Eileen has 4 times as many beads as Fiona. Eileen has twice as many beads as Giselle. Fiona has 207 fewer beads than Eileen. How many beads do they have altogether?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Fiona = 1 unit, so Eileen = 4 units. The difference is 4 - 1 = 3 units = 207, so 1 unit = 207 divided by 3 = 69. Fiona = 69, Eileen = 276, Giselle = half of Eileen = 138. Total = 69 + 276 + 138 = 483. (Equivalently, in units: Fiona 1u + Eileen 4u + Giselle 2u = 7u = 7 x 69 = 483.)


Jeanette and Nicole have a total of 197 stickers. Nicole and Scarlett have a total of 203 stickers. The 3 girls have a total of 292 stickers.
(a) How many stickers does Scarlett have?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many stickers does Jeanette have?
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Jeanette + Nicole = 197, so Scarlett = total 292 - 197 = 95. (b) Nicole + Scarlett = 203, so Jeanette = total 292 - 203 = 89.


The amount of sugar in Box A is 250 \(g\) more than the amount of sugar in Box B. After Mrs Lim used 350 \(g\) of sugar in Box B to bake some cupcakes, the amount of sugar in Box A is 5 times as much as the amount of sugar in Box B.
(a) How much sugar is left in Box B?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(g\)
(b) How much sugar is there in Box A?
<input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> \(g\)

After Box B loses 350 g, let Box B = 1 unit and Box A = 5 units. Box A is unchanged, so the difference is now 250 + 350 = 600 g = 4 units. 1 unit = 600 divided by 4 = 150 g, so (a) Box B has 150 g left. (b) Box A = 5 units = 5 x 150 = 750 g.


What is the value of the digit 7 in \(70\ 246\)?

The digit 7 is in the ten-thousands place. Its value is \(7 \times 10\,000 = 70\ 000\).


Which of the following is a multiple of 8?

A multiple of 8 can be divided exactly by 8. \(32 = 8 \times 4\), so 32 is a multiple of 8.


Which of the following is a multiple of both 4 and 5?

A common multiple of 4 and 5 must be in both times tables. \(40 = 4 \times 10 = 5 \times 8\), so 40 is a multiple of both.


Sarah and Tom had the same amount of money. After Sarah spent $336, Tom had 7 times as much money as Sarah in the end. How much money did Sarah have left?

Tom's money never changed, and at first both were equal. Let the starting amount be the whole. After Sarah spends $336, Tom = 7 units and Sarah = 1 unit, so 6 units = $336 → 1 unit = $56. Sarah had $56 left.


Arrange the following numbers from the smallest to the greatest.
\(54\ 678\), \(54\ 867\), \(45\ 876\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Compare digit by digit from the left. 45 876 starts with 4 (smallest). Between 54 678 and 54 867, compare hundreds: 6 < 8, so 54 678 < 54 867. Order: 45 876, 54 678, 54 867.


Write the missing number in the number pattern.<br>\(88\ 520\), \(88\ 720\), \(88\ 920\), <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, \(89\ 320\),


A number is \(29\ 800\) when rounded to the nearest 100. What is the greatest possible whole number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Numbers that round to 29 800 (nearest 100) range from 29 750 up to 29 849. The greatest whole number is 29 849 (29 850 would round up to 29 900).


Some factors of 32 are 1, 2, 4 and 32. What are the other two factors of 32? <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 (\(8 \times 4 = 32\), \(16 \times 2 = 32\)).


A shop had 104 boxes of oranges. Each box had 73 oranges. How many oranges were there altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiply boxes by oranges per box: \(104 \times 73 = 7592\).


A given number is a common factor of 12 and 21. It is greater than 1. What is the number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Factors of 12: 1, 2, 3, 4, 6, 12. Factors of 21: 1, 3, 7, 21. The common factors are 1 and 3. The one greater than 1 is 3.


I am a number between 25 and 35. I am a multiple of 3. One of my factors is 5. What number am I? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 3 between 25 and 35: 27, 30, 33. Of these, only 30 has 5 as a factor (\(30 \div 5 = 6\)). The number is 30.


Alex and Betty had a total of 308 stickers at first. After Alex gave away 56 stickers, Betty had 3 times as many stickers as Alex. How many stickers did Alex have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After Alex gives away 56, the remaining total is \(308 - 56 = 252\). Then Betty : Alex = 3 : 1, so 4 units = 252 → 1 unit = 63. Alex had 63 after, so at first \(63 + 56 = 119\).


A chair costs $280 lesser than a bed. A bed and 4 identical chairs cost $880. How much does each chair cost? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

A bed = 1 chair + $280. So 1 bed + 4 chairs = 5 chairs + $280 = $880 → 5 chairs = $600 → 1 chair = $120.


Ryan baked 3 times as many cookies as Chloe. Ryan sold 66 of his cookies and Chloe sold 10 of her cookies. They then had the same number of cookies left. How many cookies did Ryan bake? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Ryan = 3 units, Chloe = 1 unit. After selling, 3 units − 66 = 1 unit − 10, so 2 units = 66 − 10 = 56 → 1 unit = 28. Ryan baked 3 units = \(28 \times 3 = 84\).


Write the missing number in the number pattern.<br>3489, 3639, 3789, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, 4089

The pattern increases by 150 each step: 3489, 3639, 3789, ... The missing term = 3789 + 150 = 3939 (and 3939 + 150 = 4089, confirming).


Write \(4\dfrac{2}{3}\) as an improper fraction.

Multiply the whole number by the denominator and add the numerator: 4 x 3 + 2 = 14. Keep the denominator: 14/3.


Round 34 578 to the nearest 100.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Look at the tens digit (7). Since 7 is 5 or more, round the hundreds up: 34 578 rounds to 34 600.


14 043 = 14 thousands and 43 ones = Fourteen thousand and forty-three. There are no hundreds.


What is the first common multiple of 6 and 9?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 6: 6, 12, 18, ... Multiples of 9: 9, 18, ... The first (lowest) common multiple is 18.


Find the value of \(1 - \dfrac{1}{4} - \dfrac{5}{12}\)<br>Express your answer in the simplest form.


Which two of the fractions are equivalent?
\(\dfrac{8}{12}\), \(\dfrac{3}{9}\), \(\dfrac{4}{6}\), \(\dfrac{6}{8}\)
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


There are 75 fruits in a box. \(\dfrac{1}{5}\) of the fruits are apples and the rest are oranges. How many oranges are there?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


At a party, there were 3 times as many boys as girls. There were 30 more boys than girls. How many girls were there?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Boys = 3 units, girls = 1 unit, so boys are 2 units more than girls. 2 units = 30, so 1 unit = 30 / 2 = 15 girls.


Mrs Lee is planning a class activity. She has 18 students and wants to divide them into equal groups. Each group must have more than 1 student and there must be more than 1 group. List down 3 possible groupings she can make.
(i) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> groups of <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> students
(ii) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> groups of <input type="text" id="input_3" class="fill-blank-input" placeholder="?" /> students
(iii) <input type="text" id="input_4" class="fill-blank-input" placeholder="?" /> groups of <input type="text" id="input_5" class="fill-blank-input" placeholder="?" /> students

18 can be split into equal groups whose factors are both greater than 1: 2 x 9, 3 x 6, and 6 x 3 (also 9 x 2). Any three valid factor pairs are accepted. Key gives: 2 groups of 9, 3 groups of 6, 6 groups of 3.


Ali, Bobby and Calvin had $4000 altogether. Ali had $1000 more than Bobby. Calvin had $300 less than Bobby. How much money did Calvin have?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Bobby = 1 unit. Ali = 1 unit + 1000, Calvin = 1 unit - 300. Total = 3 units + 1000 - 300 = 4000, so 3 units = 4000 - 700 = 3300, 1 unit = 1100. Calvin = 1100 - 300 = $800. (The printed answer of 2400 is the value of 3 units before division; Calvin actually has $800.)


Mary had some money. She spent \(\dfrac{1}{4}\) of her money on food and \(\dfrac{5}{8}\) of her money on books. She spent $24 more on books than food. How much money did she have at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Cathy and Donna had 465 stickers. After Cathy used \(\dfrac{1}{3}\) of her stickers and Donna used 30 stickers, they had the same number of stickers left. How many stickers did Donna have at first?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After Donna uses 30, the remaining total = 465 - 30 = 435. Cathy keeps 2/3 of her stickers; this 2/3 of Cathy equals Donna's remaining (Donna - 30 originally... ). Using the key method: 435 / 5 = 87 (one part), so Cathy's 1/3 = 87 used. Donna's stickers left = 87 x 2 = 174, and Donna at first = 174 + 30 = 204.


The table shows the favourite colours of some children.
Colour: Red, Green, Blue, Black, Yellow
Number of children: 12, 9, 13, 3, 6
Which colour is liked by twice as many children as those who like the colour yellow?

Yellow is liked by 6 children. Twice 6 is \(2 \times 6 = 12\). Red is liked by 12 children, so the answer is Red.


Express \(3\dfrac{1}{8}\) as an improper fraction.

Multiply the whole number by the denominator and add the numerator: \(3 \times 8 + 1 = 25\). So \(3\dfrac{1}{8} = \dfrac{25}{8}\).


Which of the following is not an equivalent fraction of \(\dfrac{3}{4}\)?

\(\dfrac{6}{8}, \dfrac{9}{12}, \dfrac{15}{20}\) all simplify to \(\dfrac{3}{4}\). \(\dfrac{13}{14}\) does not, so it is not equivalent.


Find the difference between \(\dfrac{1}{3}\) and \(\dfrac{5}{8}\).


The table shows the number of pupils in two CCAs.
Concert Band: 15 girls, 17 boys, total ?
Robotics Club: 17 girls, ? boys, total 97
How many more boys than girls are there in Robotics Club? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Number of boys in Robotics Club \(= 97 - 17 = 80\). More boys than girls \(= 80 - 17 = 63\).


The table shows the number of pupils in two CCAs.
Concert Band: 15 girls, 17 boys, total ?
Robotics Club: 17 girls, ? boys, total 97
How many fewer pupils joined Concert Band than Robotics Club? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Concert Band total \(= 17 + 15 = 32\) pupils. Robotics Club has 97 pupils. Fewer \(= 97 - 32 = 65\).


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


The table shows the number of P4 pupils who took part in different activities at 'Sports Day'.
Relay Race: 48, Soccer: 36, Tug-of-war: 52, Volleyball: 64
(a) How many pupils took part in the activities? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Some pupils took part in an activity at 'Sports Day' that had \(\dfrac{3}{4}\) as many pupils who took part in Volleyball. Which activity was it? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Total \(= 48 + 36 + 52 + 64 = 200\) pupils. (b) \(\dfrac{3}{4}\) of Volleyball \(= 64 \div 4 = 16\), then \(16 \times 3 = 48\). The activity with 48 pupils is Relay Race.


\(\dfrac{3}{8}\) of counters in a container are red and the rest are blue.<br>(a) What fraction of the counters are blue?


Rena and Sebastian shared 72 stickers. Rena had \(\dfrac{4}{9}\) of the stickers.
(a) How many stickers did Rena have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many stickers would Sebastian give to Rena so that both had an equal number of stickers? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


(a) Round 168.205 to 2 decimal places.
(b) Express \(\dfrac{3}{25}\) as a decimal.
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) The digit in the 3rd decimal place is 5, so round the 2nd decimal place up: \(168.205 \approx 168.21\). (b) Make the denominator 100: \(\dfrac{3}{25} = \dfrac{12}{100} = 0.12\).


Find the value of \(3.9 + 15.72\). Round your answer to the nearest tenth.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

\(3.90 + 15.72 = 19.62\). The hundredths digit is 2, so it rounds down: \(19.62 \approx 19.6\) to the nearest tenth.


What is the product of 6 ones and 72 hundredths?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

6 ones = 6 and 72 hundredths = 0.72. The product is \(6 \times 0.72 = 4.32\).


Arrange the following in increasing order.
\(4\dfrac{3}{4}\) , 4.90, \(4\dfrac{7}{10}\) , 4.65
<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="?" />
(smallest)


5 identical bags of flour weigh \(28.15\) \(kg\) in total. How much do 8 identical bags of flour weigh?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg


A tailor used \(42.1\) \(m\) of fabric on Monday. He used \(28.62\) \(m\) more fabric on Monday than on Tuesday.
(a) How many metres of fabric did the tailor use on Tuesday?
(b) How many metres of fabric did he use altogether over the two days?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m
(b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> m


James had 3 times as much money as Sally at first. When Mrs Lee gave $7.20 to James and $22.50 to Sally, both James and Sally had the same amount of money.
(a) Find the amount of money Sally had at first.
(b) Find the amount of money James had at first.
(a) $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Let Sally = 1 unit, James = 3 units. After: Sally has 1u + $22.50, James has 3u + $7.20, and they are equal. So 3u + 7.20 = 1u + 22.50, giving 2u = 22.50 − 7.20 = $15.30. (a) Sally at first = 1u = $15.30 ÷ 2 = $7.65. (b) James at first = 3u = $7.65 × 3 = $22.95.


Which of the following is not true about both squares and rectangles?

A rectangle has its two pairs of opposite sides equal but not all four sides equal, so 'All the sides are equal' is true only for squares, not both shapes. The other three statements hold for both.


A bag of flour has a mass of \(\dfrac{3}{4}\) \(kg\). The bag of flour is \(\dfrac{1}{8}\) \(kg\) heavier than a bag of sugar. What is the total mass of the two bags?


There are 72 black and white buttons in a box. \(\dfrac{5}{6}\) of them are white buttons and the rest are black buttons. How many more white than black buttons are there?


Mr Pang sold some packets of sugar and 24 packets of salt. \(\dfrac{4}{7}\) of the total packets sold were sugar. How many packets of sugar were sold? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Sugar is \(\dfrac{4}{7}\) of the total, so salt is \(\dfrac{3}{7}\) of the total. 3 units = 24, so 1 unit = \(24 \div 3 = 8\). Sugar = 4 units = \(8 \times 4 = 32\) packets.


Gabby gave \(\dfrac{5}{8}\) of her stickers to Hani and \(\dfrac{1}{4}\) of them to Ivy. Ivy received 12 fewer stickers than Hani. How many stickers did Gabby have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Hani got \(\dfrac{5}{8}\) and Ivy got \(\dfrac{1}{4} = \dfrac{2}{8}\). The difference is \(\dfrac{5}{8} - \dfrac{2}{8} = \dfrac{3}{8}\), which equals 12 stickers. So 3 units = 12, 1 unit = \(12 \div 3 = 4\). Total = 8 units = \(8 \times 4 = 32\) stickers.


Mrs Goh had some tea. She poured \(\dfrac{2}{5}\) \(\ell\) of it into a jug. She then poured the remaining amount of tea into 2 equal cups. Each cup contained \(\dfrac{3}{10}\) \(\ell\) less amount of tea than the amount of tea in the jug. (a) How much tea did she pour into each cup? (b) How much tea did she make? Express your answer in its simplest form. <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


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

Twenty-seven thousand = 27000, three hundred = 300, nine = 9. Combine: 27000 + 300 + 9 = 27309.


Round 10 247 to the nearest ten. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Look at the ones digit of 10247, which is 7. Since 7 is 5 or more, round the tens digit up: 10247 rounds to 10250.


Write down the common factors of 15 and 20. <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Factors of 15: 1, 3, 5, 15. Factors of 20: 1, 2, 4, 5, 10, 20. The common factors are 1 and 5.


Arrange the following fractions from the smallest to the greatest.
\(\dfrac{1}{3}\)    \(\dfrac{1}{10}\)    \(\dfrac{1}{6}\)
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />   (c) <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

For unit fractions, the larger the denominator, the smaller the fraction. Denominators are 3, 10, 6. From smallest to greatest fraction: 1/10 (denom 10), 1/6 (denom 6), 1/3 (denom 3).


What is the remainder when 5840 is divided by 7? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


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


What is the missing number in the box?<br>\(\dfrac{1}{3} = \dfrac{<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />}{12}\)

To change the denominator from 3 to 12, multiply by 4. Multiply the numerator by the same: 1 \(\times\) 4 = 4. So \(\dfrac{1}{3} = \dfrac{4}{12}\).


A number is a multiple of 9 and a factor of 6.
It is between 60 and 80.
What is the number?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 9 between 60 and 80: 63 and 72. The number must also be a multiple of 6. 63 \(\div\) 6 = 10 remainder 3 (not a multiple of 6); 72 \(\div\) 6 = 12 (a multiple of 6). So the number is 72.


The sum of two numbers is 7390.
The greater number is 4 times the smaller number.
What is the greater number?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the smaller number be 1 unit; the greater is 4 units. Together 5 units = 7390. 1 unit = 7390 \(\div\) 5 = 1478. Greater number = 4 units = 1478 \(\times\) 4 = 5912.


Xavier, Yusof and Zachary scored a total of 561 points in a game.
Xavier scored 93 more than Yusof.
Zachary scored twice the total number of points Xavier and Yusof scored.
How many points did Xavier score?
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Xavier + Yusof = 1 unit. Zachary = 2 units. Total = 3 units = 561, so 1 unit = 561 \(\div\) 3 = 187 (Xavier + Yusof). Xavier is 93 more than Yusof: Yusof = (187 - 93) \(\div\) 2 = 47, Xavier = 47 + 93 = 140.


Aisyah sold some cupcakes at a carnival. For every 30 cupcakes sold, she would donate $5 to a charity. In the end, Aisyah donated $80 to the charity.
(a) How many cupcakes did Aisyah sell?
(b) Aisyah sold each cupcake for $3. After donating $80, how much did she earn from the sale?
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Arrange the fractions in increasing order.<br>\(\dfrac{15}{7}\), \(1\dfrac{4}{9}\), \(\dfrac{5}{3}\)


Ms Lim is planning for a class party. She wants to buy enough pizza such that each of her 35 students can have \(\dfrac{1}{6}\) of a pizza. The shop only sells whole pizza. What is the least number of whole pizza Ms Lim need to buy?

Total pizza needed = \(35\times\dfrac{1}{6} = \dfrac{35}{6} = 5\dfrac{5}{6}\) pizzas. Since only whole pizzas are sold, round up to 6 (option 2).


(a) Express \(\dfrac{22}{4}\) as a mixed number in its simplest form.<br>(b) \(\dfrac{2}{9}\) of 63 = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mdm Siti had 5 \(l\) of orange juice. She drank \(\dfrac{3}{8}\) \(l\) of orange juice. How much orange juice did she have left?


Alice jogs \(\dfrac{3}{4}\) \(km\) at a park. She walks \(\dfrac{5}{12}\) \(km\) less than the distance she jogs. What is the total distance she jogs and walks?


A box is filled with some balls. \(\dfrac{4}{11}\) of the balls are yellow and the rest of the balls are red. There are 42 more red balls than yellow balls. How many balls are there in the box altogether? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Yellow = 4 units, red = 11 − 4 = 7 units. Difference = 7 − 4 = 3 units = 42, so 1 unit = 14. Total = 11 units = 14 × 11 = 154 balls.


Lucy had \$954. She spent \(\dfrac{5}{9}\) of her money to buy a pair of shoes. How much had she left after buying the pair of shoes? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: the money is 9 equal units. She spent \(\dfrac{5}{9}\), so \(\dfrac{4}{9}\) is left. 9 units = \$954, so 1 unit = \(954\div9=106\)... using the unitary method 4 units left = \$424. The answer is \$424.


Bag A weighs \(\dfrac{1}{4}\) kg. Bag B weighs \(\dfrac{3}{5}\) kg. Bag C weighs \(\dfrac{5}{8}\) kg.
(a) Which 2 bags, when added together, will be heavier than 1 kg? Answer: Bag <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> and Bag <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />
(b) Muthu puts a laptop into Bag B. The total mass of Bag B and the laptop is 3 kg. What is the mass of the laptop, in kg?

(a) Check each pair against 1 kg. Bag B + Bag C = \(\dfrac{3}{5}+\dfrac{5}{8}=\dfrac{24}{40}+\dfrac{25}{40}=\dfrac{49}{40}\) which is more than 1 kg; the other pairs are less. So Bag B and Bag C. (b) Laptop mass = total minus Bag B = \(3-\dfrac{3}{5}=2\dfrac{2}{5}\) kg.


Ali drank \(\dfrac{7}{10}\) \(\ell\) of water. He drank \(\dfrac{1}{5}\) \(\ell\) of water more than Harry. How much water did Ali and Harry drink in total? Give your answer as a mixed number.


Jim had 3 pieces of rope. Rope A is the longest. Its length is \(\dfrac{9}{10}\) m. The difference between the lengths of Rope A and Rope B is \(\dfrac{3}{4}\) m.
(a) What is the length of Rope B, in m? Give your answer in its simplest form.
(b) Rope B is the shortest. The difference between the lengths of Rope B and Rope C is \(\dfrac{1}{2}\) m. What is the length of Rope C, in m?
(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 fruit seller sold some apples, pears and watermelons. \(\dfrac{2}{7}\) of the fruits sold were pears, \(\dfrac{4}{7}\) of the fruits sold were apples and the rest of the fruits sold were watermelons. He sold 360 more apples than watermelons.
(a) How many pears did the fruit seller sell?
(b) How many apples, pears and watermelons did the fruit seller sell 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="?" />

Method: treat the total as 7 units. Pears = 2 units, apples = 4 units, watermelons = \(7-2-4=1\) unit. Apples minus watermelons = \(4-1=3\) units = 360, so 1 unit = \(360\div3=120\). (a) Pears = 2 units = \(2\times120=240\). (b) Total = 7 units = \(7\times120=840\).


Which number has the digit 3 in the thousands place?

The thousands place is the 4th digit from the right. In 73 648 the digits are 7 (ten thousands), 3 (thousands), 6 (hundreds), 4 (tens), 8 (ones). So 73 648 has 3 in the thousands place.


Which of the following is not an equivalent fraction of \(\dfrac{1}{4}\)?

Equivalent fractions of 1/4: multiply top and bottom by the same number. 2/8 (x2), 3/12 (x3), 5/20 (x5) all equal 1/4. But 4/12 = 1/3, not 1/4. So 4/12 is the odd one out.


Which of the following decimals is the greatest?

Compare the tenths digit first: 0.030 (0 tenths), 0.42 (4 tenths), 0.176 (1 tenth), 0.234 (2 tenths). The largest tenths value is 4, so 0.42 is the greatest.


At a carnival, every 6th participant receives a cup of drink and every 8th participant receives a key chain. Which is the first participant to receive both a cup of drink and a key chain?

Find the lowest common multiple of 6 and 8. Multiples of 6: 6, 12, 18, 24... Multiples of 8: 8, 16, 24... The smallest common multiple is 24, so the 24th participant receives both.


Arrange the following from the greatest to the smallest.
\(1\dfrac{1}{9}\), \(\dfrac{4}{5}\), \(\dfrac{7}{6}\)
Greatest: <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="?" /> :Smallest


Use all the digits 5, 2, 7, 0, 4 to form
(a) the largest 5-digit number <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) the smallest 5-digit even number <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Largest: arrange digits from greatest to least: 7, 5, 4, 2, 0 = 75420. (b) Smallest even: the number must end in an even digit and cannot start with 0. Smallest leading digit is 2, then smallest remaining with an even last digit gives 20574 (ends in 4).


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

Make denominators the same: 2/3 = 4/6. Then 5/6 + 4/6 = 9/6 = 3/2. As a mixed number, 3/2 = 1 1/2.


What is the value of \(4 \div 7\)? Correct your answer to 1 decimal place.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

4 / 7 = 0.5714... To 1 decimal place, look at the second decimal digit (7), which rounds up. So 0.57... rounds to 0.6.


The table shows the number of times Primary Four students in a school jog in a week.
Number of times jogged in a week: 1, 2, 3, 4, 5
Number of students: 61, 50, 42, 75, 80
How many students jogged more than 2 times in a week?
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

More than 2 times means 3, 4 or 5 times. Add those student counts: 42 + 75 + 80 = 197.


Tina baked some cookies. She gave \(\dfrac{3}{10}\) of the cookies to her neighbour and had 84 cookies left. How many cookies did she give to her neighbour?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

She gave 3/10, so the 84 left represent the remaining 7/10. 1/10 = 84 / 7 = 12. She gave 3/10 = 3 x 12 = 36 cookies.


\(\dfrac{13}{25}=0.5+\) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Joseph had 1378 marbles and Kumar had 1490 marbles. Kumar gave some marbles to Joseph. In the end Joseph had twice as many marbles as Kumar.
(a) How many marbles did Kumar have in the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many marbles did Kumar give Joseph? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

Total marbles stay the same: 1378 + 1490 = 2868. In the end Joseph = twice Kumar, so they share into 3 equal parts. (a) Kumar's end = 2868 / 3 = 956. (b) Kumar gave away = his start minus his end = 1490 - 956 = 534.


Amy read \(\dfrac{1}{4}\) of a book on Saturday, \(\dfrac{1}{8}\) of the book on Sunday and the remaining pages on Monday. She read 72 fewer pages on Saturday than on Monday. How many pages were there in the book?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Saturday = 1/4 = 2/8, Sunday = 1/8. Together = 3/8, so Monday = 8/8 - 3/8 = 5/8. Difference between Monday and Saturday = 5/8 - 2/8 = 3/8, which equals 72 pages. So 1/8 = 72 / 3 = 24, and the whole book = 8/8 = 24 x 8 = 192 pages.


Round 25 571 to the nearest hundred. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The hundreds digit of 25 571 is 5. The digit after it (tens) is 7, which is 5 or more, so round up. 25 571 rounds to 25 600.


How many one-fifths are there in 3 wholes? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Each whole contains 5 one-fifths. For 3 wholes: \(3 \times 5 = 15\) one-fifths.


Find the value of \(\dfrac{11}{12} - \dfrac{2}{3}\) in its simplest form.


Find the value of
a) \(4269 \times 3\)
b) \(217 \times 15\)
(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


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


I am a number greater than 20 but less than 40. I am a multiple of 6 and a factor of 48. What number am I? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 6 between 20 and 40: 24, 30, 36. Factors of 48: 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. The only number in both lists is 24.


A number is 15 000 when rounded to the nearest thousand. What is the greatest possible value of the number? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To round to 15 000, the number must be from 14 500 to 15 499. The greatest whole number that still rounds down to 15 000 is 15 499.


Find the quotient and remainder when 4505 is divided by 6. <br>(a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />   (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Rihana had $105. She used \(\dfrac{1}{3}\) of it on a watch and spent the rest of her money on a present. How much did the present cost? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Janice had twice as many stamps as Kenneth at first. After Kenneth had given away 24 stamps, Janice had 5 times as many stamps as Kenneth. How many stamps did Kenneth have? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Janice is unchanged. Let Kenneth's start = K, so Janice = 2K. After giving away 24, Kenneth = K - 24 and 2K = 5(K - 24). So \(2K = 5K - 120\), \(3K = 120\), \(K = 40\). Kenneth had 40 stamps.


Raphael has some chocolates to give to his friends at a party. The number of chocolates he has is less than 30. If he gives 4 chocolates to each friend, he will have 2 extra chocolates. If he gives 5 chocolates to each friend, he will need 1 more chocolate.
a) How many chocolates does Raphael have?
b) How many friends does Raphael have at the party?
(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 f = number of friends. Chocolates = \(4f + 2\) (2 extra) and also \(5f - 1\) (needs 1 more). So \(4f + 2 = 5f - 1\), giving \(f = 3\). Chocolates \(= 4 \times 3 + 2 = 14\) (less than 30, checks out).


Giresh had $108 more than Beng Huat. After both of them spent an equal amount of money to buy some stationery, the amount of money Giresh had left was 3 times as much as Beng Huat. Given that Giresh had $198 at first, how much did each of them spend? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Beng Huat at first \(= 198 - 108 = \$90\). After spending the same amount, Giresh = 3 units and Beng Huat = 1 unit, so the difference of 2 units still equals $108 (the difference is unchanged). \(1 \text{ unit} = 108 \div 2 = \$54\) = Beng Huat's money left. So each spent \(90 - 54 = \$36\).


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

Hundredths is the second place after the decimal point. In 92.54, the 4 is in the hundredths place, so it stands for 4 hundredths (0.04).


(a) Write \(\dfrac{15}{7}\) as a mixed number. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Express 0.75 as a fraction in its simplest form. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) \(15 \div 7 = 2\) remainder \(1\), so \(\dfrac{15}{7} = 2\dfrac{1}{7}\). (b) \(0.75 = \dfrac{75}{100} = \dfrac{3}{4}\) after dividing numerator and denominator by 25.


(a) Arrange the following in decreasing order. \(\dfrac{13}{5}\), \(2\dfrac{3}{4}\), \(\dfrac{7}{8}\)
<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="?" />
(b) What is the missing number in the box? \(\dfrac{15}{24} = \dfrac{<input type="text" id="input_3" class="fill-blank-input" placeholder="?" />}{8}\)


Leonard had $120. He spent \(\dfrac{5}{8}\) of his money and saved the rest. How much did Leonard save? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Sophia drank \(\dfrac{7}{10}\) \(\ell\) of apple juice. John drank \(\dfrac{1}{5}\) \(\ell\) of apple juice less than her. How much apple juice did they drink altogether? Give your answer as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(\ell\)


Helen was preparing for her Science examination. She managed to revise \(\dfrac{1}{4}\) of her textbook on Saturday and \(\dfrac{1}{6}\) of it on Sunday. She had 98 more pages to read. How many pages were there in the textbook? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Revised over the weekend: \(\dfrac{1}{4}+\dfrac{1}{6}=\dfrac{3}{12}+\dfrac{2}{12}=\dfrac{5}{12}\). Left to read: \(1-\dfrac{5}{12}=\dfrac{7}{12}\), which equals 98 pages. So \(\dfrac{1}{12}=98\div7=14\) pages, and the whole textbook = \(14\times12=168\) pages.


Ali, Benny and Charles have some marbles. Benny has three times as many marbles as Ali. Charles has \(\dfrac{1}{2}\) of the total number of marbles that Ali and Benny have altogether.
(a) The total number of marbles the 3 boys have is 1260. How many marbles does Benny have? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Charles gave \(\dfrac{5}{6}\) of his marbles to his brother. How many marbles did he have left? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Let Ali = 1 unit, then Benny = 3 units, Ali+Benny = 4 units, Charles = half of that = 2 units. Total = 1+3+2 = 6 units = 1260, so 1 unit = 1260 ÷ 6 = 210. Benny = 3 × 210 = 630. (b) Charles = 2 units = 420 marbles. He gave away \(\dfrac{5}{6}\), so he kept \(\dfrac{1}{6}\) = 420 ÷ 6 = 70 marbles.


There are some beads in a box. \(\dfrac{7}{9}\) of them are red beads and the rest are blue beads. There are 130 more red beads than blue beads.<br>(a) What fraction of the beads are blue?

(a) Blue fraction = \(1-\dfrac{7}{9}=\dfrac{2}{9}\). (b) Red is \(\dfrac{7}{9}\) and blue is \(\dfrac{2}{9}\), so red exceeds blue by \(\dfrac{5}{9}\) = 130 beads. So \(\dfrac{1}{9}=130\div5=26\) beads, and total = \(26\times9=234\) beads.


Express \(\dfrac{26}{7}\) as a mixed number.


Mdm Ling bought \(1\ \ell\) of orange juice. She drank \(\dfrac{1}{6}\ \ell\) of the juice and bought another \(\dfrac{1}{3}\ \ell\) of juice. How much juice was left in the end?


Hanz ran a distance of \(\dfrac{5}{7}\) km. The distance Sam ran was \(\dfrac{1}{2}\) km shorter than Hanz. What was the total distance that Hanz and Sam ran?


A tank is \(\dfrac{3}{8}\) filled with water. \(120\ \ell\) more of water are needed to fill the tank completely. What is the capacity of the tank?<br>\(<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />\) \(\ell\)

The empty part is \(1 - \dfrac{3}{8} = \dfrac{5}{8}\), which equals 120 L. So \(\dfrac{1}{8} = 120 \div 5 = 24\) L. Capacity = \(24 \times 8 = 192\) L.


Mrs Lim used \(\dfrac{3}{4}\) kg of flour to bake some cupcakes. She used \(\dfrac{1}{3}\) kg of flour more than Mdm Siti. How much flour did they use altogether? Express your answer as a mixed number in its simplest form.


There were some adults and children at a carnival. \(\dfrac{5}{6}\) of the people were children and the rest were adults. There were 240 more children than adults. How many people were there altogether?<br>\(<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />\)

Children = \(\dfrac{5}{6}\), adults = \(\dfrac{1}{6}\). Difference = \(\dfrac{5}{6} - \dfrac{1}{6} = \dfrac{4}{6}\) of the people = 240, so 4 units = 240, 1 unit = 60. Total = 6 units = \(60 \times 6 = 360\).


At a stationery shop, ribbons are sold by the piece. The price of each type of ribbon is: Embroidery $4 per piece, Silk $2 per piece, Lace $1 per piece. Trisha and Kate have a total of $21 to spend on ribbons. Trisha bought 3 pieces of silk ribbon. How much money is left for Kate to spend? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: cost of silk = price x quantity, then subtract from total. Silk: \(\$2 \times 3 = \$6\). Money left for Kate \(= \$21 - \$6 = \$15\). Answer: $15.


What is fifty-three thousand, four hundred and eight in numbers?


What is 28 349 when rounded to the nearest hundred?

Look at the tens digit (4). Since \(4 < 5\), round down. 28 349 to the nearest hundred is 28 300.


A 2-digit number is a factor of 56 and a multiple of 4. It is more than 10 but less than 40. What is the number?

Factors of 56: 1, 2, 4, 7, 8, 14, 28, 56. The 2-digit factors are 14, 28, 56. Of these, a multiple of 4 is 28 (\(4 \times 7 = 28\)). It is between 10 and 40. Answer: 28.


Arrange the following numbers from the greatest to the smallest.<br>62 354 , 62 435 , 62 345

All share 62 _ _ _. Compare hundreds: 62 435 has 4, while 62 354 and 62 345 have 3. So 62 435 is greatest. Then compare 62 354 and 62 345 by tens: 5 > 4, so 62 354 > 62 345. Greatest to smallest: 62 435, 62 354, 62 345.


What is the remainder when 7013 is divided by 5? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


I am a multiple of 6 and 9. I am between 20 and 40. What number am I? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Common multiples of 6 and 9 are multiples of 18: 18, 36, 54, ... The one between 20 and 40 is 36. Answer: 36.


What is the sum of the common factors of 36 and 81? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A tailor sews 16 buttons on a shirt. How many buttons are needed to sew 589 shirts? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiply the buttons per shirt by the number of shirts: \(589 \times 16 = 9424\). The tailor needs 9424 buttons.


A number is 5090 when rounded to the nearest 10.
(a) The smallest possible number is <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) The greatest possible number is <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

To round to 5090 to the nearest 10, the number must be at least 5085 (rounds up) and at most 5094 (rounds down). (a) smallest = 5085. (b) greatest = 5094.


Adam bought 28 boxes of balloons from a party store. Each box contained 36 balloons and costs $18. He paid the cashier some money and received $46 change.
(a) How many balloons did he buy?
(b) How much money did he give to the cashier?
(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) Balloons: \(28 \times 36 = 1008\). (b) Cost of boxes: \(28 \times 18 = 504\). He received $46 change, so the money given = \(504 + 46 = \$550\).


Andrea and Ben had 3678 strawberries altogether. After Andrea gave 34 strawberries to Ben, she had 5 times as many strawberries as Ben. How many more strawberries did Andrea have than Ben at first? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The total stays 3678. After giving, Andrea : Ben = 5 : 1, which is 6 equal units. \(3678 \div 6 = 613\) per unit. After: Ben = 613, Andrea = \(5 \times 613 = 3065\). At first: Andrea = \(3065 + 34 = 3099\), Ben = \(613 - 34 = 579\). Difference = \(3099 - 579 = 2520\).


Rosie bought a table and 5 similar chairs at $2885. The table cost $245 more than a chair. How much did the table cost? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


There were 830 blue and 124 red buttons in a box. After an equal amount of buttons were added for both colours, the number of blue buttons was three times the number of red buttons. How many blue buttons were added? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the amount added to each colour be the same. The difference between blue and red stays \(830 - 124 = 706\). After, blue = 3 × red, so the difference is 2 units = 706, giving 1 unit (red after) = \(706 \div 2 = 353\). Added = \(353 - 124 = 229\).


Express \(3\dfrac{4}{6}\) as an improper fraction.

To convert a mixed number to an improper fraction: \(3\dfrac{4}{6} = \dfrac{(3 \times 6) + 4}{6} = \dfrac{18 + 4}{6} = \dfrac{22}{6}\). The answer is \(\dfrac{22}{6}\).


Which fraction is greater than \(\dfrac{1}{2}\)?

Half of each denominator gives the value equal to \(\dfrac{1}{2}\). For \(\dfrac{3}{5}\), half of 5 is 2.5, and the numerator 3 > 2.5, so \(\dfrac{3}{5} > \dfrac{1}{2}\). The others (4 of 9, 2 of 7, 3 of 8) are all less than half. The answer is \(\dfrac{3}{5}\).


Find the sum of \(\dfrac{1}{4}\) and \(\dfrac{1}{12}\).

Make the denominators the same: \(\dfrac{1}{4} = \dfrac{3}{12}\). Then \(\dfrac{3}{12} + \dfrac{1}{12} = \dfrac{4}{12} = \dfrac{1}{3}\). The answer is \(\dfrac{1}{3}\).


Express \(\dfrac{48}{7}\) as a mixed number in its simplest form.

Divide the numerator by the denominator: \(48 \div 7 = 6\) remainder \(6\). So \(\dfrac{48}{7} = 6\dfrac{6}{7}\). The answer is \(6\dfrac{6}{7}\).


The total mass of a bowl and a mug is \(\dfrac{2}{3}\) kg. Given that the bowl weighs \(\dfrac{2}{5}\) kg, what is the mass of the mug? Express your answer in its simplest form. Give your answer in \(kg\).

Mass of mug = total - bowl. Common denominator 15: \(\dfrac{2}{3} = \dfrac{10}{15}\) and \(\dfrac{2}{5} = \dfrac{6}{15}\). So mug = \(\dfrac{10}{15} - \dfrac{6}{15} = \dfrac{4}{15}\) kg. The answer is \(\dfrac{4}{15}\).


What is the value of the digit 9 in 5.092?

In \(5.092\) the digits after the decimal point are tenths, hundredths and thousandths. The digit 9 is in the second place after the point, which is the hundredths place. So its value is 9 hundredths.


Round 19.536 to the nearest hundredths.<br>\(19.536\approx\) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To round to the nearest hundredth, look at the thousandths digit. In \(19.536\) the thousandths digit is 6, which is 5 or more, so round the hundredths digit up: \(19.53\to19.54\).


Arrange the following decimals from the greatest to the smallest.
\(6.4\)   \(0.64\)   \(60.4\)   \(6.04\)
<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 whole-number parts first: \(60.4\) is the largest. Then \(6.4\) and \(6.04\) both start with 6, but \(6.4=6.40\) is greater than \(6.04\). Smallest is \(0.64\). Greatest to smallest: \(60.4, 6.4, 6.04, 0.64\).


A pot contained \(3.4\) \(l\) of water. A kettle contained \(2.25\) \(l\) less water than the pot. How much water was there in 3 such kettles?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(l\)


David saved $5.50 a day for 4 days. He needed to save another $23.90 to buy a pair of shoes. What was the price of the pair of shoes?<br>$ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Money David saved: \(\$8.50\times4=\$34.00\). Price of shoes = money saved + money still needed: \(\$34.00+\$23.90=\$57.90\).


Mrs Tan bought a blouse and a dress. The blouse cost $22.30. The dress cost 4 times as much as the blouse.
(a) What was the cost of the dress? $ <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How much more did Mrs Tan pay for the dress than the blouse? $ <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />


Mrs Yeo mixed \(5.7\) \(l\) of orange syrup with \(9.55\) \(l\) of water to make an orange drink.
(a) How much orange drink did Mrs Yeo make? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> \(l\)
(b) She poured all the orange drink that she made equally into 5 jugs. How many litres of orange drink was in each jug? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> \(l\)

(a) Total drink = \(5.7+9.55=15.25\) l. (b) Poured equally into 5 jugs: \(15.25\div5=3.05\) l per jug.


Arrange the fractions from the smallest to the greatest.<br>\(\dfrac{9}{4}\) , \(\dfrac{7}{3}\) , \(2\dfrac{7}{12}\)


Find the value of \(\dfrac{3}{5}+\dfrac{5}{7}\) .<br>Give your answer as a mixed number in the simplest form.


Siti baked 36 muffins.
She gave \(\dfrac{5}{9}\) of them to her neighbours.
How many muffins had she left? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

She gave away 5/9, so she kept 4/9. 9 units = 36 muffins, 1 unit = 4 muffins, 4 units = 4 x 4 = 16 muffins left.


Sue has \(\dfrac{5}{6}\) m of ribbon. Her ribbon is \(\dfrac{1}{3}\) m shorter than Halimah's.
Find the length of Halimah's ribbon.
Give your answer in the simplest form.


Eric had \(\dfrac{7}{8}\) kg of strawberry. He ate \(\dfrac{1}{4}\) kg of the strawberry.
How much strawberry had he left?
Give your answer in its simplest form.


Mr. Lee sells 4 similar laptops and 1 printer for $5775.
1 printer is sold at $1000 less than 1 laptop.
What is the price of a printer? $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

A printer costs $1000 less than a laptop. Make all 5 items the same by lowering each of the 4 laptops by $1000 to match the printer: subtract 4 x 1000 = 4000 from the total. 5 printer-priced units = 5775 - 4000 = 1775, so 1 printer = 1775 ÷ 5 = $355. (Check: laptop = 355 + 1000 = 1355; 4 x 1355 + 355 = 5420 + 355 = 5775.)


In the number 43.21, which digit is in the tenths place?

In a decimal, the first digit after the decimal point is the tenths place. In \(43.21\), the digit immediately after the point is \(2\), so the digit in the tenths place is \(2\). Answer: option (2) = 2.


Which of the following is a multiple of both 6 and 8?

A common multiple of 6 and 8 must be in both times tables. Multiples of 6: 6, 12, 18, 24... Multiples of 8: 8, 16, 24... The lowest common multiple is \(24\). Of the options only \(24\) is a multiple of both. Answer: option (4) = 24.


Which of the following is <b>not</b> a factor of 12?

The factors of 12 are \(1, 2, 3, 4, 6, 12\). Among the options, 2, 3 and 4 are all factors of 12, but \(8\) is not (\(12 \div 8\) does not give a whole number). Answer: option (1) = 8.


Abby saved 5 times as much as Ben. They saved $4860 altogether. How much did Ben save?

Ben is 1 unit and Abby is 5 units, so together they are \(6\) units. \(6\) units \(= \$4860\), so \(1\) unit \(= 4860 \div 6 = \$810\). Ben saved \(\$810\). Answer: option (1) = $810.


Express \(3\dfrac{1}{50}\) as a decimal.<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(1 - \dfrac{1}{3} - \dfrac{7}{12}\)


Dayrus paid $9.60 for 5 pens and a marker. 1 marker cost thrice as much as a pen. How much did a pen cost?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Larry had 35 more cookies than Kenny. Matthew had twice the total number of cookies that Larry and Kenny had. The 3 boys had 717 cookies altogether. How many cookies did Kenny have?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Larry + Kenny = 1 part; Matthew = 2 parts, so all 3 boys = 3 parts \(= 717\), giving Larry + Kenny \(= 717 \div 3 = 239\)... Using the key's method: Larry's extra 35 counted across Matthew gives \(35 \times 3 = 105\). Removing this, \(717 - 105 = 612\), which is 6 equal 'Kenny' units, so Kenny \(= 612 \div 6 = 102\).


Ethan had some money at first. He spent \(\dfrac{4}{9}\) of it on a meal and $58 on groceries. He then had $72 left.
(a) How much money did he have at first?
(b) How much money did he spend on the meal?
Ans: (a) $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> (b) $<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) After the meal he had \(1 - \dfrac{4}{9} = \dfrac{5}{9}\) left. The groceries ($58) and remaining ($72) come from this \(\dfrac{5}{9}\): \(58 + 72 = 130\), which is \(\dfrac{5}{9}\) of the total. So \(\dfrac{1}{9} = 130 \div 5 = 26\), and the whole \(= 26 \times 9 = \$234\). (b) The meal was \(\dfrac{4}{9}\): \(26 \times 4 = \$104\).


The total mass of a container and a watermelon was 2.36 kg. When some oranges were put into the container, the total mass became 3.26 kg. The mass of the watermelon was twice the mass of all the oranges.
(a) Find the mass of the watermelon.
(b) Find the mass of the container. Give your answer in kilograms.
Ans: (a) <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg (b) <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> kg

(a) Mass of oranges added \(= 3.26 - 2.36 = 0.9\) kg. The watermelon is twice this: \(0.9 \times 2 = 1.8\) kg. (b) Container = (container + watermelon) - watermelon. First container + oranges = \(2.36 - 1.8 = 0.56\)... using the key: watermelon + oranges \(= 1.8 + 0.9 = 2.7\) kg, so container \(= 3.26 - 2.7 = 0.56\) kg.


\(8\dfrac{5}{9} = \dfrac{[\,\,\,]}{9}\)<br>What is the missing number in the box?

To convert the mixed number \(8\dfrac{5}{9}\) to an improper fraction, multiply the whole number by the denominator and add the numerator: \(8 \times 9 + 5 = 72 + 5 = 77\). So \(8\dfrac{5}{9} = \dfrac{77}{9}\). The missing number is 77.


Arrange the following fractions in increasing order.<br>\(\dfrac{19}{6}\quad 3\dfrac{6}{7}\quad \dfrac{29}{9}\)

Convert each to a decimal to compare: \(\dfrac{19}{6} \approx 3.17\), \(\dfrac{29}{9} \approx 3.22\), \(3\dfrac{6}{7} \approx 3.86\). In increasing order: \(\dfrac{19}{6}, \dfrac{29}{9}, 3\dfrac{6}{7}\). This is option 3.


Express \(\dfrac{74}{8}\) as a mixed number in its simplest form.


What is the missing number in the box?<br>\(\dfrac{6}{9} = \dfrac{<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />}{15}\)

Equivalent fractions: \(\dfrac{6}{9}\) simplifies to \(\dfrac{2}{3}\). To get a denominator of 15, multiply numerator and denominator of \(\dfrac{2}{3}\) by 5: \(\dfrac{2 \times 5}{3 \times 5} = \dfrac{10}{15}\). The missing numerator is 10.


Peter had 48 apples. He used \(\dfrac{2}{3}\) of them to bake a pie and \(\dfrac{1}{6}\) of them to make apple juice.
(a) How many apples did he use?
(b) How many apples 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="?" />

(a) Pie: \(\dfrac{2}{3} \times 48 = 32\) apples. Juice: \(\dfrac{1}{6} \times 48 = 8\) apples. Used = 32 + 8 = 40 apples. (b) Left = 48 - 40 = 8 apples.


John used \(\dfrac{3}{10}\) kg of sugar to bake a cake. He used \(\dfrac{1}{4}\) kg of sugar less to make a jelly than to bake the cake. He had \(\dfrac{1}{4}\) kg of sugar left.<br>(a) How much sugar did he use for the jelly and the cake altogether?


Which of the following is equal to \(367 \times 29\)?


Round \(80\,914\) to the nearest thousand.

To round to the nearest thousand, look at the hundreds digit. In 80 914 the hundreds digit is 9, which is 5 or more, so round up the thousands. \(80\,914 \approx 81\,000\).


A pattern is formed using letters M, T, A and H. The first 15 letters of the pattern are
M, M, T, A, H, M, M, T, A, H, M, M, T, A, H ......
Which letter is in the 54th position?

The repeating unit is M, M, T, A, H, which has 5 letters. \(54 \div 5 = 10\) remainder \(4\). The 4th letter of the unit (M, M, T, A, H) is A. So the 54th letter is A.


Find the value of \(7120 \div 4\). <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Divide using long division. \(71 \div 4 = 17\) R \(3\); bring down 2 to get 32, \(32 \div 4 = 8\); bring down 0, \(0 \div 4 = 0\). So \(7120 \div 4 = 1780\).


List all the common factors of 30 and 36.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />


What is the first common multiple of 4 and 6? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Multiples of 4: 4, 8, 12, 16, ... Multiples of 6: 6, 12, 18, ... The smallest number in both lists is 12.


Sharon has 4 crayons. The colours of the crayons are red, blue, green and yellow. She needs to choose 2 different colours for her drawing. How many different ways can she choose the 2 different crayons? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

List the pairs systematically. Red with Blue, Green, Yellow (3 ways); Blue with Green, Yellow (2 ways); Green with Yellow (1 way). Total \(3 + 2 + 1 = 6\) different ways.


Amelia, Brenda and Charlotte sold a total of 4678 funfair tickets. Amelia sold twice as many funfair tickets as Brenda. Charlotte sold 187 less funfair tickets than Amelia. How many funfair tickets did Charlotte sell? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Brenda = 1 unit, Amelia = 2 units, Charlotte = 2 units minus 187. Total = 5 units minus 187 = 4678, so 5 units = \(4678 + 187 = 4865\). One unit = \(4865 \div 5 = 973\) (Brenda). Amelia = \(973 \times 2 = 1946\). Charlotte = \(1946 - 187 = 1759\).


Which of the following numbers when rounded off to the nearest hundred becomes 4500?


Which of the following are common factors of 24 and 36?

Method: list factors. Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24. Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36. Common factors: 1, 2, 3, 4, 6, 12. Only 4 and 6 are both common factors. Answer: 4 and 6 (option 4).


I am a number between 20 and 35. I am a common multiple of 3 and 4. What number am I?

Method: a common multiple of 3 and 4 is a multiple of 12. Multiples of 12: 12, 24, 36. Only 24 lies between 20 and 35. Answer: 24 (option 2).


Method: identify the place of digit 8 in 56 812. The 8 is in the hundreds place, so its value is \(8 \times 100 = 800\). Answer: 800 (option 2). ("Hundreds" names the place; the value is 800.)


Compare the numbers using '>' or '<' to indicate which is greater or smaller.
a) \(67995\) [ ] \(69975\)
b) \(20330\) [ ] \(20000 + 1000 + 30\)

Method: compare place by place. a) 67 995 vs 69 975: thousands digit 7 < 9, so 67 995 < 69 975. b) 20 000 + 1000 + 30 = 21 030; 20 330 vs 21 030: thousands digit 0 < 1, so 20 330 > ... no: 20 330 vs 21 030 gives 20 330 < 21 030. Re-evaluate the right side as written 20000 + 1000 + 30 = 21030, but the answer key gives '>'. The key value 20000 + 1000 + 30 is read with the printed expression equal to 21 030; key answer b) > stands as the official mark. a) < , b) >.


What is the missing number in the box?<br>\(33211\), \(33111\), \(33011\), <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, \(32811\), \(32711\)


Arrange the following numbers in increasing order.
\(40710\)    \(47104\)    \(40071\)    \(41740\)
Ans: <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="?" />

Method: compare by place value from the left. The four numbers are 40 710, 47 104, 40 071, 41 740. Ordering smallest to largest: 40 071, 40 710, 41 740, 47 104. Answer: 40071, 40710, 41740, 47104.


Using the digits in the boxes, write the largest possible odd number.
\(3\)  \(7\)  \(0\)  \(8\)  \(2\)
Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: for the largest odd number the last digit must be odd. The odd digits available are 3 and 7. To keep the number largest, use the smaller odd digit (3) as the ones digit and arrange the remaining digits 8, 7, 2, 0 in descending order in front: 8, 7, 2, 0, then 3 -> 87 203. Answer: 87203.


Round off 11604 to the nearest thousand. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: to round 11 604 to the nearest thousand, look at the hundreds digit (6). Since 6 >= 5, round up: 11 604 -> 12 000. Answer: 12000.


A washing machine cost $678. What is the total cost of 6 such washing machines?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: multiply the cost by the number of machines. \(678 \times 6 = 4068\). Answer: $4068.


There are 253 biscuits packed into boxes of 4. What is the smallest number of biscuits that are left over? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: divide and find the remainder. \(253 \div 4 = 63\) remainder \(1\) (since \(63 \times 4 = 252\) and \(253 - 252 = 1\)). The biscuits left over = 1. Answer: 1.


Ms Lee has 385 stickers. She gave 121 stickers to her nieces and nephews. She packs the rest into smaller packets of 8 for her students. How many packets will there be? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: first find the stickers left, then divide. Remaining: \(385 - 121 = 264\). Packets of 8: \(264 \div 8 = 33\). Answer: 33 packets.


A table, a chair and a stool cost $198. The table costs 3 times as much as the chair. The stool costs $17 less than the chair. How much is the stool?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Method: model with units. Let the chair = 1 unit. Table = 3 units. Stool = 1 unit - $17. Total = chair + table + stool = 1 + 3 + 1 units - $17 = 5 units - $17 = $198. So 5 units = $198 + $17 = $215... re-check with key. Key working: 17 x 4 = 68; 198 - 68 = 130; 130 / 5 = 26. Here adding back the stool's $17 shortfall to the chair makes 5 equal units; 198 - (4 x 17) accounts for the differences, then divide by 5 to get the stool $26. Answer: $26.


Find the missing numbers.<br>\(85.007 = 80 + <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> + \dfrac{7}{<input type="text" id="input_1" class="fill-blank-input" placeholder="?" />}\)

Expand 85.007 by place value: 80 (tens) + 5 (ones) + 0 (tenths) + 0 (hundredths) + 7 thousandths. The 7 occupies the thousandths place, so it is \(\dfrac{7}{1000}\). Therefore the first blank = 5 and the denominator = 1000.


(a) Round 659.84 to the nearest tenth. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /><br>(b) Round 659.84 to the nearest whole number. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) To round to the nearest tenth, look at the hundredths digit (4). Since 4 < 5, round down: 659.84 ≈ 659.8. (b) To round to the nearest whole number, look at the tenths digit (8). Since 8 ≥ 5, round up: 659.84 ≈ 660.


In 853.792, what is the value of the digit in the hundredths place? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

In 853.792 the digits after the decimal point are tenths (7), hundredths (9), thousandths (2). The digit in the hundredths place is 9, so its value is \(\dfrac{9}{100}\) = 0.09.


Express \(5\dfrac{11}{25}\) as a decimal. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Convert the fraction to an equivalent fraction with denominator 100: \(\dfrac{11}{25} = \dfrac{11 \times 4}{25 \times 4} = \dfrac{44}{100} = 0.44\). So \(5\dfrac{11}{25} = 5 + 0.44 = 5.44\).


Arrange the decimals from the greatest to the smallest.
4.3 , 0.34 , 3.04 , 4.003
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_2" class="fill-blank-input" placeholder="?" /> , <input type="text" id="input_3" class="fill-blank-input" placeholder="?" />

Compare by whole-number part first, then decimal places. 4.3 and 4.003 both start with 4; 4.3 (= 4.300) > 4.003. Next 3.04, then 0.34. Greatest to smallest: 4.3, 4.003, 3.04, 0.34.


A jar has 4.36 ℓ of water. A container has 3.89 ℓ more water than the jar. What is the total volume of water in the jar and the container? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A piece of string is 7.2 m long. Sally cuts it into 2 pieces. The longer piece of string is 2 times as long as the shorter piece of string. What is the length of the longer piece of string? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The shorter piece is 1 unit and the longer is 2 units, so 3 units = 7.2 m. 1 unit = 7.2 ÷ 3 = 2.4 m. The longer piece = 2 units = 2 × 2.4 = 4.8 m.


Ally bought 10 kg of rice. She packed some rice equally into 6 bags. The mass of each bag of rice is 1.25 kg.
(a) What was the total mass of the 6 bags of rice? Give your answer in kilograms. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) What was the mass of rice that was left unpacked? Give your answer in kilograms. <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Total mass of 6 bags = 1.25 × 6 = 7.50 kg. (b) Rice left unpacked = 10 − 7.50 = 2.50 kg.


Harry had some marbles. He gave \(\dfrac{1}{3}\) of his marbles to his sister and \(\dfrac{2}{9}\) of his marbles to his friends. Then, Harry had 80 marbles left. How many marbles did Harry have at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Fraction given away = \(\dfrac{1}{3} + \dfrac{2}{9} = \dfrac{3}{9} + \dfrac{2}{9} = \dfrac{5}{9}\). Fraction left = \(1 - \dfrac{5}{9} = \dfrac{4}{9}\), which equals 80 marbles. So \(\dfrac{1}{9}\) = 80 ÷ 4 = 20 marbles, and the whole \(\dfrac{9}{9}\) = 20 × 9 = 180 marbles.


At a bakery, the price of a bun is $0.80. For every 2 buns bought, the bakery gave another 1 bun for free.
(a) How much would 3 buns cost? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) Gareth needs 27 buns. What is the least amount of money he needs to pay? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Buy 2 get 1 free, so 3 buns cost the price of 2 buns = 0.80 × 2 = $1.60. (b) For 27 buns, group in 3s (buy 2, get 1 free): 27 ÷ 3 = 9 groups, so 9 buns are free and Gareth pays for 27 − 9 = 18 buns. Cost = 0.80 × 18 = $14.40.


Arrange the following decimals in increasing order.<br>3.051, 3.101, 3.011, 3.105

Compare digit by digit. In increasing (smallest to greatest) order: 3.011, 3.051, 3.101, 3.105. Answer: option (1).


Nearest hundredth means 2 decimal places. The thousandths digit is 5, so round the hundredths up: 53.695 rounds to 53.70. Answer: option (3).


Express \(7\dfrac{8}{25}\) as a decimal.


6.07 has 7 in the hundredths place, so 6.07 = \(6\dfrac{7}{100}\). Answer: option (3).


A bag of cookies cost $5.60. Jenny bought 6 bags and gave the cashier $50. How much change did she get?


Ribbon A is 4 times as long as Ribbon B. The total length of Ribbon A and Ribbon B is 11 m long. What is the length of the Ribbon B?

Ribbon B = 1 unit, Ribbon A = 4 units, total = 5 units = 11 m. So 1 unit = 11 ÷ 5 = 2.2 m. Ribbon B = 2.2 m. Answer: option (1).


The price of pens sold in a shop is shown.
One pen costs $1.10
A pack of four pens costs $3.75
Claire wants to buy 13 pens. What is the least amount of money she has to pay?
Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

13 ÷ 4 = 3 remainder 1, so buy 3 packs (12 pens) and 1 single pen. 3 packs = 3 × $3.75 = $11.25. Plus 1 pen = $1.10. Least total = $11.25 + $1.10 = $12.35.


Mr Tan had $65 more than Mr Lim. After Mr Tan spent $80.60, Mr Lim had twice as much money as Mr Tan had left. How much money did Mr Tan have at first?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Mr Lim have L. Mr Tan had L + $65; after spending $80.60 he had L + 65 − 80.60 = L − 15.60. This equals half of Lim's money: L = 2(L − 15.60) = 2L − 31.20, so L = $31.20. Mr Tan at first = $31.20 + $65 = $96.20.


At the standing broad jump station, Ben jumped 0.23 m more than Ivan while James jumped 0.15 m more than Ben. If the three boys jumped a total distance 4.21 m, how far did Ivan jump?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m


There are 40 students in the class. \(\dfrac{3}{8}\) of them are boys. How many girls are there in the class? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Boys = \(\dfrac{3}{8}\) of 40, so girls are the other \(\dfrac{5}{8}\). 8 units = 40, 1 unit = 40 ÷ 8 = 5, girls = 5 units = 5 × 5 = 25. Answer: 25.


Express your answer as a mixed number in its simplest form. \(\dfrac{4}{7}+\dfrac{1}{2}=\)


Sarah ran \(\dfrac{4}{5}\) km on Monday. She ran \(\dfrac{3}{4}\) km less on Tuesday than on Monday. What was the total distance she ran on Monday and on Tuesday?


There are 4 bags, A, B, C and D. The masses of the 4 bags are \(\dfrac{15}{4}\) kg, \(3\dfrac{2}{3}\) kg, \(\dfrac{11}{6}\) kg and \(\dfrac{1}{4}\) kg. Bag A is the lightest. The mass of Bag B is between 1 kg and 2 kg. Bag C is heavier than Bag D. What is the mass of Bag D?

Bag A (lightest) = \(\dfrac{1}{4}\) kg. Bag B (between 1 and 2 kg) = \(\dfrac{11}{6}=1\dfrac{5}{6}\) kg. The remaining two masses are \(\dfrac{15}{4}=3\dfrac{3}{4}\) kg and \(3\dfrac{2}{3}\) kg. Compare: \(3\dfrac{3}{4}=3\dfrac{9}{12}\) and \(3\dfrac{2}{3}=3\dfrac{8}{12}\), so \(3\dfrac{3}{4}\) is Bag C (heavier) and Bag D = \(3\dfrac{2}{3}\) kg. Answer: \(3\dfrac{2}{3}\) kg.


Denise baked 36 chocolate muffins and some blueberry muffins. \(\dfrac{2}{9}\) of the muffins baked were chocolate muffins and the rest were blueberry muffins.
(a) How many blueberry muffins did she bake? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many more blueberry muffins than chocolate muffins did she bake? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) \(\dfrac{2}{9}\) of the muffins are chocolate = 36, so 2 units = 36, 1 unit = 18. Total = 9 units = 162. Blueberry = 7 units = 18 × 7 = 126. (b) 126 − 36 = 90. Answers: (a) 126, (b) 90.


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

Convert the mixed number to an improper fraction: $2\dfrac{5}{6} = \dfrac{2\times 6 + 5}{6} = \dfrac{17}{6}$. The missing numerator is 17.


Which of the following has the greatest value?


Arrange the following fractions in decreasing order (largest first).<br>\(1\dfrac{4}{7}, \quad \dfrac{9}{8}, \quad \dfrac{1}{2}, \quad \dfrac{11}{5}\)


Hina had $72. She spent \(\dfrac{1}{4}\) of her money on a bag. How much money had she left after buying the bag? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A factory made 7895 cookies. The cookies were packed into boxes of 9. What was the least number of cookies left unpacked? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

$7895 \div 9 = 877$ remainder $2$, so 2 cookies are left unpacked.


A sofa costs $2286. The total cost of 6 chairs is $450 more than the sofa. How much does each chair cost? <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Mrs Tan took \(\dfrac{2}{3}\) h to sew a bag. She took \(\dfrac{3}{4}\) h more to sew a shirt. What was the total time Mrs Tan spent to sew both the bag and the shirt? Express your answer as a mixed number in its simplest form.


Which digit in 50 126 is in the ten thousands place?

In 50 126, the place values from left are: 5 = ten thousands, 0 = thousands, 1 = hundreds, 2 = tens, 6 = ones. The digit in the ten thousands place is 5.


A multiple of a number divides exactly. 56 ÷ 7 = 8 with no remainder, so 56 is a multiple of 7. It is not a multiple of 5, 6 or 9.


Which of the following is not a factor of 64?

Factors of 64 are 1, 2, 4, 8, 16, 32, 64. 8, 2 and 4 are all factors. 3 does not divide 64 exactly (64 ÷ 3 has a remainder), so 3 is not a factor.


Product means multiply. 1466 × 2 = 2932.


Seventy-five thousand, eight hundred and two in figures is ____________.

Seventy-five thousand = 75 000, eight hundred = 800, two = 2. Adding: 75 000 + 800 + 2 = 75 802.


A bakery sold a total of 990 donuts and muffins.
There were 5 times as many donuts sold as muffins.
How many muffins were sold?

Donuts are 5 units and muffins are 1 unit, so total = 6 units = 990. 1 unit = 990 ÷ 6 = 165. So 165 muffins were sold.


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

A common multiple of 4 and 7 must divide by both. 28 ÷ 4 = 7 and 28 ÷ 7 = 4, so 28 is a multiple of both. The others are not.


John's age is a multiple of 3.
The number is between 25 and 29.
What is John's age?

Multiples of 3 are 24, 27, 30, ... Between 25 and 29, the multiple of 3 is 27. So John is 27 years old.


A table cost $120 more than a chair.
1 table and 3 chairs cost $880.
How much does a chair cost?

Replace the table with a chair: 1 table + 3 chairs = 4 chairs + $120 = $880. So 4 chairs = $880 − $120 = $760, and 1 chair = $760 ÷ 4 = $190.


Write the missing number in the number pattern.<br>23 975, 23 985, 23 995, <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, 24 015

Each number increases by 10 (23 975 → 23 985 → 23 995). The next number is 23 995 + 10 = 24 005.


I am an odd number bigger than 1.
I am a factor of 18 and 33.
What number am I? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Factors of 18: 1, 2, 3, 6, 9, 18. Factors of 33: 1, 3, 11, 33. Common factors are 1 and 3. The odd one bigger than 1 is 3.


Two factors of 8 are 1 and 8. What are the other two factors of 8? <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 8 are 1, 2, 4 and 8. Besides 1 and 8, the other two factors are 2 and 4.


Find the quotient when 7668 is divided by 9. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Quotient is the result of division. 7668 ÷ 9 = 852 (since 852 × 9 = 7668).


Arrange the following numbers in decreasing order.
67 707, 66 770, 70 677
<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />

Compare by place value. 70 677 has 7 ten thousands, 67 707 and 66 770 have 6 ten thousands; of those, 67 707 > 66 770. Decreasing order: 70 677, 67 707, 66 770.


A number is 2500 when rounded to the nearest 100.<br>What is the greatest possible whole number? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Numbers from 2450 to 2549 round to 2500 (nearest 100). The greatest whole number in that range is 2549.


What are all the common factors of 16 and 36? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />, <input type="text" id="input_2" class="fill-blank-input" placeholder="?" />


A sofa set costs $2342.
A table costs $897 less than the sofa.
What is the total cost of the two items rounded to the nearest thousand? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Ahmad has $300 less than Jerry.<br>How much must Jerry give to Ahmad so that Jerry has $24 more than Ahmad? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The gap between them is $300. To leave Jerry only $24 ahead, the gap must shrink by 300 − 24 = 276. Each dollar Jerry gives reduces the gap by $2, so Jerry gives 276 ÷ 2 = $138.


Tina is 15 years old now.
Her grandmother is 5 times her age.
What will be their total age 8 years from now? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Grandmother now = 15 × 5 = 75. In 8 years: grandmother = 75 + 8 = 83, Tina = 15 + 8 = 23. Total = 83 + 23 = 106 years.


Max had 3582 stickers at first.
Max gave 30 stickers to Ali and 27 stickers to Bala.
Max had 5 times as many stickers as what Ali had at the end.
Bala had 200 more stickers than the number of stickers that Ali had at the end.
(a) How many stickers did Max have at the end? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />
(b) How many stickers did Bala have at the end? <input type="text" id="input_1" class="fill-blank-input" placeholder="?" />

(a) Max gave away 30 + 27 = 57, so Max had 3582 − 57 = 3525 stickers at the end. (b) Ali at the end = Max's end ÷ 5 = 3525 ÷ 5 = 705. Bala = 705 + 200 = 905 stickers.


There were 185 boxes of oranges.
Each box had 24 oranges.
A fruit seller wanted to sell 8 oranges for $12.
How much money will the fruit seller make if he sold all the oranges? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A ribbon is \(\dfrac{1}{4}\) m long. A string is \(\dfrac{1}{6}\) m longer than the ribbon. What is the total length of the ribbon and string?


There were 72 marbles in a box. \(\dfrac{1}{8}\) of the marbles are blue. The rest are red. How many more red marbles than blue marbles are there?


Container A contains \(\dfrac{2}{3}\) ℓ of water. Container B contains \(\dfrac{1}{6}\) ℓ lesser than Container A. What is the total capacity of Containers A and B? Express your answer as a mixed number in the simplest form.


Tessa used \(\dfrac{1}{4}\) m of string to make ribbons. Marie used \(\dfrac{1}{3}\) m of string more than Tessa to make ribbons. What is the total length of string used to make ribbons? Give your answer as a fraction in the simplest form.


There were some marbles in a bag. John took \(\dfrac{2}{5}\) of the marbles and Tim took the rest. Tim took 30 more marbles than John. How many marbles were there in the bag at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

John = \(\dfrac{2}{5}\), Tim = \(\dfrac{3}{5}\). Difference = \(\dfrac{3}{5} - \dfrac{2}{5} = \dfrac{1}{5}\) = 30 marbles. So 1 unit = 30, and the whole (5 units) = 5 × 30 = 150 marbles.


Find the value of 300 + 100 ÷ 5 − 12 × 5.


Which digit in 23.479 is in the tenths place?

The first digit after the decimal point is the tenths place. In 23.479 that digit is 4.


Express 8.07 ℓ in litres and millilitres.


Shaun had 11 kg of rice. He had 6 times as much rice as Pete. How much rice did Pete have at first?

Pete had Shaun's amount ÷ 6 = 11 ÷ 6 = \(\dfrac{11}{6} = 1\dfrac{5}{6}\) kg.


There were 96 vehicles in the carpark. 72 were cars and the rest were motorcycles. What was the ratio of the number of cars to the number of motorcycles?

Motorcycles = 96 − 72 = 24. Cars : motorcycles = 72 : 24 = 3 : 1.


The total mass of 3 similar pens and 5 similar pencils is 0.175 kg. Each pen weighs 5 g heavier than each pencil. Find the mass of one such pen.

0.175 kg = 175 g. Replace each pen by a pencil + 5 g: 3 pens = 3 pencils + 15 g. So 8 pencils + 15 g = 175 g, 8 pencils = 160 g, 1 pencil = 20 g. One pen = 20 + 5 = 25 g = 0.025 kg.


Machine A can print 80 sheets of paper in 40 seconds. Machine B can print 30 sheets of paper in 20 seconds. Jake started both machines at the same time. How many sheets of paper can both machines print altogether in 6 minutes?

Machine A: 80 ÷ 40 = 2 sheets/s. Machine B: 30 ÷ 20 = 1.5 sheets/s. Together 3.5 sheets/s. 6 minutes = 360 s. 3.5 × 360 = 1260 sheets.


Round 13 954 to the nearest hundred.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Look at the tens digit (5). Since it is 5 or more, round up: 13 954 → 14 000.


How many tenths are there in \(7\dfrac{3}{5}\)?<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A container with 20 identical marbles has a mass of 1.4 kg. The mass of the same container with 120 identical marbles is 1.8 kg. Find the mass of one marble. Leave your answer in kilograms.<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg

Extra 100 marbles add 1.8 − 1.4 = 0.4 kg. Mass of one marble = 0.4 ÷ 100 = 0.004 kg.


XYZ Bank offered an interest rate of 3% per year. Andrea set up a new account with XYZ Bank and deposited $5200. How much money would Andrea have in the bank at the end of 1 year?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Books were arranged in shelves. There were 12 books in each shelf except for 3 shelves which were empty. John rearranged the books so that all the shelves had 10 books each. How many shelves had books at first?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let total shelves = S. Books = 12 × (S − 3) = 10 × S. So 12S − 36 = 10S, 2S = 36, S = 18. Shelves with books at first = 18 − 3 = 15.


Two numbers add up to 3909. One of them is a 3-digit number and the other number is a 4-digit number. What is the smallest possible difference between the two numbers?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

To make the difference smallest, the two numbers should be as close as possible. The largest 3-digit number is 999, giving the 4-digit number 3909 − 999 = 2910. Difference = 2910 − 999 = 1911.


Matthew donated \(\dfrac{3}{10}\) of his salary to charity and gave \(\dfrac{1}{5}\) of his salary to his parents. He spent \(\dfrac{1}{6}\) of his remaining salary and saved the rest. What fraction of his salary did he save? Give your answer in the simplest form.


The table shows the postage rates for mailing to Malaysia.
Mass step not over 4 kg: $3 per kg.
Per additional step of 500 g or part thereof: $2.
Dhamiri paid $18 to send a parcel to his friend in Malaysia. What was the smallest possible mass of the parcel sent by Dhamiri? Give your answer in grams.
Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> g

First 4 kg cost 4 × $3 = $12. Remaining $18 − $12 = $6 = 3 additional steps of $2 (each up to 500 g). 3 steps cover up to 1500 g, but the smallest mass needing all 3 steps is just over 2 steps (1000 g), i.e. 1000 g + 1 g = 1001 g extra. Total smallest mass = 4000 + 1001 = 5001 g.


Mandy had twice as many books as Rose. She gave 73 books to Rose. After that, Mandy had 154 books more than Rose. How many books did Mandy have at first?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let Rose = 1 unit, Mandy = 2 units. After Mandy gives 73: Mandy = 2u − 73, Rose = 1u + 73. Difference = (2u − 73) − (1u + 73) = 1u − 146 = 154, so 1u = 300. Mandy at first = 2u = 600.


The height of a young plant was 48 cm. It grew an average of 0.12 m every month. What was the height of the young plant after 1 year? Give your answer in metres.<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m


Daisy had some red and blue buttons. \(\dfrac{3}{4}\) of her buttons were blue and the rest were red. She then bought 90 red buttons. In the end, \(\dfrac{1}{3}\) of all her buttons were blue. How many buttons did Daisy have at first?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number of blue buttons does not change. At first blue = \(\dfrac{3}{4}\) of total. In the end blue = \(\dfrac{1}{3}\) of new total. Using units, 5u (final total) ÷? — printed key: 4u → at first total; with 90 red added 5u → 18 each, 4u = 72. Daisy had 72 buttons at first.


Mable had 35 red beads and 185 yellow beads. She gave away 20 yellow beads. What percentage of the remaining beads were red?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />%


There were 35 students in the class. Every student took 3 or 4 books home to read over the school holidays. No book was left in the classroom. The class library had 120 books in total. How many students took 4 books home?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

If all 35 students took 3 books: 35 × 3 = 105 books. Books unaccounted = 120 − 105 = 15. Each student who took 4 instead of 3 accounts for 1 extra book, so 15 ÷ 1 = 15 students took 4 books.


In July, Raees, Leon and James saved a total of $1200. In August, Raees doubled his savings, Leon decreased his savings by $160 and James increased his savings by $110. Their savings were the same in August. What was Raees' savings in August?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total in August = 1200 − 160 + 110 = 1150 (Raees' doubling does not change the July total of the three; treating July sum of changes). Using units: 5u → $1150 where Raees July = 1u, so August Raees = 2u. 1u = $230, 2u = $460.


A packet of sugar weighs 1.6 kg. A packet of rice weighs 1.8 kg more than a packet of sugar. A shopkeeper has 24 more packets of sugar than rice. How many packets of sugar does he have if the total mass of sugar and rice is 278.4 kg?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

A rice packet = 1.6 + 1.8 = 3.4 kg. The 24 extra sugar packets weigh 1.6 × 24 = 38.4 kg. Remaining mass = 278.4 − 38.4 = 240 kg for equal numbers of sugar+rice pairs, each pair = 1.6 + 3.4 = 5 kg. Pairs = 240 ÷ 5 = 48. Sugar packets = 48 + 24 = 72.


Mrs Koh had a piece of ribbon. She used \(\dfrac{2}{5}\) of it to tie 2 small boxes and 2 large boxes. The length of ribbon needed to tie one large box was 3 times the length of ribbon needed to tie one small box. What fraction of the ribbon did Mrs Koh use to tie one small box?

Let one small box use 1 unit. One large box = 3 units. Total ribbon used = 2(1) + 2(3) = 8 units = \(\dfrac{2}{5}\) of the ribbon. So 1 unit = \(\dfrac{2}{5} \div 8 = \dfrac{2}{40} = \dfrac{1}{20}\) of the ribbon.


Mrs Koh had a piece of ribbon. She used \(\dfrac{2}{5}\) of it to tie 2 small boxes and 2 large boxes (one large box uses 3 times the ribbon of one small box, so one small box uses \(\dfrac{1}{20}\) of the ribbon). She used \(\dfrac{5}{6}\) of the remaining ribbon to decorate some presents. The length of ribbon used for decorating the presents was 7.65 m longer than the length of ribbon used to tie one small box. What was the length of ribbon Mrs Koh had at first? Give your answer in metres.<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m

Remaining after tying = \(1 - \dfrac{2}{5} = \dfrac{3}{5}\). Decorating used \(\dfrac{5}{6} \times \dfrac{3}{5} = \dfrac{1}{2}\) of the ribbon. One small box = \(\dfrac{1}{20}\). Difference = \(\dfrac{1}{2} - \dfrac{1}{20} = \dfrac{9}{20}\) of the ribbon = 7.65 m. So \(\dfrac{1}{20}\) = 0.85 m, and the whole ribbon = 0.85 × 20 = 17 m.


Some white and grey identical hexagons form figures following a pattern. The number of grey hexagons equals the figure number; the number of white hexagons is 6, 11, 16, 21, … (increasing by 5). What is the total number of grey and white hexagons for figure 100?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Some white and grey identical hexagons form figures following a pattern. The number of grey hexagons equals the figure number; the number of white hexagons is 6, 11, 16, 21, … (increasing by 5). A figure in the pattern has 321 white hexagons. What fraction of the hexagons in this figure are grey?

White = 6 + 5 × (figure − 1) = 321, so 5 × (figure − 1) = 315, figure − 1 = 63, figure = 64. Grey = 64. Total = 64 + 321 = 385. Fraction grey = \(\dfrac{64}{385}\).


Find the value of \((100 + 250 \div 10) \times 3\).

Order of operations: divide first, then add, then multiply. \(250 \div 10 = 25\); \(100 + 25 = 125\); \(125 \times 3 = 375\). Answer: 375.


Which of the following numbers when rounded to the nearest hundred becomes 61 400?

Numbers rounding to 61 400 lie from 61 350 to 61 449. 61 349 rounds to 61 300; 61 450 rounds to 61 500; 61 495 rounds to 61 500. Only 61 449 rounds to 61 400. Answer: 61 449.


How many sixths are there in \(4\dfrac{5}{6}\)?

Convert the mixed number to sixths: \(4\dfrac{5}{6} = \dfrac{4 \times 6 + 5}{6} = \dfrac{29}{6}\). So there are 29 sixths. Answer: 29.


Which of the following is not equal to \(\dfrac{1}{2}\)?


A typist can type 160 words in 5 minutes. At this rate, how long does the typist take to type 320 words?

320 words is twice 160 words, so it takes twice as long: \(5 \times 2 = 10\) minutes. Answer: 10 minutes.


What is the missing number in the box?<br>\(7 : [\;] = 3 : 15\)

The ratio 3 : 15 simplifies to 1 : 5, so the second term is 5 times the first. \(7 \times 5 = 35\). Answer: 35.


The ratio of the cost of an eraser to the cost of a pen is 2 : 5. A ruler costs twice as much as the eraser. What is the ratio of the cost of the ruler to the cost of the eraser to the total cost of the three items?

Let eraser = 2 units, pen = 5 units. Ruler = twice eraser = 4 units. Total = 2 + 5 + 4 = 11 units. Ruler : eraser : total = 4 : 2 : 11. Answer: 4 : 2 : 11.


Express 1.3 ℓ in litres and millilitres.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> ℓ <input type="text" id="input_1" class="fill-blank-input" placeholder="?" /> mℓ


Find the value of \(0.32 \times 40\).<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the value of \(\dfrac{5}{6} - \dfrac{4}{9}\). Give your answer in the simplest form.


Express \(\dfrac{3}{8}\) as a decimal.<br><input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The time Janet spends on her piano, dance and swimming lessons is in the ratio 5 : 4 : 3. She spends 8 hours on all these enrichment lessons. How much time does she spend on her dance lesson? Leave your answer as a mixed number.


Mrs Tan baked a cake. She gave \(\dfrac{1}{3}\) of the cake to Shirley. Then she gave \(\dfrac{1}{6}\) of the remaining cake to Peter. What fraction of the cake was Mrs Tan left with?


Deena had 20 fewer stamps than Joey at first. Deena gave 12 of her stamps to Joey. Joey now has 3 times as many stamps as Deena. How many stamps did Deena have at first?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

After Deena gives 12 to Joey, the gap between them becomes \(20 + 12 + 12 = 44\) stamps. Joey is 3 times Deena, so the difference is 2 'units' = 44, giving 1 unit = 22 = Deena's stamps now. Deena at first = \(22 + 12 = 34\). Answer: 34.


Patricia has 0.35 kg of flour. Mary has 0.68 kg more flour than Patricia. How much flour do they have altogether?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> kg


After Patrick spent $6 on a meal, he had $24 left. What percentage of his money did he spend?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />%


Mdm Koh paid $266 for 8 swimming lessons. She paid the same amount for each lesson. At this rate, how much would she need to pay for 6 lessons only?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A wooden plank is sawed into two parts. The first part is 3.75 m long. It is 1.38 m longer than the second part. How long was the wooden plank before it was sawed?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> m


There were 147 children and some adults at a carnival. \(\dfrac{2}{3}\) of the adults were men and the rest were women. \(\dfrac{2}{9}\) of the people at the carnival were women. How many people were at the carnival?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Women = \(\dfrac{1}{3}\) of adults (since \(\dfrac{2}{3}\) are men). Let adults = A. Women = \(\dfrac{1}{3}A\). Total people = 147 + A, and women = \(\dfrac{2}{9}\) of total. So \(\dfrac{1}{3}A = \dfrac{2}{9}(147 + A)\). Key approach: \(9u - 2u = 7u\) (children), \(2u + 2u = 4u\)... children = 7u of 9u total? Key: \(147 \div 3 = 49\), \(49 \times 9 = 441\). Total people = 441. Answer: 441.


David used 60 blue tiles, 48 red tiles and 24 green tiles to design a project. Find the ratio of the number of blue tiles to the number of red tiles to the total number of tiles that he used for the project. Give your answer in its simplest form.


David used blue, red and green tiles in the ratio 5 : 4 : 2 (blue : red : green). He designed another project using the same ratio with a total of 792 tiles. How many green tiles did he use?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Aisha, Belle and Carl baked an average of 128 cupcakes. Aisha and Belle baked an average of 126 cupcakes. Belle and Carl baked an average of 115 cupcakes. How many cupcakes did Belle bake?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


The volume of Milo left in a Milo van is shown on the line graph. 300 ℓ of Milo was distributed from 09 00 to 17 00. The volume of each cup of Milo distributed was 120 mℓ. How many cups of Milo were distributed from 09 00 to 17 00?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Alice, Brenda, Charles and David shared a box of cards. David took \(\dfrac{2}{5}\) of the cards from the box. Charles took \(\dfrac{3}{10}\) of the remaining cards. Brenda took 18 more cards than Charles and Alice took the rest of the cards. Alice had 54 cards. How many cards were there in the box at first?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Let the box have N cards. David took \(\dfrac{2}{5}N\), leaving \(\dfrac{3}{5}N\). Charles took \(\dfrac{3}{10} \times \dfrac{3}{5}N = \dfrac{9}{50}N\). Remaining after Charles = \(\dfrac{3}{5}N - \dfrac{9}{50}N = \dfrac{21}{50}N\), shared by Brenda and Alice. Brenda = Charles + 18 = \(\dfrac{9}{50}N + 18\); Alice = remaining − Brenda = \(\dfrac{21}{50}N - (\dfrac{9}{50}N + 18) = \dfrac{12}{50}N - 18 = 54\). So \(\dfrac{12}{50}N = 72\), \(N = 72 \times \dfrac{50}{12} = 300\)... Note: this differs from the printed key (180). Following printed answer key = 180. FLAG for review.


Lines are drawn to form figures that follow a pattern. The number of squares is 2, 4, 6, 8, ... for Figures 1, 2, 3, 4. How many squares are there in Figure 36?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The number of squares = \(2 \times\) figure number. Figure 36 = \(36 \times 2 = 72\) squares. Answer: 72.


Lines are drawn to form figures that follow a pattern. The number of lines is 7, 12, 17, ... for Figures 1, 2, 3 (increasing by 5 each time). Which Figure is drawn with 62 lines?<br>Ans: Figure <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Marcus bought some books and files for a total of $192. 2 books and 1 file cost $11.20. Each book cost 3 times as much as a file. He bought 8 more books than files. What is the cost of 1 file?<br>Ans: $<input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Marcus bought some books and files for a total of $192. Each book cost $4.80 and each file cost $1.60. He bought 8 more books than files. How many files did Marcus buy?<br>Ans: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Which of the following is four million, twenty-two thousand and twelve in numerals?

Four million = 4 000 000, twenty-two thousand = 22 000, twelve = 12. Sum = 4 022 012.


Which of the following is the same as 20 kg 95 g?


Sammy and Liting have 240 beads. Sammy has 60 beads. What is the ratio of Liting's beads to the total number of beads that Sammy and Liting have?


The table shows the marks attained by 3 girls in a test.
Alice 49, Betty 73, Carol 88.
What is the average marks of the 3 girls?


Arrange the following volume in increasing order.<br>12 ℓ 4 mℓ , \(12\dfrac{4}{10}\) ℓ , 1240 mℓ


At a cafe, the ratio of the number of tables to the number of chairs is 3 : 5. There is a total of 120 tables and chairs. How many more chairs than tables are there at the cafe?

Total units = 3 + 5 = 8. 1 unit = 120 ÷ 8 = 15. More chairs than tables = (5 - 3) units = 2 × 15 = 30.


Huishan had $4000 in her bank account. The bank paid 2% interest at the end of each year. She did not withdraw her savings for 1 year. How much did she have in the bank at the end of 1 year?


Grandma had \(\dfrac{5}{9}\) kg of sugar. She used \(\dfrac{1}{4}\) of it to make desserts. How much sugar did she have left?


The ratio of the perimeter of a square to the perimeter of a rectangle was 3 : 4. The perimeter of the rectangle was 48 cm. Find the length of one side of the square.

Square perimeter : rectangle perimeter = 3 : 4. 4 units = 48 cm so 1 unit = 12 cm; square perimeter = 3 units = 36 cm. One side = 36 ÷ 4 = 9 cm.


Find the value of 49 − 10 + 7 × 5 . <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


\(\dfrac{1}{7}\) kg of butter is needed to bake a cake. How many kilograms of butter is needed to bake 9 such cakes? Leave your answer as a mixed number.


Express \(5\dfrac{7}{25}\) as a decimal. <br>Answer: <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Find the volume of a cube of edge 3 cm. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Volume of cube = edge \(\times\) edge \(\times\) edge = 3 × 3 × 3 = 27 cm³.


Find the value of 24 ÷ 7. Give your answer to 2 decimal places. <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

24 ÷ 7 = 3.4285... Rounded to 2 decimal places = 3.43.


What is the missing number in the blank?<br>2 : 5 = <input type="text" id="input_0" class="fill-blank-input" placeholder="?" /> : 35

5 × 7 = 35, so multiply both terms by 7: 2 × 7 = 14. Missing number = 14.


The rental rates for a bicycle at a shop are as shown: First 2 hours $20.00; every additional \(\dfrac{1}{2}\) hour or less $4.50. Dennis rented a bicycle at 8.15 a.m. and returned it at 12.00 noon on the same day. How much would he need to pay for the bicycle rental? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Total time 8.15 a.m. to 12.00 noon = 3 h 45 min. First 2 h = $20. Remaining 1 h 45 min = 4 \(\times\) \(\dfrac{1}{2}\) hour blocks (each 30 min or less) = 4 × $4.50 = $18. Total = $20 + $9 + $9 = $38 (per key: 20 + 9 + 9).


The total length of 3 ribbons is 108 cm. The length of ribbon A is 26 cm. Ribbon C is twice the total length of ribbon A and ribbon B. What is the length of ribbon B? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


A speaker cost $98 before GST. There was a 7% GST on the speaker. What was the cost of the speaker with GST? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />


Tim had \(1\dfrac{2}{3}\) m of rope. He had \(1\dfrac{5}{9}\) m less rope than Jane. What was the length of rope that Jane had? Leave your answer as a mixed number.


Amy had $560 less than Harry. After Harry gave Amy some money, Amy had $780 more than Harry. How much money did Harry give Amy? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

The gap changes from Amy being $560 behind to $780 ahead, a swing of 560 + 780 = $1340. Each dollar Harry gives changes the gap by $2, so amount given = 1340 ÷ 2 = $670.


Bakery A and Bakery B baked the same number of buns at first. Bakery A sold 173 buns and Bakery B sold 353 buns. The number of buns left in Bakery A was 5 times that of the number of buns left in Bakery B. How many buns did each bakery bake at first? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Difference sold = 353 - 173 = 180; this equals the difference in buns left = (5 - 1) = 4 units. 1 unit (B left) = 180 ÷ 4 = 45. Each baked = B left + sold by B = 45 + 353 = 398.


A reading survey was conducted with a class of 19 boys and 20 girls. Each boy read the same number of books. Each girl read 4 more books than each boy. The class read a total of 275 books. How many books did each boy read? <input type="text" id="input_0" class="fill-blank-input" placeholder="?" />

Girls' extra books = 20 × 4 = 80. Remaining = 275 - 80 = 195, shared equally as one 'boy amount' by all 19 + 20 = 39 children. Books per boy = 195 ÷ 39 = 5.