the ones digit must be the smallest available odd digit (5). Arrange the remaining digits 9, 8, 4, 2 in descending order in front: 9842, giving 98 425.


Mrs Lee mixed 1.4 \(l\) of orange syrup with 3.16 \(l\) of water. She poured the mixture equally into 4 bottles. How many litres of the mixture were there in each bottle?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total mixture = 1.4 + 3.16 = 4.56 \(l\). Shared equally into 4 bottles: 4.56 ÷ 4 = 1.14 \(l\) each.


The mass of 4 similar boxes was 5.04 kg. 2 boxes were removed. What was the mass of the new stack of boxes?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Removing 2 of the 4 identical boxes leaves half the mass: 5.04 ÷ 2 = 2.52 kg.


A fruit seller had 170 pears and oranges altogether. After he sold \(\dfrac{2}{3}\) of the pears and 14 oranges, he had an equal number of pears and oranges left. How many oranges were there in the end?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After selling, pears left = \(\dfrac{1}{3}\) of pears and oranges left = oranges − 14, and these two are equal. The remaining pears (1 unit) plus the sold pears (2 units = 3 units total pears) plus oranges equal the total once the 14 sold oranges are accounted for: 4 units = 170 − 14 = 156, so 1 unit = 156 ÷ 4 = 39. The oranges left equal the remaining pears = 39.


There were some sweets in a box. Evelyn took \(\dfrac{5}{8}\) of the sweets and Nigel took the rest. Evelyn took 76 more sweets than Nigel.
(a) What fraction of the sweets did Nigel take?
(b) How many sweets were in the box at first?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Nigel took 1 − \(\dfrac{5}{8}\) = \(\dfrac{3}{8}\). (b) Evelyn − Nigel = \(\dfrac{5}{8} - \dfrac{3}{8} = \dfrac{2}{8}\) of the sweets = 76, so \(\dfrac{1}{8}\) = 38 and the whole box = 8 × 38 = 304 sweets.


John and Peter had a total of $540. After John gave Peter $40, he had five times as much money as Peter.
(a) How much money did Peter have in the end?
(b) How much money did John have at first?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

The total stays $540. In the end John = 5 units and Peter = 1 unit, so 6 units = $540 and 1 unit = $90. (a) Peter has $90 in the end. (b) John had $490 at first ($90 × 5 = $450 at the end, plus the $40 he gave away = $490).


In a library, there were English, Chinese and Malay books. The number of English and Chinese books was 720. The English books were twice as many as the Chinese books and three times as many as the Malay books. Find the total number of books in the library.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Chinese = 3 units, then English = 6 units (twice Chinese). English + Chinese = 9 units = 720, so 1 unit = 80. Malay = English ÷ 3 = 6 ÷ 3 = 2 units. Total = 9 + 2 = 11 units = 11 × 80 = 880 books.


43 thousands and 8 tens is the same as .


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


What is the missing number in the box?<br>\(6\dfrac{5}{9}\) = \(\dfrac{ }{9}\)

Convert the mixed number to an improper fraction: \(6\dfrac{5}{9} = \dfrac{6\times 9 + 5}{9} = \dfrac{54+5}{9} = \dfrac{59}{9}\). The missing numerator is 59.


The volume of water in a tank is 19 000 \(\ell\) when rounded to the nearest thousand litres. Which one of the following is the greatest possible volume of water in the tank?

Rounded to the nearest thousand, values from 18 500 to 19 499 give 19 000. The greatest possible value is 19 499 (19 500 would round up to 20 000).


Which one of the following pairs of numbers have 3 and 9 as their common factors?

Both numbers must be divisible by 3 and by 9. 27 = 9x3 and 36 = 9x4, so both share factors 3 and 9. (12, 18, 21 are not multiples of 9.)


Mr Lim bought \(\dfrac{4}{5}\) kg of cherries. He and his sons ate \(\dfrac{3}{10}\) kg of the cherries. What was the mass of cherries left?


James bought 1.27 kg of sweets. His sister bought 0.18 kg more than him. What was the total mass of sweets they bought altogether?


Janet's age is a multiple of 7 this year. Next year, her age will be a multiple of 6. Which one of the following is Janet's age this year?

Age this year is a multiple of 7; next year (age + 1) is a multiple of 6. 49 is a multiple of 7 and 49 + 1 = 50 is not a multiple of 6... check: 14+1=15 no; 35+1=36 yes (36=6x6, 35=7x5). So 35 works. Re-check key: key gives option 4 = 49? 49+1=50 not multiple of 6. The valid answer is 35.


When it is 09 00 in Singapore, it is 10 30 in Australia. Mr Kim makes a call at 14 50 from Singapore to his wife who is in Australia. What is the time in Australia when Mr Kim calls his wife?

Australia is 1 h 30 min ahead of Singapore (10 30 vs 09 00). At 14 50 in Singapore, Australia time = 14 50 + 1 h 30 min = 16 20.


A bus departed from Singapore and arrived in Kuala Lumpur at 13 40. The bus ride took 5 hours and 30 minutes. At what time did the bus depart from Singapore?


Write fifteen thousand and thirty-six in figures.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Write the missing number in the number pattern.<br>14 000, 13 400, 12 800, 12 200, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, 11 000


Some factors of 32 are 1, 2, 4 and 32. What are the other two factors of 32?<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 32 are 1, 2, 4, 8, 16, 32. The two not listed are 8 and 16.


What is the missing number in the box?<br>\(\dfrac{4}{7}\) = \(\dfrac{<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />}{49}\)

49 = 7 x 7, so multiply numerator and denominator of \(\dfrac{4}{7}\) by 7: \(\dfrac{4\times 7}{7\times 7} = \dfrac{28}{49}\). The missing numerator is 28.


Arrange the following fractions from the greatest to the smallest.
\(\dfrac{1}{2}\), \(\dfrac{2}{3}\), \(\dfrac{7}{12}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


What is the value of \(\dfrac{5}{8} + \dfrac{3}{4}\)? Express your answer as a mixed number.


Find the value of 20.7 ÷ 7. Round your answer to the nearest hundredths.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

20.7 ÷ 7 = 2.957... Rounding to the nearest hundredth (2 decimal places) gives 2.96.


A movie started at 11 35 and ended at 14 10. How long was the movie?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> h <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> min


Mr Lee cuts a 5-m rope into three pieces, A, B and C. Rope A measures 2.88 m and it is twice as long as rope B. What is the length of rope C?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m


A rectangle has a perimeter of 32 cm. The length is 3 times as long as its breadth. Find the area of the rectangle.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> cm²

Length + breadth = half the perimeter = 16 cm. With length = 3 x breadth, that is 4 units = 16 cm, so 1 unit (breadth) = 4 cm and length = 12 cm. Area = 12 x 4 = 48 cm².


At a fruit stall, there were 150 more apples than pears. After 46 pears were sold, there were 5 times as many apples as pears. How many pears were there at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After selling 46 pears, apples are unchanged and apples = 5 x (remaining pears). Apples are 150 more than the original pears, i.e. 150 + 46 = 196 more than the remaining pears. So 4 units (apples - remaining pears) = 196, 1 unit (remaining pears) = 49. Pears at first = 49 + 46 = 95.


Weijian had three times as much money as Xavier. After Weijian bought 8 erasers at $1.30 each he had $3.85 left.
(a) How much money did Weijian have at first?
$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much money did Xavier have?
$<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Cost of erasers = 8 x $1.30 = $10.40. Weijian at first = $10.40 + $3.85 = $14.25. (b) Weijian had 3 times Xavier, so Xavier = $14.25 ÷ 3 = $4.75.


A water container had 1 \(\ell\) of water. Mr Muthu used \(\dfrac{2}{5}\) \(\ell\) of it to make a drink and \(\dfrac{1}{4}\) \(\ell\) of it to water his plants.
(a) How much water did Mr Muthu use altogether?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(\ell\)
(b) How much water was left?
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> \(\ell\)


Mrs Raja baked some cookies. She gave \(\dfrac{1}{3}\) of the cookies to her daughter, \(\dfrac{5}{8}\) of them to her friend and kept the rest for herself. Mrs Raja gave her friend 42 more cookies than what she had given to her daughter. How many cookies did Mrs Raja bake?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Friend got \(\dfrac{5}{8}\) and daughter got \(\dfrac{1}{3}\). Difference = \(\dfrac{5}{8} - \dfrac{1}{3} = \dfrac{15}{24} - \dfrac{8}{24} = \dfrac{7}{24}\) of the cookies = 42. So \(\dfrac{1}{24}\) = 6, and the total (24 units) = 24 x 6 = 144 cookies.


Cynthia had two times as many $2 notes as $5 notes. The total amount of money that Cynthia had was $243. How many $2 notes did Cynthia have?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Take 1 group = two $2 notes + one $5 note = $2 + $2 + $5 = $9. Number of groups = $243 ÷ $9 = 27. Each group has two $2 notes, so $2 notes = 27 x 2 = 54.


32 769 rounded to the nearest hundred is .

Look at the tens digit (6). Since 6 ≥ 5, round the hundreds up: 32 769 → 32 800.


\(7\dfrac{4}{5}\) = \(\dfrac{ }{5}\) <br> What is the missing number in the box?

Convert the mixed number to an improper fraction: 7 × 5 + 4 = 39, so \(7\dfrac{4}{5}=\dfrac{39}{5}\). Missing number = 39.


Express 0.08 as a fraction in its simplest form.

0.08 = \(\dfrac{8}{100}\). Divide numerator and denominator by 4: \(\dfrac{8}{100}=\dfrac{2}{25}\).


Arrange the following fractions from the greatest to the smallest. <br> \(1\dfrac{1}{9}\) , \(\dfrac{11}{7}\) , \(\dfrac{8}{7}\)


Abby reached the bus stop at 12.20 p.m. She waited 15 minutes for the bus and the bus journey was 40 minutes. What time did she reach her destination?

12.20 p.m. = 1220. Add 15 min wait → 1235. Add 40 min journey → 1315 (in 24-hour time).


The difference between two numbers is 50. The smaller number is 300. What is the sum of the two numbers?


A flask contained 2 \(l\) of hot water. Ms Tan used \(\dfrac{3}{4}\) \(l\) of the hot water to make chocolate drinks and \(\dfrac{7}{8}\) \(l\) of the hot water to make coffee. How much water was left in the flask?


There are three electric stars on a Christmas tree. The three electric stars will light up every 3 minutes, 4 minutes, and 6 minutes respectively. The three electric stars are switched on and light up together for the 1st time at 10 00. What time will the electric stars light up together for the 3rd time?

LCM of 3, 4 and 6 = 12, so they light together every 12 min. 1st at 1000, 2nd at 1012, 3rd at 1024.


Some factors of 12 are 1, 2, 3 and 12. What are the other two factors of 12? <br> Ans : <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Factors of 12 are 1, 2, 3, 4, 6, 12. The two not yet listed are 4 and 6.


Write the missing number in the number pattern. <br> 32 400 , 32 000 , 31 600 , 31 200 , <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , 30 400

The pattern decreases by 400 each step. 31 200 − 400 = 30 800.


Which two of the fractions are in the simplest form?
 \(\dfrac{2}{5}\) , \(\dfrac{3}{6}\) , \(\dfrac{4}{10}\) , \(\dfrac{5}{12}\)
 Ans : <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

A fraction is in simplest form when numerator and denominator share no common factor. \(\dfrac{3}{6}=\dfrac{1}{2}\) and \(\dfrac{4}{10}=\dfrac{2}{5}\) can be simplified; \(\dfrac{2}{5}\) and \(\dfrac{5}{12}\) cannot.


Find the value of 4.72 × 6. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The table shows the times taken by four girls to complete a 100 m race.
 Amy: 16.1 , Bess: 17.0 , Cleo: 15.8 , Dawn: 15.9 (time in seconds)
 Write down the names of the girls from the 1st to the 4th position.
 Ans : <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> (1st) , <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="?" /> (4th)

The fastest runner (smallest time) is 1st. Times: Cleo 15.8 < Dawn 15.9 < Amy 16.1 < Bess 17.0. So 1st Cleo, 2nd Dawn, 3rd Amy, 4th Bess.


In a factory, sweets are equally packed into boxes. Bill bought two boxes of sweets. He received 1044 sweets altogether. How many sweets would Bill receive in total, if he buys five more boxes of sweets? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


James took a flight from Singapore to Taiwan. The plane left Singapore 20 min before midnight and he arrived in Taiwan at 04 50. What is the duration of the flight? <br> Ans : <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> h <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> min

20 min before midnight = 2340. From 2340 to 2400 is 20 min; from 0000 to 0450 is 4 h 50 min. Total = 4 h 50 min + 20 min = 5 h 10 min.


A number is between 30 and 40. When it is divided by 3, the answer is a whole number. When it is divided by 4, the remainder is 3. What is the number? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 3 between 30 and 40: 30, 33, 36, 39. Check remainder 3 when divided by 4: 39 ÷ 4 = 9 R3. So the number is 39.


Bill is 4 times as heavy as Charlotte. He is 98.4 kg. What is the total mass of Bill and Charlotte? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Bill = 4 units = 98.4 kg, so 1 unit (Charlotte) = 98.4 ÷ 4 = 24.6 kg. Total = 5 units = 5 × 24.6 = 123 kg.


Ben had a piece of string. He cut it into three pieces, String A, String B and String C. String B is 0.15 m longer than String A and 2.7 m longer than String C. String A is 4.36 m long. What is the length of String C? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


John had some money. He spent \(\dfrac{1}{4}\) of his money on food and \(\dfrac{5}{8}\) of his money on books. He spent $12 more on books than food. How much money did he have at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Ravi and Sam had 1780 stickers altogether. After Sam gave Ravi 40 stickers, they had the same number of stickers. How many stickers did Sam have at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After the transfer each has 1780 ÷ 2 = 890. Sam gave away 40, so Sam had 890 + 40 = 930 at first.


A television costs 10 times as much as a chair. 1 television and 1 table cost $1820. 1 table and 1 chair cost $560. What is the cost of 1 television and 2 tables? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


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


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


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


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


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


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


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


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


Let James = 1 unit. Paul = 2 units, Henry = 1 unit - 30. Total = 4 units - 30 = 386, so 4 units = 416, 1 unit = 104. (a) James = 104. (b) Paul = 2 x 104 = 208, Henry = 104 - 30 = 74, Henry + Paul = 208 + 74 = 282.


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


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


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


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


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


A 1-decimal-place number rounds to 89 if it lies from 88.5 up to 89.4 (88.5 rounds up, 89.4 rounds down, 89.5 would round to 90). Greatest = 89.4; smallest = 88.5.


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


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


(a) Monday + Tuesday = 2/9 + 1/3 = 2/9 + 3/9 = 5/9, so Wednesday = 1 − 5/9 = 4/9. (b) Tuesday − Monday = 3/9 − 2/9 = 1/9 of the book = 25 pages, so the whole book = 25 × 9 = 225 pages.


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


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


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


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


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


Total stays $348, so after giving each has 348 / 2 = $174. Paul gave away $33, so at first Paul had 174 + 33 = $207.


For a number below 5000 the thousands digit must be 3 (0 not allowed as leading digit; 9 and 7 are too big). The remaining 3 digits (9, 7, 0) can be arranged in 3 x 2 x 1 = 6 ways. So 6 numbers.


Compare digit by digit after the decimal point: 1.702 has 7 tenths (largest), then 1.207 has 2 tenths, then 1.027 has 0 tenths. Greatest to smallest: 1.702, 1.207, 1.027.


The numerator goes from 3 to 15, which is x5. Multiply the denominator by 5 too: 8 x 5 = 40. So 3/8 = 15/40.


Make a common denominator of 12: 1/4 = 3/12. Then 11/12 + 3/12 = 14/12 = 1 2/12. (The answer key leaves it as 1 2/12.)


Work backwards from 00 20 by 1 h 55 min. 00 20 minus 1 h = 23 20 (previous day); minus 55 min more = 22 25. The movie started at 2225.


The factors of 39 are 1, 3, 13 and 39. Their sum = 1 + 3 + 13 + 39 = 56.


8th multiple minus 3rd multiple = 5 of the number. This equals 35, so the number = 35 / 5 = 7.


Lengths from 167.75 up to (but below) 167.85 round to 167.8 (1 d.p.). The least value that rounds up to 167.8 is 167.75 cm.


(a) Total eggs = 36 x 30 = 1080. Unbroken = 1080 - 82 = 998. (b) 998 / 8 = 124 remainder 6, so 124 full cartons and 6 eggs left over (not packed).


Convert mixed number to improper fraction: 9 5/8 = (9×8 + 5)/8 = (72 + 5)/8 = 77/8. Missing number is 77.


A common multiple of 7 and 9 must be divisible by both. 63 = 7×9, so 63 is a multiple of both 7 and 9.


He was 45 min late, so the appointment was 45 min before 12.05 p.m. 12.05 p.m. − 45 min = 11.20 a.m.


LCM of 8 and 12 = 24. To exceed 40 fruits of each kind, use the next common multiple: 48 of each. Apples: 48 ÷ 8 = 6 bags; oranges: 48 ÷ 12 = 4 bags. Total = 6 + 4 = 10 bags... key answer is option (1) = 5. With 24 of each (>40 total fruits combined is 48): apples 24÷8 = 3 bags, oranges 24÷12 = 2 bags, total 5 bags.


The tens digit is 2 (<5), so round down. 54 620 to the nearest hundred is 54 600.


Big box = 2 units, each small box = 1 unit. Three small + one big = 3 + 2 = 5 units = 60. 1 unit = 60 ÷ 5 = 12. Big box = 2 × 12 = 24.


Let Susanna start with 1 unit, Hugh with 3 units. After Susanna gives $20: Hugh = 3u + 20, Susanna = 1u − 20. Difference = (3u+20) − (1u−20) = 2u + 40 = 110, so 2u = 70, u = 35. Susanna in the end = 35 − 20 = $15.


Place value of digit 6: in 4659 the 6 is in the hundreds place, so it stands for 600. (6549: 6000; 5946: 6; 9465: 60.) Answer: 4659.


Factors of 16: 1,2,4,8,16. Factors of 24: 1,2,3,4,6,8,12,24. Common factors: 1,2,4,8. Only '4 and 8' are both common factors. Answer: 4 and 8.


4 tenths = 0.4, the first digit after the decimal point. In 15.45 the digit 4 is in the tenths place = 0.4. Answer: 15.45.


Monday = 1 unit, Tuesday = 6 units, total = 7 units = 4242. 1 unit = 4242 / 7 = 606. Monday produced 606. Answer: 606.


1 minute = 60 s (Lucy's time). Paul takes 10 s more than Lucy: 60 + 10 = 70 s. Answer: 70 s.


The extra calculator accounts for 2.94 - 2.76 = 0.18 kg (1 calculator). Box + 4 books = 2.76 - 0.18 = 2.58 kg. Answer: 2.58 kg.


Perimeter = 2 x (length + breadth), so length + breadth = 12 / 2 = 6 m. Length = 6 - 2 = 4 m. Answer: 4 m.


Bob = 198 / 3 = 66. Charlie = 66 + 76 = 142. Charlie shares equally with Bob: (66 + 142) / 2 = 104 each, so Bob now has 104. Aminah - Bob = 198 - 104 = 94. Answer: 94.


Day 3 = 30 + 45 = 75. Days 1-3 = 30 + 45 + 75 = 150. For the 4-day total to round to 230, the total is 225 to 234, so Day 4 is 75 to 84. Greatest is 84. Answer: 84.


Try each pair: Folder+Comic = $7.50; Folder+Stapler = $2.95; Notebook+Calculator = $13.25 (over $13); Comic+Notebook = $6.65 + $5.45 = $12.10 (more than $10 and within $13). Answer: Comic Book and Notebook.


1 whole = 5/5, which is 5 one-fifths. Answer: 5.


Divide numerator and denominator by 3: 3/9 = (3 / 3)/(9 / 3) = 1/3. Answer: 1/3.


Compare tenths first: 0.504 and 0.405 have 5 and 4 tenths, 0.045 has 0 tenths. So 0.504 > 0.405 > 0.045. Greatest to smallest: 0.504, 0.405, 0.045.


The tenths digit is 5, so round up: 18.55 rounds to 19. Answer: 19.


Area of a square = length x length = 49. 7 x 7 = 49, so the length is 7 cm. Answer: 7 cm.


2nd to 5th tree = 3 gaps = 2340 m, so 1 gap = 780 m. 1st to 10th tree = 9 gaps = 9 x 780 = 3 x 2340 = 7020 m. Answer: 7020 m.


Container B = 13.5 x 4 = 54 l. Bottles = 54 / 3 = 18. Answer: 18 bottles.


Dinner from 17 15 to 19 05 = 1 h 50 min. Total = 1 h 50 min + 2 h 55 min = 3 h 105 min = 4 h 45 min. Answer: 4 h 45 min.


They started equal. The difference in what they spent is $50 - $8.80 = $41.20, which equals the difference in money left = 4 units (Michelle 5 units, Bridget 1 unit). 4 units = $41.20, 1 unit = $10.30. (a) Michelle's end = 5 units = $51.50. (b) Bridget at first = money left + spent = $10.30 + $50 = $60.30. Answers: (a) $51.50; (b) $60.30.


Oliver - Nina = (May+Oliver) - (May+Nina) = 618 - 274 = 344. Oliver = 9 x Nina, so Oliver - Nina = 8 units = 344, 1 unit (Nina) = 43. May = 274 - Nina = 274 - 43 = 231. Answer: 231 beads.


If all 13 were cupcakes: 13 x $2 = $26. Extra = $38 - $26 = $12. Each swap to a tart adds $5 - $2 = $3, so tarts = $12 / $3 = 4. Cupcakes = 13 - 4 = 9. More cupcakes than tarts = 9 - 4 = 5. Answer: 5.


Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. 56 is not divisible by 6 (56 / 6 = 9 r 2), so 6 is not a factor.


In 97.85, the first digit after the decimal point is the tenths place. That digit is 8.


Compare whole-number parts first: 0.58 and 0.85 are less than 1; 5.08 and 5.8 are over 5. Within each: 0.58 < 0.85 and 5.08 < 5.8. Order: 0.58, 0.85, 5.08, 5.8.


9 glasses = 9 x 0.4 l = 3.6 l fills 2 jugs. So 1 jug = 3.6 / 2 = 1.8 l.


Chairs in one row = 7 (right) + 9 (left) + 1 (Mark) = 17. Total = 17 x 11 rows = 187.


Compare hundreds digit: 831 and 813 start with 8, 183 and 138 start with 1. Within 8xx: 831 > 813. Within 1xx: 183 > 138. Greatest to smallest: 831, 813, 183, 138.


Half of each denominator: 2/11 (half is 5.5, 2<5.5 so smaller), 3/10 (half is 5, 3<5 smaller), 4/8 = 1/2 (equal, not smaller), 5/7 (half is 3.5, 5>3.5 larger). The two smaller than 1/2 are 2/11 and 3/10.


Remove the extra: 250 - 71.50 = 178.50 equals 3 equal skirts. 178.50 / 3 = $59.50 per skirt.


Let Tom first = t, so Siti first = t + 604. After Siti gives 902: Tom = t + 902, Siti = t + 604 - 902 = t - 298. Tom is 4 times Siti: t + 902 = 4(t - 298). t + 902 = 4t - 1192, so 3t = 2094, t = 698. Tom had 698 stamps at first.


In 72 415, the digit 2 is in the thousands place. Its value is 2 x 1000 = 2000.


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


1/6 = 2/12 = 4/24 = 6/36. But 3/15 = 1/5, which is not equal to 1/6. So 3/15 is not equivalent.


In 14.57 the digit immediately after the decimal point is the tenths place. So 5 stands for 5 tenths.


Side x side = 64, so side = 8 cm (8 x 8 = 64). Perimeter = 4 x 8 = 32 cm.


1 cake = 3 muffins. 2 cakes = 6 muffins. So 2 cakes + 4 muffins = 6 + 4 = 10 muffins = $30. 1 muffin = $3. 1 cake = 3 muffins = $9.


The pattern decreases by 25 each time: 450, 425, 400, 375, 350. The missing number is 375.


1 whole = 5/5, which is 5 one-fifths. So there are 5.


7/100 means 7 hundredths. As a decimal, hundredths is the second place after the point: 0.07.


The tenths digit is 6, which is 5 or more, so round up. 18.64 rounds to 19.


Factors of 81: 1, 3, 9, 27, 81. Apart from 1, 9 and 81, the other two factors are 3 and 27.


The least common multiple of 6 and 9 is 18. To get 18 erasers in packets of 9, Paul needs 18 / 9 = 2 packets of erasers.


Remaining string = 10 - 3.16 = 6.84 m. Cut into 6 equal pieces: 6.84 / 6 = 1.14 m each.


Removing 3 balls reduced the mass from 9.48 kg to 5.67 kg, so 3 balls = 9.48 - 5.67 = 3.81 kg. 1 ball = 3.81 / 3 = 1.27 kg.


Let the smaller be 1 unit, the greater 3 units. Total = 4 units = 36.56, so 1 unit = 36.56 / 4 = 9.14. Greater number = 3 x 9.14 = 27.42.


They meet again after the least common multiple of 3 and 4 days = 12 days. 10 March + 12 days = 22 March.


5/8 has no common factor other than 1, so it is in simplest form. 2/6 = 1/3, 3/9 = 1/3, 6/10 = 3/5 can all be simplified.


14 = 7x2, 35 = 7x5, 49 = 7x7 are all divisible by 7. 72 is not divisible by 7 (72 / 7 leaves a remainder), so 7 is not a factor of 72.


The 30 left is 1/3 of the total, so total = 90. He gave away 2/3 x 90 = 60 stickers to 5 students. Each student got 60 / 5 = 12.


The pattern repeats every 4 letters (ABCD), with A in position 1 of each block. 42 / 4 = 10 remainder 2, giving 10 full blocks (10 A's) plus 'A B', adding one more A. Total = 11 A's.


The number must be a common multiple of 2 and 3 (a multiple of 6) between 10 and 25: 12, 18 or 24. One possible answer is 12.


3 cakes x 30 min = 90 min = 1 h 30 min of baking. Counting back from 12.45 p.m. by 1 h 30 min gives 11.15 a.m.


(a) Carin has the most (Bala = Alice + 30, Carin = Bala + 40). (b) Take Bala as a unit. Alice = Bala - 30, Carin = Bala + 40. Total: (Bala-30) + Bala + (Bala+40) = 850, so 3 Bala + 10 = 850, 3 Bala = 840, Bala = 280.


(a) Total purple = 15 + 15.42 = 30.42 l. (b) Big is 5 times the small, so together they are 6 equal parts: 30.42 / 6 = 5.07 l in the small container.


(a) The 15 remaining trays each gained 2 donuts, so the 5 removed trays held 15 x 2 = 30 donuts in total. (b) Those 30 donuts came from 5 equal trays, so each tray had 30 / 5 = 6 donuts at first.


(a) She gave away 1/3, so 1 - 1/3 = 2/3 of red marbles were left. (b) Red left (2/3 of red) = blue. So red : blue = 3 : 2, total 5 units = 280, 1 unit = 56. Difference = 3 units - 2 units = 1 unit = 56.


Factors of 12: 1,2,3,4,6,12. Factors of 56: 1,2,4,7,8,14,28,56. The common factor among the options is 4.


7/25 = 28/100 = 0.28 (multiply numerator and denominator by 4). So 8 7/25 = 8.28.


2/8, 3/12 and 4/16 all simplify to 1/4. 6/20 simplifies to 3/10, which is not 1/4. So 6/20 is the odd one out.


63 = 9 × 7 and 63 = 21 × 3. The full list of factors is 1, 3, 7, 9, 21, 63. The two missing factors are 21 and 9.


1 whole = 8/8, which is eight one-eighths. So there are 8.


Starting at East, a 3/4-turn clockwise = 270°. East → South (1/4) → West (1/2) → North (3/4). He faces North.


Odd means the last digit is odd (3 or 7). For the smallest number, the leading digit cannot be 0. Put the smallest non-zero digit first (3), then arrange remaining for smallest value while keeping an odd last digit: 3 0 4 8 7 = 30487.


Letters with a line of symmetry: V (vertical), H (vertical and horizontal), M (vertical). P and S have no line of symmetry. So 3 letters are symmetric.


07 45 + 35 min = 08 20 (arrives). 08 20 + 10 min wait = 08 30. The library opened at 0830.


Numbers that round to 700 to the nearest hundred range from 650 to 749. The greatest is 749.


A 2-decimal-place number using digits 6,7,5 that rounds to 6 must be from 5.50 to 6.49. 5.76 rounds to 6. (Key gives 5.76; 5.67 also works.)


Table = 5 chairs. 3 chairs + 1 table = 3 chairs + 5 chairs = 8 chairs = 73.36 kg. One chair = 73.36 ÷ 8 = 9.17 kg.


Both are wiped together every common multiple of 3 and 9, i.e. every 9 days (LCM of 3 and 9 = 9). Starting from 30 June, the next together-days are 9 Jul, 18 Jul, 27 Jul — 3 occasions in July.


There are 2 adults and 4 children = 6 tickets. If all 6 were adult price, replace the 4 child tickets: 4 × $170 = $680 less. So 6 adult tickets = $1600 + $680 = $2280. One adult = $2280 ÷ 6 = $380. Child = $380 - $170 = $210.


(a) Eighty-five thousand = 85 000, and twenty-one = 21, so the numeral is 85 021. (b) In 21 435, the place values are 2 (ten thousands), 1 (thousands), 4 (hundreds), 3 (tens), 5 (ones). The digit in the hundreds place is 4.


(a) The ones digit of 24 568 is 8 (5 or more), so round up: 24 570. (b) The hundreds digit of 89 542 is 5 (5 or more), so round the thousands up: 89 000.


(a) Factors of 15 are the numbers that divide 15 exactly: 1, 3, 5, 15. Besides 1 and 15, the other two are 3 and 5. (b) Multiples of 6: 6, 12, 18, ...; multiples of 9: 9, 18, ... The first common multiple is 18.


(a) 30 745 = 30 000 + 700 + 40 + 5, so the missing number is 30 000. (b) In 9276 the digit 7 is in the tens place, so its value is 7 tens = 70.


Compare the fractions. 2/9 and 3/9 share denominator 9, so 2/9 < 3/9. Then 3/9 = 1/3 ≈ 0.33 and 3/7 ≈ 0.43, so 3/9 < 3/7. From smallest to greatest: 2/9, 3/9, 3/7.


To round to 21 300 at the nearest hundred, the number must be from 21 250 up to 21 349 (21 350 would round up to 21 400). The largest such whole number is 21 349.


Use a common denominator. 2/3 = 24/36 and 3/4 = 27/36, so 25/36 and 26/36 lie between them. 25/36 is already in simplest form; 26/36 = 13/18. The two fractions are 25/36 and 13/18.


The listed factors 1, 2, 3, 6, 14, 21 suggest the number is 42. The factors of 42 are 1, 2, 3, 6, 7, 14, 21, 42 (8 factors). The missing ones, in order, are 7 (between 6 and 14) and 42 (after 21).


(a) 1250 kg over 2 months = 1250 ÷ 2 = 625 kg each month. (b) A year has 12 months, so 625 × 12 = 7500 kg.


After Jack donates $170, the remaining total is 1730 − 170 = $1560. Now Bill = 3 × Jack, so they form 4 equal units: 1 unit = 1560 ÷ 4 = $390 (Jack). Bill = 3 units = 3 × 390 = $1170.


Total stickers = 15 × 25 = 375. After keeping 100: 375 − 100 = 275. Shared among 5 friends: 275 ÷ 5 = 55 stickers each.


Assume all 50 were children: 50 × $5 = $250. The extra $304 − $250 = $54 comes from adults paying $3 more each ($8 − $5). Number of adults = 54 ÷ 3 = 18, so children = 50 − 18 = 32. More children than adults = 32 − 18 = 14.


Sixteen thousand = 16 000, four hundred = 400, and nine = 9. Adding them gives 16 000 + 400 + 9 = 16 409.


All numbers share 18 thousands. Compare the hundreds: 18 769 and 18 796 have 7 hundreds, smaller than 9. Then compare tens: 6 tens (18 769) is smaller than 9 tens (18 796). So 18 769 is the smallest.


Rounding to the nearest hundred, the result 38 500 comes from values 38 450 to 38 549. Among the options, 38 549 rounds to 38 500. (38 409 and 38 449 round to 38 400; 38 550 rounds up to 38 600.)


Factors of 16: 1, 2, 4, 8, 16. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. A common factor is 8 (it divides both). 6 divides 24 but not 16; 40 and 48 are larger than 16 so cannot be its factors.


Multiples of 8: 8, 16, 24, ... Multiples of 12: 12, 24, 36, ... The number 24 appears in both lists, so it is a common multiple. (20 is a multiple of neither; 16 is a multiple of 8 only; 4 is a factor, not a multiple.)


Find the difference: 832 - 164 = 668. There are 668 more boys than girls.


Total jogged in one day = 1650 + 2480 = 4130 m. Over 7 days = 4130 x 7 = 28 910 m.


First 3 months saved: $100 x 3 = $300. Remaining over the last 6 months: $4320 - $300 = $4020. Monthly amount in the last 6 months: $4020 ÷ 6 = $670.


The digits after the decimal point (08) are hundredths. So 1.08 = \(1\dfrac{8}{100}\).


Let a small bottle be 1 unit; the large bottle is 3 units. Total = 4 small + 1 large = 4 + 3 = 7 units = 3.85 l. So 1 unit = 3.85 ÷ 7 = 0.55 l. A large bottle = 0.55 × 3 = 1.65 l.


Read the place values of 34 765 from the right: 5 ones, 6 tens, 7 hundreds, 4 thousands, 3 ten thousands. The digit 7 sits in the hundreds place.


Round to the nearest thousand: 4513 → 5000 and 971 → 1000. Then 5000 − 1000 = 4000.


Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 32: 1, 2, 4, 8, 16, 32. The common factor among the options is 4.


8412 ÷ 9 = 934 remainder 6. The quotient is the whole-number result, 934.


40 = 4 × 10, so 123 × 40 = 123 × 4 × 10. The missing number is 4.


Multiples of 8: 8, 16, 24, 32, 40. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The number in both lists that is between 20 and 40 is 24.


(a) 9 950: the tens digit is 5, so round up the hundreds → 10 000. (b) 23 439: the tens digit is 3 (less than 5), so round down → 23 400.


(a) Ninety-six thousand = 96 000, and eighteen = 18, giving 96 018. (b) Thirty-one thousand = 31 000, two hundred = 200, and seventy = 70, giving 31 270.


A girl wears both if her position is a multiple of both 2 and 3, i.e. a multiple of 6. Within 20: 6, 12, 18 — that is 3 girls.


354 ÷ 5 = 70 remainder 4. The 70 tables seat 350 people; the remaining 4 need one more table. So 70 + 1 = 71 tables.


The difference is 4364 − 2468 = 1896. To make them equal, Susan gives May half the difference: 1896 ÷ 2 = 948.


The block SAFETY repeats every 6 letters. 44 ÷ 6 = 7 remainder 2, so the 44th letter is the 2nd letter of the block, which is A.


If 10 is a factor of the number, the number is a multiple of 10, and every multiple of 10 is also a multiple of 5. So the statement is True.


A number with 10 as a factor is a multiple of 10 and ends in 0, so it is always even. It can never be odd, so the statement is False.


Knowing 10 is a factor only tells us the number is a multiple of 10 (e.g. 10, 20, 30...). Some are multiples of 12 (like 60) and some are not (like 10), so we cannot tell.


A multiple of 10 may or may not have 4 as a factor: 20 does (4 × 5), but 10 and 30 do not. So we cannot tell from the information given.


Banana muffins earned 63 × $4 = $252. So chocolate muffins earned $486 − $252 = $234. At $3 each, the number sold is $234 ÷ $3 = 78.


(a) Karl + Andy = $800 and Andy = Karl + $128. So 2 units of Karl = $800 − $128 = $672, giving Karl = $672 ÷ 2 = $336. (b) Sam had 6 × $336 = $2016. Each of 8 lego sets cost $2016 ÷ 8 = $252.


(a) Children are split into boys and girls. Children = 2 × women and women = 2 × boys, so children = 4 × boys; girls = children − boys = 3 units = 486, so 1 unit (boys) = 486 ÷ 3 = 162. Children = boys + girls = 162 + 486 = 648. (b) Total girls' tokens = 486 × 20 = 9720.


Work backwards from the finishing time. 18 25 minus 2 h gives 16 25. Then subtract 47 min: 16 25 - 47 min = 15 38. So John started at 15 38.


Find the duration from 15 15 to 16 40. From 15 15 to 16 15 is 1 h, then 16 15 to 16 40 is 25 min. Total = 1 h 25 min.


Total washing time = 8 \(\times\) 20 min = 160 min = 2 h 40 min. Add to the start time: 07 00 + 2 h 40 min = 09 40.


Subtract 40 s from Jacob's time. 2 min 38 s = 158 s. 158 s - 40 s = 118 s = 1 min 58 s.


Find the duration from 11.30 a.m. to 3.40 p.m. From 11.30 a.m. to 3.30 p.m. is 4 h, then 3.30 p.m. to 3.40 p.m. is 10 min. Total = 4 h 10 min.


There are 3 intervals between the 1st and 4th trains. 3 \(\times\) 12 min = 36 min. 7.45 p.m. + 36 min = 8.21 p.m.


Hours per week = 4 \(\times\) 2 h = 8 h. Number of weeks = 200 h \(\div\) 8 h = 25 weeks.


The watch is 12 min fast (7.15 - 7.03). When the watch showed 10.40 a.m., the real time was 10.40 - 12 min = 10.28 a.m. He was due at 9.45 a.m. Lateness = 9.45 a.m. to 10.40 a.m. on the watch = 55 min, minus the 12 min watch error = 43 min late. (9.45 to 10.40 = 55 min; 55 - 12 = 43 min.)


Seoul is 1 h ahead of Singapore. Departure in Seoul time = 08 15 + 1 h = 09 15. Add the flight time: 09 15 + 4 h 50 min = 14 05. The flight landed at 1405 Seoul time.


Country A is 1 h 20 min ahead of Singapore (10 00 vs 08 40). Departure 09 00 in Country A = 09 00 - 1 h 20 min = 07 40 in Singapore time. Add the flight time: 07 40 + 3 h 29 min = 11 09. The flight landed at 1109.


Find the lowest common multiple of 24 and 60. Multiples of 24: 24, 48, 72, 96, 120; multiples of 60: 60, 120. LCM = 120 s = 2 min. So they flash together again 2 min after 8.40 p.m. = 8.42 p.m.


A complete turn is 360°. A quarter turn is \(\dfrac{1}{4}\) of 360° = 360° ÷ 4 = 90°.


The minute hand sweeps a full circle (360°) in one hour. In half an hour it moves \(\dfrac{1}{2}\) of 360° = 180°.


A \(\dfrac{3}{4}\) turn to the right is 270° clockwise. From East, clockwise in 90° steps: E → S → W → N. So I now face North.


23 thousandths means \(\dfrac{23}{1000}\). The thousandths digit is the 3rd decimal place, so 23 thousandths = 0.023.


37.15 = 37 + 0.15. The decimal part 0.15 = \(\dfrac{15}{100}\), so the missing numerator is 15.


Nearest tenth = 1 decimal place. Look at the hundredths digit, 5: since it is 5 or more, round the tenths digit up from 3 to 4. So 42.351 rounds to 42.4.


Compare the whole-number parts first: 8.46 and 8.6 (both 8), 6.08 (6), 0.86 (0). Between 8.6 and 8.46, compare tenths: 6 > 4, so 8.6 > 8.46. Order greatest to smallest: 8.6, 8.46, 6.08, 0.86.


2.7 x 5 = 13.5. Rounding 13.5 to the nearest whole number: the tenths digit is 5, so round up to 14.


\(\dfrac{2}{5}\) of the beads = 78, so 2 units = 78 and 1 unit = 78 ÷ 2 = 39. The whole box = 5 units = 39 x 5 = 195 beads.


Total mass = 4.05 + 3.9 = 7.95 kg. Divided equally into 5 packets: 7.95 ÷ 5 = 1.59 kg per packet.


Let each start with the same amount. After the changes Ahmad has (start + 30.50) and Caili has (start - 20), and Ahmad = 3 x Caili. The difference between them is 30.50 + 20 = $50.50, which equals 2 of Caili's units (since 3 units - 1 unit = 2 units). So 1 unit (Caili after) = 50.50 ÷ 2 = $25.25. Caili's starting amount = 25.25 + 20 = $45.25. Each had $45.25 at first.


Let Randy = 1 unit. Morris = twice Randy = 2 units. Timothy = three times Morris = 6 units. Total = 1 + 2 + 6 = 9 units = 2439, so 1 unit = 2439 ÷ 9 = 271. Timothy = 6 units = 271 x 6 = 1626 stickers.


One cupcake plus one muffin (a pair) costs (1 x $4) + (1 x $3) = $4 + $3 = $7. Number of pairs = 357 ÷ 7 = 51. Each pair has 2 items, so total = 51 x 2 = 102 cupcakes and muffins.


57 809 = 50 000 + 7000 + 800 + 9. The 8 is in the hundreds place, so the missing number is 800.


In 43 120: 4 ten-thousands, 3 thousands, 1 hundred, 2 tens, 0 ones. The digit in the hundreds place is 1.


Multiples of 3: 3, 6, 9, ... Multiples of 9: 9, 18, ... The smallest common multiple is 9.


A 180° turn is half a turn = 30 minutes. 9.25 p.m. + 30 min = 9.55 p.m.


A \(\dfrac{3}{4}\)-turn anticlockwise is 270° anticlockwise, which is the same as 90° clockwise. To end facing south, he must have started facing east (east turned 90° clockwise gives south).


Numbers rounding to 6000 (nearest hundred) range from 5950 to 6049. The largest is 6049.


430 ÷ 8 = 53 remainder 6. So 53 cards fit on each page (424 in total) and 6 cards were left out.


Adding 398 yellow and 594 blue changes the difference by 398 − 594 = −196. New difference = 2389 − 196 = 2193.


Factors of 28: 1, 2, 4, 7, 14, 28. The ones not listed are 7 and 14.


6039 ÷ 7 = 862 remainder 5. The quotient is 862.


Total time = 20 min + 1 h 30 min = 1 h 50 min. 12.00 noon − 1 h 50 min = 10.10 a.m.


Seventh multiple of 6 = 7 × 6 = 42, so Mrs Toh is 42. Daughter's age = 42 ÷ 3 = 14.


The pattern w x y z repeats every 4 letters. 48 ÷ 4 = 12 exactly, so the 48th letter is the last in the block = z.


Adults = 1846 − 289 = 1557. Removing the extra 349 women: 1557 − 349 = 1208, which is twice the number of men. Men = 1208 ÷ 2 = 604.


Fri + Sat = 800 × 2 = 1600. Mon–Thu total = 3400 − 1600 = 1800. Each of the 4 equal days (incl. Wednesday) = 1800 ÷ 4 = 450.


Breadth = 10 ÷ 2 = 5 cm. Area = length × breadth = 10 × 5 = 50 cm².


Claire = 4 units, Diana = 1 unit, so Diana is 3 units fewer = 201, giving 1 unit = 201 ÷ 3 = 67. Diana = 67, Claire = 268, Eliane = 268 ÷ 2 = 134. Altogether = 67 + 268 + 134 = 469.


Lydia = total − (Fiona + Nicole) = 1292 − 1197 = 95. Nicole = (Nicole + Lydia) − Lydia = 1203 − 95 = 1108.


End: Tank B = 2135 ml, Tank A = 4 × 2135 = 8540 ml. Tank A started with 9 litres = 9000 ml, so water transferred = 9000 − 8540 = 460 ml.


The digit 3 stands for 300 when it is in the hundreds place. In 9360, the 3 is in the hundreds place, so it stands for 300.


Equivalent fractions of \(\dfrac{1}{4}\) have the denominator equal to 4 times the numerator: \(\dfrac{2}{8}\), \(\dfrac{3}{12}\), \(\dfrac{6}{24}\) all simplify to \(\dfrac{1}{4}\). \(\dfrac{5}{16}\) does not (16 ÷ 5 ≠ 4), so it is not equivalent.


Compare the tenths digit first: 0.357 and 0.324 both have 3 tenths, the others have fewer. Between them, 5 hundredths > 2 hundredths, so 0.357 is the greatest.


Rounding to the nearest ten, the result 72 400 comes from numbers between 72 395 and 72 404. 72 396 rounds up to 72 400. (72 349→72 350, 72 405→72 410, 72 443→72 440.)


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


From 22 50 to 24 00 (midnight) is 1 h 10 min. From 00 00 to 04 05 is 4 h 5 min. Total = 5 h 15 min.


A rectangle has TWO pairs of parallel sides, not one. So the statement 'There is only one pair of parallel lines' is not correct.


Test each multiple of 4: 16 + 5 = 21 = 7 × 3 (a multiple of 7). So the number is 16. (28+5=33, 32+5=37, 36+5=41 are not multiples of 7.)


Remove the extra 140 boys: 460 − 140 = 320, which is twice the number of girls. Girls = 320 ÷ 2 = 160.


Let the start amount be n. Siti = n − 24, Tina = n + 84, and Tina = 4 × Siti. So n + 84 = 4(n − 24) = 4n − 96, giving 3n = 180, n = 60.


The pattern increases by 150 each time (6649 → 6799 → 6949). So the missing number is 6949 + 150 = 7099 (and 7099 + 150 = 7249).


A fraction is in simplest form when numerator and denominator share no common factor other than 1. \(\dfrac{3}{6}=\dfrac{1}{2}\) and \(\dfrac{4}{8}=\dfrac{1}{2}\) can be simplified. \(\dfrac{2}{3}\) and \(\dfrac{5}{9}\) cannot, so they are in simplest form.


The factors of 10 are 1, 2, 5 and 10. Apart from 1 and 10, the other two factors are 5 and 2.


Concert starts at 5 p.m. = 1700. She arrived 30 min early at 1630. She walked 45 min, so she left at 1630 − 45 min = 1545.


From the graph, the amount of water at 08 00 was 24 \(\ell\). At 13 00 it is one-third of that: 24 ÷ 3 = 8 \(\ell\).


Buy as many sets of 4 as possible: 49 ÷ 4 = 12 sets remainder 1. 12 sets × $11 = $132, plus 1 single muffin × $3 = $3. Least amount = $132 + $3 = $135.


(a) Each friend gets 1 more eraser in the first case, needing 4 + 3 = 7 extra erasers in total, so there are 7 friends. (b) With 5 each: 7 × 5 + 3 = 38 erasers (check: 7 × 6 − 4 = 38).


The total stays constant. Before, Lydia : Kenneth = 2 : 1 (3 parts). After, 4 : 1 (5 parts). Make totals equal at 15: before 10 : 5, after 12 : 3. Kenneth drops from 5u to 3u, i.e. 2u = $24, so 1u = $12. Kenneth at first = 5u = 5 × $12 = $60.


The digit 7 stands for 700 when it is in the hundreds place. In 5740, the 7 is in the hundreds place, so it stands for 700. Answer: 5740.


To round 27 358 to the nearest hundred, look at the tens digit (5). Since 5 ≥ 5, round up: the hundreds digit 3 becomes 4 and the tens/ones become 0. Answer: 27 400.


In a decimal, the first digit after the decimal point is the tenths place. In 68.59 the digit right after the point is 5. Answer: 5.


Check each: 56 ÷ 2 = 28, 56 ÷ 8 = 7, 56 ÷ 4 = 14 (all exact, so they are factors). 56 ÷ 6 = 9 remainder 2, so 6 is NOT a factor. Answer: 6.


Convert the mixed number to an improper fraction: 5 × 9 + 2 = 47, over 9. So the missing numerator is 47. Answer: 47.


Make an equivalent fraction with denominator 100: \(\dfrac{3}{4}=\dfrac{75}{100}\) = 0.75. Answer: 0.75.


A common multiple of 3 and 7 must be a multiple of 21. 42 = 21 × 2, and 42 ÷ 3 = 14, 42 ÷ 7 = 6, both exact. Answer: 42.


Compare by place value: 0.204 < 0.24 < 0.402 < 0.42. (0.204 and 0.24 share tenths 2, then hundredths 0 < 4; 0.402 and 0.42 share tenths 4, then hundredths 0 < 2.) Answer: 0.204, 0.24, 0.402, 0.42.


From 09 35 to 11 50: 09 35 to 11 35 is 2 h, plus 35 to 50 is 15 min, total 2 h 15 min. That matches Dino Dash. Answer: Dino Dash.


Henry = 1 unit, John = 3 units, total = 4 units = 2700. 1 unit = 2700 ÷ 4 = 675. Henry has 675 stamps. Answer: 675.


Subtract the duration from the end time: 18 00 − 2 h = 16 00, then − 15 min = 15 45. Answer: 15 45.


A length rounds to 12.1 if it is from 12.05 up to but not including 12.15. Among the options, the greatest value that still rounds to 12.1 is 12.14 m (12.19 rounds to 12.2). Answer: 12.14 m.


Six thousand = 6000, twenty = 20, with no hundreds and no tens-of-hundreds in between. 6000 + 20 = 6020. Answer: 6020.


Number = quotient × divisor + remainder = 1006 × 6 + 3 = 6036 + 3 = 6039. Answer: 6039.


An even number must end in an even digit (4 or 6). To make it largest, put the biggest digits first; the smaller even digit (4) goes last. Largest arrangement of 9, 6, 3 then 4 → 9634. Answer: 9634.


Side of square = perimeter ÷ 4 = 64 ÷ 4 = 16 cm. Area = side × side = 16 × 16 = 256 cm². Answer: 256 cm².


Flour packed = 6 × 175 = 1050 g. Total bought = flour used + flour packed = 250 + 1050 = 1300 g. Answer: 1300 g.


\(\dfrac{3}{4}\) of the number = 21, so \(\dfrac{1}{4}\) = 21 ÷ 3 = 7. The whole number = 7 × 4 = 28. Answer: 28.


Let a small box = 1 unit, so a big box = 2 units. 3 big + 2 small = 3×2 + 2×1 = 8 units = 136, so 1 unit = 17. A big box = 2 units = 2 × 17 = 34 tarts. Answer: 34.


1 unit = 135 ÷ 9 = 15. Chicken pies = 2 units = 30. Mushroom pies = 7 units = 105. Difference = 105 − 30 = 75. Answer: 75.


Add the place values: 60 000 + 4 000 + 800 + 7 = 64 807. The ten-thousands digit is 6, thousands 4, hundreds 8, tens 0, ones 7.


The pattern increases by 4 each time: 7, 11, 15, 19, 23, 27. So the two missing numbers are 19 and 23.


1 whole = 6 sixths, so 2 wholes = 2 x 6 = 12 sixths. (2 = 12/6.)


Compare after the decimal point. 4.032 has 0 tenths and 3 hundredths; 4.07 has 0 tenths, 7 hundredths. 4.032 < 4.07 < 4.18 < 4.85, so 4.032 is smallest.


7 tenths means the 7 is in the first place after the decimal point. In 413.75 the digit 7 is in the tenths place (0.7). The others have 7 in tens, ones or hundredths places.


The factors of 12 are 1, 2, 3, 4, 6, 12. Given 1, 2, 6 and 12, the remaining two factors are 3 and 4.


A fraction is in simplest form when numerator and denominator share no common factor besides 1. 2/3 and 3/7 cannot be simplified. 10/12 = 5/6 and 6/8 = 3/4 can be simplified.


Thousandths is the third place after the decimal point. 5 thousandths = 0.005.


Look at the tenths digit (6). Since 6 is 5 or more, round up: 117.65 rounds to 118.


Numbers between 10 and 40 leaving remainder 2 when divided by 7: 16, 23, 30, 37. Of these, the one divisible by 3 (no remainder) is 30 (30 = 7x4 + 2 and 30 = 3x10).


To round to 10.05 (nearest hundredth), the thousandths digit must be 0-4 to round down. The greatest 3-decimal-place number that rounds to 10.05 is 10.054.


Let Shop C = x. Then Shop A = 2x. Shop B = A - 50 = 2x - 50. Total: x + 2x + (2x - 50) = 250, so 5x - 50 = 250, 5x = 300, x = 60. Shop C has 60 apples.


Let 1 packet of sugar = 1 unit, so 1 packet of flour = 2 units. Total units = 2 sugar + 2 flour = 2(1) + 2(2) = 6 units = 6.54 kg. 1 unit = 6.54 / 6 = 1.09 kg. Flour = 2 units = 2 x 1.09 = 2.18 kg.


(a) Children = total - adults = 2590 - 1770 = 820 children. (b) Boys = adults / 3 = 1770 / 3 = 590. Girls = children - boys = 820 - 590 = 230 girls.


Both spent the same amount on plates, so the difference in money stays $304 - $166 = $138. After buying, Larry = 4 x Mary, so the difference = 3 units = $138, 1 unit = $46. (a) Mary had $46 left. (b) Mary spent 166 - 46 = $120 on 5 plates, so 1 plate = 120 / 5 = $24.


(a) From 8.45 a.m. to 5.30 p.m. is 8 h 45 min total. Subtract the 40 min lunch: 8 h 45 min - 40 min = 8 h 5 min working. (b) He reached the gym at 5.45 p.m., exercised 1 h 40 min, finishing at 7.25 p.m. He reached home at 7.50 p.m., so driving took 7.50 - 7.25 = 25 min.


Ben at first = 1250 + 490 = 1740. Total stickers = 1740 + 1250 = 2990 (unchanged). In the end Ben = Andrew - 626. So Andrew + (Andrew - 626) = 2990, 2 x Andrew = 3616, Andrew = 1808, Ben = 1182. Ben gave away = 1740 - 1182 = 558 stickers.


Look at the tens digit (4). Since 4 < 5, round down: 28 549 → 28 500.


Make the denominators the same: \(\dfrac{1}{3} = \dfrac{4}{12}\). Then \(\dfrac{5}{12} - \dfrac{4}{12} = \dfrac{1}{12}\).


4 tenths = 0.4, so the digit 4 must be the first digit after the decimal point. In 30.42 the 4 is in the tenths place.


Finished at 12 00 (noon). Start time = 12 00 − 50 min = 11 10, which is 11.10 a.m.


To round to 5.9, the value must be from 5.85 up to (but not including) 5.95. Only 5.88 lies in this range (5.84 rounds to 5.8; 5.95 and 5.99 round to 6.0).


Six thousand = 6000, and eight = 8 in the ones place (no hundreds or tens). So 6000 + 8 = 6008.


Compare whole-number parts first: 8.4 is largest. Among the others (all 0.something) compare tenths: 0.095 (0 tenths) < 0.784 < 0.804. Order: 0.095, 0.784, 0.804, 8.4.


The factors of 32 are 1, 2, 4, 8, 16, 32. The two not listed are 4 and 16 (4 × 8 = 32, 2 × 16 = 32).


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


For the greatest odd number, the ones digit must be the smallest available odd digit (5). Arrange the remaining digits 9, 8, 4, 2 in descending order in front: 9842, giving 98 425.


Total mixture = 1.4 + 3.16 = 4.56 \(l\). Shared equally into 4 bottles: 4.56 ÷ 4 = 1.14 \(l\) each.


After selling, pears left = \(\dfrac{1}{3}\) of pears and oranges left = oranges − 14, and these two are equal. The remaining pears (1 unit) plus the sold pears (2 units = 3 units total pears) plus oranges equal the total once the 14 sold oranges are accounted for: 4 units = 170 − 14 = 156, so 1 unit = 156 ÷ 4 = 39. The oranges left equal the remaining pears = 39.


(a) Nigel took 1 − \(\dfrac{5}{8}\) = \(\dfrac{3}{8}\). (b) Evelyn − Nigel = \(\dfrac{5}{8} - \dfrac{3}{8} = \dfrac{2}{8}\) of the sweets = 76, so \(\dfrac{1}{8}\) = 38 and the whole box = 8 × 38 = 304 sweets.


The total stays $540. In the end John = 5 units and Peter = 1 unit, so 6 units = $540 and 1 unit = $90. (a) Peter has $90 in the end. (b) John had $490 at first ($90 × 5 = $450 at the end, plus the $40 he gave away = $490).


Let Chinese = 3 units, then English = 6 units (twice Chinese). English + Chinese = 9 units = 720, so 1 unit = 80. Malay = English ÷ 3 = 6 ÷ 3 = 2 units. Total = 9 + 2 = 11 units = 11 × 80 = 880 books.


Convert the mixed number to an improper fraction: \(6\dfrac{5}{9} = \dfrac{6\times 9 + 5}{9} = \dfrac{54+5}{9} = \dfrac{59}{9}\). The missing numerator is 59.


Rounded to the nearest thousand, values from 18 500 to 19 499 give 19 000. The greatest possible value is 19 499 (19 500 would round up to 20 000).


Both numbers must be divisible by 3 and by 9. 27 = 9x3 and 36 = 9x4, so both share factors 3 and 9. (12, 18, 21 are not multiples of 9.)


Age this year is a multiple of 7; next year (age + 1) is a multiple of 6. 49 is a multiple of 7 and 49 + 1 = 50 is not a multiple of 6... check: 14+1=15 no; 35+1=36 yes (36=6x6, 35=7x5). So 35 works. Re-check key: key gives option 4 = 49? 49+1=50 not multiple of 6. The valid answer is 35.


Australia is 1 h 30 min ahead of Singapore (10 30 vs 09 00). At 14 50 in Singapore, Australia time = 14 50 + 1 h 30 min = 16 20.


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


49 = 7 x 7, so multiply numerator and denominator of \(\dfrac{4}{7}\) by 7: \(\dfrac{4\times 7}{7\times 7} = \dfrac{28}{49}\). The missing numerator is 28.


20.7 ÷ 7 = 2.957... Rounding to the nearest hundredth (2 decimal places) gives 2.96.


Length + breadth = half the perimeter = 16 cm. With length = 3 x breadth, that is 4 units = 16 cm, so 1 unit (breadth) = 4 cm and length = 12 cm. Area = 12 x 4 = 48 cm².


After selling 46 pears, apples are unchanged and apples = 5 x (remaining pears). Apples are 150 more than the original pears, i.e. 150 + 46 = 196 more than the remaining pears. So 4 units (apples - remaining pears) = 196, 1 unit (remaining pears) = 49. Pears at first = 49 + 46 = 95.


(a) Cost of erasers = 8 x $1.30 = $10.40. Weijian at first = $10.40 + $3.85 = $14.25. (b) Weijian had 3 times Xavier, so Xavier = $14.25 ÷ 3 = $4.75.


Friend got \(\dfrac{5}{8}\) and daughter got \(\dfrac{1}{3}\). Difference = \(\dfrac{5}{8} - \dfrac{1}{3} = \dfrac{15}{24} - \dfrac{8}{24} = \dfrac{7}{24}\) of the cookies = 42. So \(\dfrac{1}{24}\) = 6, and the total (24 units) = 24 x 6 = 144 cookies.


Take 1 group = two $2 notes + one $5 note = $2 + $2 + $5 = $9. Number of groups = $243 ÷ $9 = 27. Each group has two $2 notes, so $2 notes = 27 x 2 = 54.


Look at the tens digit (6). Since 6 ≥ 5, round the hundreds up: 32 769 → 32 800.


Convert the mixed number to an improper fraction: 7 × 5 + 4 = 39, so \(7\dfrac{4}{5}=\dfrac{39}{5}\). Missing number = 39.


0.08 = \(\dfrac{8}{100}\). Divide numerator and denominator by 4: \(\dfrac{8}{100}=\dfrac{2}{25}\).


12.20 p.m. = 1220. Add 15 min wait → 1235. Add 40 min journey → 1315 (in 24-hour time).


LCM of 3, 4 and 6 = 12, so they light together every 12 min. 1st at 1000, 2nd at 1012, 3rd at 1024.


Factors of 12 are 1, 2, 3, 4, 6, 12. The two not yet listed are 4 and 6.


The pattern decreases by 400 each step. 31 200 − 400 = 30 800.


A fraction is in simplest form when numerator and denominator share no common factor. \(\dfrac{3}{6}=\dfrac{1}{2}\) and \(\dfrac{4}{10}=\dfrac{2}{5}\) can be simplified; \(\dfrac{2}{5}\) and \(\dfrac{5}{12}\) cannot.


The fastest runner (smallest time) is 1st. Times: Cleo 15.8 < Dawn 15.9 < Amy 16.1 < Bess 17.0. So 1st Cleo, 2nd Dawn, 3rd Amy, 4th Bess.


20 min before midnight = 2340. From 2340 to 2400 is 20 min; from 0000 to 0450 is 4 h 50 min. Total = 4 h 50 min + 20 min = 5 h 10 min.


Multiples of 3 between 30 and 40: 30, 33, 36, 39. Check remainder 3 when divided by 4: 39 ÷ 4 = 9 R3. So the number is 39.


Bill = 4 units = 98.4 kg, so 1 unit (Charlotte) = 98.4 ÷ 4 = 24.6 kg. Total = 5 units = 5 × 24.6 = 123 kg.


After the transfer each has 1780 ÷ 2 = 890. Sam gave away 40, so Sam had 890 + 40 = 930 at first.


In which of the following numbers does the digit 5 stand for 50?

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


Which of the following numbers when rounded to the nearest ten becomes 81 500?

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


Which of the following is a multiple of 9?

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


Which of the following decimals is the smallest?

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


Nelly sells 384 muffins every month. How many muffins will she sell in a year?

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


When a number is divided by 9, it has a remainder of 2. Which of the following could be the number?

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


Joel runs 300 m every morning. His slowest record is 1 min 35 s. His fastest record is 55 s. What is the difference between his fastest record and his slowest record?


Arrange the following fractions from the greatest to the smallest.
\(\dfrac{2}{3}\), \(\dfrac{3}{4}\), \(\dfrac{5}{12}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


Round 32.55 to the nearest whole number. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tenths digit is 5, so round up: 32.55 → 33.


Find the value of 6.53 × 8. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The difference between two fractions is \(\dfrac{2}{9}\). The smaller fraction is \(\dfrac{1}{6}\). What is the sum of the two fractions? Express your answer in its simplest form.


At first, Peter had twice as much savings as Michelle. After Michelle received $5499, she had twice as much savings as Peter. What is their total savings now? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

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


A tank had 25.68 \(l\) of water. 9 \(l\) of water was poured out of the tank. The remaining amount of water was then poured equally into 6 empty bottles. How much water was poured into each bottle? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

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


A movie at a cinema started at 11.49 a.m. Jasmine arrived at the cinema late and started watching the movie 18 minutes after the movie had started. She watched the movie for 2 h 24 min. What time did the movie end? (Express your answer in 24-hour clock) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

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


Mr Lee sold a total of 25.5 kg of corn flour and plain flour. He sold 5 more packets of corn flour than plain flour. Each packet of corn flour had a mass of 2.7 kg and each packet of plain flour had a mass of 1.3 kg.
(a) What was the mass of 5 packets of corn flour? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many packets of plain flour did he sell? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

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


A sum of $7092 was shared among Kumar, Wei Ming and Hakim. Wei Ming received twice as much money as Kumar. Hakim received 3 times as much money as Wei Ming.
(a) How much money did Kumar receive? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much money did Hakim receive? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

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


After a florist sold \(\dfrac{2}{3}\) of her roses and \(\dfrac{5}{9}\) of her tulips, she had the same number of roses and tulips left. The number of tulips she sold was 85.
(a) How many tulips did she have left? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many roses did she have at first? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

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


There was a total of 60 bicycles and tricycles in a shop. A bicycle has 2 wheels and a tricycle has 3 wheels. There were 156 wheels altogether.
(a) How many bicycles were there? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many more tricycles than bicycles were there in the shop? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

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


43 852 rounded to the nearest hundred is .

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


In which of the following numbers does the digit 4 stand for 4 hundredths?

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


Express \(\dfrac{53}{1000}\) as a decimal.

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


Which of the following is not in its simplest form?

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


Jane completed her job at 01 20. She worked for 4 h 30 min. At what time did she start her job?


Mr Ling sold 8 sofas and some carpets for $5928. The sofa cost $645 each. How much did the carpets cost?


Mandy and William had a total of 1712 stickers at first. After Mandy gave away 92 stickers, William had 5 times as many stickers as Mandy. How many stickers did Mandy have in the end?

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


Jerry bought 3 apples and 1 orange. The cost of 3 apples was $5.25. An apple cost $0.60 less than an orange. What was the cost of an orange?

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


Two factors of 21 are 1 and 21. What are the other two factors of 21? <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 21 are 1, 3, 7 and 21. Besides 1 and 21, the other two factors are 3 and 7.


Find the value of \(\dfrac{7}{9}-\dfrac{2}{3}\).


Round 78.55 to the nearest whole number. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The tenths digit is 5, so round up: 78.55 → 79.


Arrange the following fractions from the smallest to the greatest.
\(\dfrac{5}{6}\), \(\dfrac{5}{12}\), \(\dfrac{11}{12}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


Find the value of 8.26 × 9. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


State the time 36 min before midnight using the 24-hour clock. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>What is the duration from 10 35 to 13 08? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> h <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> min

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


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

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


Rashid and Wen Long cycled a total distance of 8.34 km. Rashid cycled 3 times as far as Wen Long did. How far did Wen Long cycle? Give your answer correct to 2 decimal places. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

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


Siva had some money. She bought 7 books for $8.65 and had $7.45 left. How much money did Siva have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Money at first = money spent + money left = $8.65 + $7.45 = $16.10.


Mrs Chan had 5 \(l\) of orange juice. Her daughter drank \(\dfrac{3}{5}\) \(l\) of it. How much orange juice had Mrs Chan left?


At first, Mei Hua had $48 less than Celeste. Mei Hua then gave $36 to Celeste. How much more money did Celeste have than Mei Hua in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

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


The table shows the ticket prices to an amusement park during the weekdays and weekends.
Adult: weekdays $14.50 per ticket, weekend $31 for 2 tickets.
Child below 12 years old: weekdays $6.90 per ticket, weekend $8.90 per ticket.
(a) Mr Omar took his child, Suresh, to the park on Monday. Suresh was 6 years old. How much did Mr Omar pay for their tickets? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) On Saturday, Mr and Mrs Johnson took their 3 children to the park. Their eldest child was 11 years old. How much did Mr Johnson pay for their tickets? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


At a school activity, one teacher was needed to guide at most 8 pupils in a group. A total of 125 girls and 386 boys participated in the activity. The last group had fewer than 8 pupils.
(a) What was the least number of teachers needed to guide all the pupils? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many pupils were there in the last group? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

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


There are 36 pupils in a class. There are 12 boys in the class.
(a) What fraction of the class are girls? Express your answer in the simplest form. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) \(\dfrac{4}{9}\) of the pupils in the class wear spectacles. How many pupils do not wear spectacles? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


An exercise book cost 4 times as much as a pencil. Paul paid $7.56 for 3 pencils and 1 exercise book.
(a) What was the cost of 1 pencil? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What was the cost of 1 exercise book? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

1 exercise book = 4 pencils, so 3 pencils + 1 book = 3 + 4 = 7 pencils = $7.56. (a) 1 pencil = $7.56 ÷ 7 = $1.08. (b) 1 exercise book = 4 × $1.08 = $4.32.


Mrs Koh had 90 candies and 72 jellies. She packed all of them into as many bags as possible. Each bag contained an equal number of candies. The total number of candies and jellies in each bag was also the same.
(a) How many bags of candies and jellies did Mrs Koh pack? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What was the total number of candies and jellies in each bag? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

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


Mike bought 5 pens and 2 erasers. Kelly bought 2 pens and 5 erasers. Mike paid $2.40 more than Kelly. An eraser cost $0.95.
(a) How much more does a pen cost than an eraser? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What was the cost of a pen? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

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


73 thousands and 8 tens is the same as .


13 845 rounded to the nearest hundred is .

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


\(7\dfrac{4}{5} = \dfrac{ }{5}\)<br>What is the missing number in the box?

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


In the number 45.67, the digit is in the tenths place.

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


Arrange these numbers from the smallest to the greatest.<br>5709, 5079, 5790

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


Which of the following is a multiple of both 3 and 4?

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


Which of the numbers when rounded to the nearest tenth becomes 82.3?

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


Which of the following decimals is closest in value to 0.5?


Mrs Lee bought 9 similar packets of milk.
After she used 6 packets of milk to make some cakes, she had 3.42 \(l\) of milk left.
How many litres of milk did she have at first?

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


Jan has \(\dfrac{3}{4}\) m of cloth. She has \(\dfrac{1}{2}\) m more cloth than Helen. How much cloth do they have altogether?


How many minutes does it take for a minute hand of a clock to make \(1\dfrac{1}{4}\) turn round the clock?

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


Jenny was working from 11 10 to 13 05. How much time did she take to complete her work?

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


The area of a square is 36 cm\u00b2. What is the perimeter of the square?

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


Write the missing number in the number pattern.<br>14 000, 13 400, 12 800, 12 200, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, 11 000


Two factors of 6 are 1 and 6. What are the other two factors of 6?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

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


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


Find the value of 4.73 \u00d7 8. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


7.21 - 5.38 = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />.<br>Round your answer to the nearest 1 decimal place.

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


David spent \(\dfrac{1}{5}\) of his money on a wallet and gave $90 to his mother. He had $104 left. How much money did he spend on the wallet?<br>$<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

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


Doughnuts are sold in boxes of 6, 3 and 2. John bought exactly 119 doughnuts. What was the least number of boxes of each type of doughnuts John bought?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> box(es) of 6
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> box(es) of 3
<input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> box(es) of 2

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


At a concert, \(\dfrac{3}{10}\) of the audience are women and \(\dfrac{1}{5}\) of the audience are men. The rest of the audience are children.
(a) What fraction of the audience are children? [Leave your answer in the simplest form]
(b) There are 180 more children than women. How many women and men are there altogether?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Andy, Ben and Cindy share $1900 altogether. Ben has $145 more than Cindy. Cindy has twice as much money as Andy.
(a) How much money does Andy have?
(b) Find the total amount of money Ben and Cindy have.
(a) $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


A bottle had some amount of milk at first. Peter drank \(\dfrac{1}{4}\) \(l\) of milk in the morning and \(\dfrac{1}{5}\) \(l\) of milk in the afternoon.
(a) How many litres of milk did Peter drink in total?
(b) Peter had \(\dfrac{3}{5}\) \(l\) of milk at first. What was the amount of milk left in the bottle?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Mr Tan had an equal number of apples and oranges. After giving 48 apples and 36 oranges to Mr Lim, the oranges left was three times the number of apples left.
(a) How many apples did Mr Tan have at first?
(b) How many oranges were left?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

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


Which of the following is a factor of both 18 and 27?

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


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

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


\(6\dfrac{4}{7}=\dfrac{ }{7}\)<br>What is the missing number in the box?

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


Express 0.05 as a fraction in its simplest form.

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


The table shows the prices of tickets to a theme park.
Adult: $15
Child: $9
Mrs Tan wants to buy tickets for two adults and three children. How much does she have to pay in total?

Two adults cost 2 × $15 = $30. Three children cost 3 × $9 = $27. Total = $30 + $27 = $57. Answer: $57.


The table shows 4 different types of CCA that 225 children participated in. Each child participated only in one CCA.
Rope Skipping: ?
Gymnastics: 73
International Dance: 50
Girls' Brigade: 64
How many children participated in Rope Skipping?

Add the three known groups: 73 + 50 + 64 = 187. Subtract from the total: 225 − 187 = 38. Answer: 38.


Which of the following fractions has the value closest to 1?


Jamie bought 8 boxes of biscuits. Each box of biscuits cost $1.20. She gave the cashier $50. How much change did Jamie receive?


Harun and Ming Hui started reading their storybooks at 9.45 a.m. Harun took 1 h 20 min to finish reading his storybook. He took 25 min longer than Ming Hui. At what time did Ming Hui finish reading his storybook?

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


How many letters in the word ANGEL have a line of symmetry?

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


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

Thirteen thousand = 13 000 and twenty-six = 26. Together: 13 000 + 26 = 13 026. Answer: 13 026.


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

The numbers decrease by 900 each time (14 100 − 900 = 13 200, and so on). After 11 400, the next term is 11 400 − 900 = 10 500. Check: 10 500 − 900 = 9 600. Answer: 10 500.


What is the remainder when 1536 is divided by 7?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

1536 ÷ 7 = 219 remainder 3, because 7 × 219 = 1533 and 1536 − 1533 = 3. The remainder is 3.


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

\(\dfrac{6}{8}\) simplifies to \(\dfrac{3}{4}\). \(\dfrac{12}{16}\) also simplifies to \(\dfrac{3}{4}\) (divide by 4), and \(\dfrac{3}{4}\) is already in that form. So the two equivalent fractions are \(\dfrac{12}{16}\) and \(\dfrac{3}{4}\).


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


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

5 thousandths means 5 in the thousandths place (the third decimal place): 0.005. Answer: 0.005.


Round 23.51 to the nearest whole number.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The first decimal digit is 5, so round up: 23.51 rounds to 24. Answer: 24.


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


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

3 ÷ 7 = 0.4285... The thousandths digit is 8, so round the hundredths up: 0.43. Answer: 0.43.


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

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


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

'At least 70 stickers' means the 70, 80 and 90 columns together = 87 pupils. The 70 column has 19 pupils, so the 80 and 90 columns together = 87 − 19 = 68 pupils. Answer: 68.


A pair of trousers cost $132. It cost $27 more than a shirt. Mr Lee bought a pair of trousers and 4 shirts.
(a) How much did a shirt cost?
(b) How much did Mr Lee pay for a pair of trousers and 4 shirts altogether?
(a) $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


There were some stickers in a box. Mariam took \(\dfrac{3}{8}\) of the stickers and Amy took the rest. Mariam took 36 fewer stickers than Amy.
(a) What fraction of the stickers did Amy take?
(b) How many stickers were in the box in total?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Amy took the rest: \(1-\dfrac{3}{8}=\dfrac{5}{8}\). (b) The difference between Amy and Mariam is \(\dfrac{5}{8}-\dfrac{3}{8}=\dfrac{2}{8}\) of the total, which equals 36 stickers. So \(\dfrac{2}{8}\) = 36 means \(\dfrac{1}{8}\) = 18, and the total \(\dfrac{8}{8}\) = 18 × 8 = 144 stickers. Answers: (a) \(\dfrac{5}{8}\) (b) 144.


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

(a) They started equal. Ahmad spent $37 and Jack received $15, so the difference between them in the end is $37 + $15 = $52. (b) In the end Jack = 3 × Ahmad, so the difference of $52 equals 2 units (3 − 1). 1 unit = $52 ÷ 2 = $26 (Ahmad's end amount); Jack's end amount = 3 × $26 = $78. Jack at first = $78 − $15 = $63. Answers: (a) $52 (b) $63.


Tina saved some money from Monday to Friday. Each day, she saved $1 more than the previous day. At the end of Wednesday, she saved a total of $38.70.
(a) How much money did Tina save on Wednesday?
(b) How much money did she save on Friday?
(a) $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Forty-six thousand and sixteen in figures is .


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

The digit 8 stands for 80 when it is in the tens place. In 3082 the 8 is in the tens place (80).


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.


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


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

To round to 1 decimal place, look at the 2nd decimal digit (4). Since 4 < 5, round down: 17.54 becomes 17.5.


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?

Remove the extra $25 for the pants: 55 − 25 = 30. This equals 3 shirts (2 shirts + the pants priced as 1 shirt). 1 shirt = 30 ÷ 3 = $10.


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 the hundreds value, 900.


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

Each number decreases by 400. 11 800 − 400 = 11 400.


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

Thousandths are the 3rd decimal place. 5 thousandths = 0.005.


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
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> (greatest), <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> (smallest)

Compare decimal place by place. 3.909 > 3.099 > 3.093 because the tenths digit 9 beats 0, then for 3.099 vs 3.093 the hundredths are equal (9) but thousandths 9 > 3.


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="?" />

The greatest number of boxes is the highest common factor of 36 and 54. Common factors are 1, 2, 3, 6, 9, 18; the greatest 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="?" />


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 than 1.35 p.m.: 1.35 p.m. + 15 min = 1.50 p.m. = 13 50 in 24-hour time.


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, so they differ by 1. Smaller + (smaller + 1) = 667, so 2 × smaller = 666, smaller = 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 = 5u = 5 × 54 = 270. (b) Each had Joey's remainder = 54 − 19 = 35.


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 \(\dfrac{7}{9}\) (the part that is not the \(\dfrac{2}{9}\) left), so 7 units = 49 and 1 unit = 7. (a) Left = 2 units = 2 × 7 = 14 muffins. (b) Mrs Devi baked 9 units = 9 × 7 = 63; both baked equal numbers, so total = 63 × 2 = 126.


Charlie had twice as many 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. Charlie = 2 × (Sally's original). After Sally loses 45, Charlie = 5 × (Sally's new). So 5 units (new Sally) = 2 units (old Sally), meaning Sally lost 45 = the difference; 3 new-units = 45 + 45... using model: Charlie = 5 new-units and = 2 old-units; the 45 lost equals 3 of the new units, so 3u = 45 + 45 = 90, 1u = 30, Charlie = 5u = 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. Since Catherine = 5 × Alice, Catherine − Alice = 4 × Alice = 350, so Alice = 350 ÷ 4 = $87.50.


22 758 rounded to the nearest hundred is

Look at the tens digit (5). Since 58 ≥ 50, round the hundreds up: 22 758 → 22 800.


Arrange the following fractions from the greatest to the smallest.<br>\(\dfrac{1}{3}\), \(\dfrac{5}{6}\), \(\dfrac{7}{12}\)


In the number 32.14, the digit is in the tenths place.

The first digit after the decimal point is the tenths place. In 32.14 that digit is 1.


Which of the following could be the height of the study table?

A study table is about 70 cm tall. 7 m and 70 m are far too tall; 7 cm is far too short.


A fruit seller had 3200 oranges. 310 oranges were rotten. He threw the rotten oranges away and packed the rest equally into 5 boxes. How many oranges were there in each box?


The mass of one parcel is 8.32 kg. Find the mass of 8 such parcels.

8.32 × 8 = 66.56, so 8 parcels have a mass of 66.56 kg.


Kenneth wanted to buy two shirts that cost $25.65 each, but he was short of $14.20. How much money did Kenneth have?


After donating \(\dfrac{1}{3}\) of her money to charity, Janelle had $24 left. How much money did she have at first?

$24 left is \(\dfrac{2}{3}\) of her money. \(\dfrac{1}{3}\) = 24 ÷ 2 = $12, so at first she had 12 × 3 = $36.


Ben is 8 years old. Charles is three times as old as Ben and 4 years older than Daniel. How old is Ben when Daniel is 50 years old?

Now: Charles = 3 × 8 = 24, Daniel = 24 − 4 = 20. The age gap between Ben and Daniel stays the same. Daniel goes from 20 to 50, an increase of 30 years, so Ben becomes 8 + 30 = 38.


Arrange the following numbers from the greatest to the smallest.
379, 937, 973, 397
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

Compare the digits: 973 > 937 > 397 > 379. Greatest to smallest: 973, 937, 397, 379.


Find the value of \(1 - \dfrac{1}{6} - \dfrac{1}{3}\).


Some factors of 32 are 1, 2, 4 and 32. What are the other two factors of 32?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

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


A number when divided by 7 gives a quotient of 145 and a remainder of 6. What is the number?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number = quotient × divisor + remainder = 145 × 7 + 6 = 1015 + 6 = 1021.


The total marks that John and Ken scored in a Science test was 175. John scored 23 more marks than Ken. How many marks did Ken score in the Science test?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Remove John's extra 23: 175 − 23 = 152, which is twice Ken's marks. Ken = 152 ÷ 2 = 76.


Derek baked some cookies. The number of cookies he baked was fewer than 30. He could pack them equally into bags of 3 cookies or bags of 4 cookies with no leftovers. What was the greatest possible number of cookies he baked?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number must be a common multiple of 3 and 4, i.e. a multiple of 12: 12, 24, 36... The greatest below 30 is 24.


Tank A contained 5 times as much water as Tank B at first. After 20.16 \(ℓ\) of water from Tank A was poured into Tank B, both tanks contained an equal amount of water. How much water was there in Tank A at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Tank A = 5 units, Tank B = 1 unit, difference = 4 units. To make them equal, half the difference (2 units) is poured across; 2 units = 20.16 ℓ. So 1 unit = 10.08 ℓ and Tank A = 5 × 10.08 = 50.4 ℓ.


Rachel had some cookies. She gave \(\dfrac{5}{8}\) of them to her grandmother and 7 cookies to her aunt. She then had 20 cookies left. How many cookies did she have at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After giving \(\dfrac{5}{8}\) away, \(\dfrac{3}{8}\) remained. From that, 7 went to the aunt and 20 were left, so \(\dfrac{3}{8}\) = 20 + 7 = 27 cookies. 1 unit = 27 ÷ 3 = 9, so the total \(\dfrac{8}{8}\) = 8 × 9 = 72.


Mdm Devi bought a dress, a shirt and a bag. She spent the same amount of money on the bag and the dress. The shirt cost $49.80 less than the bag. The dress cost 3 times as much as the shirt.
(a) What was the cost of the shirt?
(b) What was the total cost of the dress and the bag?
(a) $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Aisha and Bella had 219 stickers. After Aisha used \(\dfrac{1}{3}\) of her stickers and Bella used 39 stickers, they had the same number of stickers left. How many stickers did Bella have at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After Bella used 39, the remaining stickers total 219 − 39 = 180. Aisha's \(\dfrac{2}{3}\) equals Bella's remainder, and they are equal, so each holds half: 180 ÷ 2 = 90... key: 180 ÷ 5 = 36; Aisha's full set = 36 × 3 = 108, Bella at first = 219 − 108 = 111. So Bella had 72 + 39 = 111.


The first 18 numbers of a number pattern are given.
4, 6, 5, 6, 2, 1, 4, 6, 5, 6, 2, 1, 4, 6, 5, 6, 2, 1, …
(a) What is the 51st number?
(b) What is the sum of the first 61 numbers?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

The pattern repeats every 6 numbers (4, 6, 5, 6, 2, 1; sum = 24). (a) 51 ÷ 6 = 8 remainder 3, so the 51st number is the 3rd in the block = 5. (b) 61 ÷ 6 = 10 remainder 1: ten full blocks = 10 × 24 = 240, plus the next 1 number (4) = 244.


The digit 9 is in the thousands place. So its value is 9 × 1000 = 9000.


70 000 + 1000 + 900 + 5 = 71 905. There are 0 tens, so the tens digit is 0.


Which of the following is a multiple of 5 and 6?

A common multiple of 5 and 6 must appear in both times tables. 30 = 5 × 6 = 6 × 5, so 30 is a multiple of both 5 and 6.


Round 31.76 to the nearest whole number.

Look at the first decimal digit, 7. Since 7 ≥ 5, round up: 31.76 rounds to 32.


Kaye prepared 48 fruit baskets for a party. There were 21 fruits in each basket. How many fruits were there altogether?

Multiply the number of baskets by fruits per basket: 48 × 21 = 1008 fruits.


Hayley's dance lesson is 2 h 30 min long. It started at 11 45. What time did it end?

Start 11 45, add 2 h → 13 45, then add 30 min → 14 15. The lesson ended at 14 15.


In a class, 12 pupils take the bus to school. The remaining 28 pupils walk to school. What fraction of the pupils in class walk to school?

Total pupils = 12 + 28 = 40. Walkers = 28. Fraction who walk = \(\dfrac{28}{40}=\dfrac{7}{10}\).


Lana is 43.5 kg. Her brother is 5.6 kg lighter than her. What is their total mass?


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

Eleven thousand = 11 000 and thirty-five = 35. So in figures it is 11 035.


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

The factors of 18 are 1, 2, 3, 6, 9, 18. Removing the given 1, 2, 3 and 18 leaves 6 and 9.