Section 3: Fractions, decimals and percentages

Give fractions a common denominator before adding or taking away, and change mixed numbers to improper fractions before multiplying.

A lesson for this section

Practice questions

Question 1Arithmetic (Paper 1 style)

Write

\frac{18}{24}

in its simplest form.

Question 2Arithmetic (Paper 1 style)

What is the missing number?

\frac{5}{8}

= \frac{\square}{40}

Question 3Arithmetic (Paper 1 style)

Write

\frac{47}{12}

as a mixed number.

Question 4Reasoning (Papers 2 and 3 style)

Kemi has painted

\frac{3}{5}

of a fence. Her brother has painted a bigger fraction of the same fence. Which of these could be the fraction her brother painted?

Question 5Reasoning (Papers 2 and 3 style)

Four friends are reading the same book. Eleanor has read

\frac{5}{8}

of it, Tom

\frac{3}{4}

, Priya

\frac{7}{12}

and Samira

\frac{2}{3}

. Who has read the least?

Question 6Reasoning (Papers 2 and 3 style)

There are 32 pupils in a class. 12 of them walk to school. What fraction of the class walk to school? Give the fraction in its simplest form.

Question 7Arithmetic (Paper 1 style)

\frac{2}{3}

{}+ \frac{1}{4} =

Question 8Arithmetic (Paper 1 style)

4\frac{1}{5}

{}- 1\frac{7}{10} =

Question 9Arithmetic (Paper 1 style)

\frac{4}{9}

{}+ \frac{7}{9} =

Question 10Reasoning (Papers 2 and 3 style)

Hana has a ribbon

2\frac{1}{2}

m long. She cuts off

\frac{3}{4}

m for a card and then

1\frac{1}{8}

m for a bow. How much ribbon is left?

Question 11Reasoning (Papers 2 and 3 style)

Ben plants

\frac{1}{3}

of his garden with vegetables and

\frac{2}{5}

with flowers. The rest is grass. What fraction of the garden is grass?

Question 12Arithmetic (Paper 1 style)

2\frac{3}{5}

{}+ 1\frac{7}{10} =

Question 13Arithmetic (Paper 1 style)

\frac{2}{3} \times \frac{3}{8} =

Question 14Arithmetic (Paper 1 style)

\frac{3}{4} \times 10 =

Question 15Arithmetic (Paper 1 style)

\frac{2}{3} \div 4 =

Question 16Reasoning (Papers 2 and 3 style)

A school trip costs £36. Mia has saved

\frac{5}{9}

of the cost. How much more money does she need?

Question 17Reasoning (Papers 2 and 3 style)

After a party,

\frac{3}{4}

of a pizza is left. Sam eats

\frac{2}{5}

of the pizza that is left. What fraction of the whole pizza does Sam eat?

Question 18Reasoning (Papers 2 and 3 style)

Leo has

\frac{3}{4}

of a litre of juice. He pours it equally into 6 cups. How much juice is in each cup?

Question 19Arithmetic (Paper 1 style)

3.47 \times 10 =

Question 20Arithmetic (Paper 1 style)

52 \div 1000 =

Question 21Arithmetic (Paper 1 style)

12 - 4.37 =

Question 22Arithmetic (Paper 1 style)

4.26 \times 7 =

Question 23Reasoning (Papers 2 and 3 style)

What is the value of the digit 7 in the number 3.072?

Question 24Reasoning (Papers 2 and 3 style)

Four children do a long jump. Ava jumps 2.35 m, Kofi 2.4 m, Lilian 2.305 m and Rajesh 2.53 m. Who jumps the second furthest?

Question 25Reasoning (Papers 2 and 3 style)

Zara buys 3 notebooks at £1.45 each and a pen for 89p. She pays with a £20 note. How much change does she get?

Question 26Reasoning (Papers 2 and 3 style)

A 2.4 kg bag of rice is shared equally into 8 smaller bags. How much rice goes in each small bag?

Question 27Arithmetic (Paper 1 style)

What is 35% of 260?

Question 28Arithmetic (Paper 1 style)

Write

\frac{7}{20}

as a percentage.

Question 29Reasoning (Papers 2 and 3 style)

Which of these is the largest: 0.6,

\frac{5}{8}

, 62% or

\frac{3}{5}

Question 30Reasoning (Papers 2 and 3 style)

A coat costs £86. In a sale the price is reduced by 25%. What is the sale price?

Question 31Reasoning (Papers 2 and 3 style)

25 children were asked to choose their favourite sport. 9 chose swimming. What percentage of the children chose swimming?

Question 32Arithmetic (Paper 1 style)

Write 0.45 as a fraction in its simplest form.

Question 33Reasoning (Papers 2 and 3 style)

A computer game costs £45 in two shops. Shop A takes 20% off the price. Shop B takes £10 off the price. Which shop is cheaper, and by how much?

Question 34Reasoning (Papers 2 and 3 style)

A jug holds 750 ml of drink. 40% of the drink is orange juice and the rest is water. How much water is in the jug?

Question 35Reasoning (Papers 2 and 3 style)

Which fraction is exactly halfway between

\frac{3}{5}

and

\frac{7}{10}

on a number line?

Question 36Reasoning (Papers 2 and 3 style)

Kit walks

2\frac{3}{4}

km to the park and then

1\frac{5}{6}

km to his grandad's house. Ella walks

5\frac{1}{3}

km. How much further does Ella walk than Kit?

Question 37Reasoning (Papers 2 and 3 style)

Kemi spends

\frac{1}{4}

of her birthday money on a book. Then she spends

\frac{2}{3}

of the money she has left on a game. She has £8.40 left. How much birthday money did she have at the start?

Question 38Reasoning (Papers 2 and 3 style)

Pens cost £1.35 each, or £7.50 for a pack of 6. Ava needs 20 pens and pays as little as possible. How much does she save compared with buying 20 single pens?

Question 39Reasoning (Papers 2 and 3 style)

There are 30 children in a class. 40% of them are girls.

\frac{3}{4}

of the girls have a pet, and 50% of the boys have a pet. What percentage of the class have a pet?

Test-style questions: type your answers

Fractions calculationsArithmetic (Paper 1 style) · 5 marks

Work out each calculation. Write fractions with a / sign, for example 3/4, and mixed numbers with a space, for example 2 1/3.

(a)

\frac{3}{8}

{}+ \frac{5}{12} =

[1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(b)

2\frac{1}{3}

{}- 1\frac{4}{5} =

[1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(c)

\frac{4}{9} \times \frac{3}{8} =

Give your answer in its simplest form. [1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(d)

\frac{2}{5} \div 4 =

[1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(e)

1\frac{3}{4} \times 3 =

Give your answer as a mixed number. [1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

Decimals and percentages calculationsArithmetic (Paper 1 style) · 6 marks

Work out each calculation.

(a)

0.87 \times 1000 =

[1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(b)

45.6 \div 100 =

[1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(c)

12.5 - 3.68 =

[1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(d)

7.09 \times 6 =

[1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(e) 15% of 260 = [1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(f)

27 \div 4 =

Give your answer as a decimal. [1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

Mixed calculationsArithmetic (Paper 1 style) · 8 marks

Work out each calculation. Write fractions with a / sign, for example 3/4, and mixed numbers with a space, for example 2 1/3. For the long multiplication and the long division, show your method.

(a) 2,607 × 38 [2]

Show your working on paper; type the final answer here. Type fractions as 3/8 and mixed numbers as 2 1/4.

(b) 6,624 ÷ 48 [2]

Show your working on paper; type the final answer here. Type fractions as 3/8 and mixed numbers as 2 1/4.

(c)

\frac{5}{12} \times \frac{3}{10} =

[1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(d)

\frac{6}{7} \div 3 =

[1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(e)

2\frac{5}{6}

{}+ 1\frac{3}{4} =

[1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(f) 65% of 240 = [1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

The cake saleReasoning (Papers 2 and 3 style) · 7 marks

Year 6 bake 48 cupcakes for a cake sale. They sell each cupcake for 45p.

(a) They sell

\frac{5}{6}

of the cupcakes in the morning. How many cupcakes do they sell in the morning? [1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(b) In the afternoon they sell

\frac{3}{4}

of the cupcakes that are left. How many cupcakes are not sold at all? [2]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(d) With the money from the other cakes, the whole cake sale raises £48. The class spends

\frac{3}{8}

of the £48 on a plant for the classroom. They also give 25% of the £48 to the school library. How much of the £48 is left? [2]

Type fractions as 3/8 and mixed numbers as 2 1/4.

A sponsored cycle rideReasoning (Papers 2 and 3 style) · 7 marks

Four friends do a sponsored cycle ride. The whole route is 24 km long. The table shows how far each of them cycled.

A table of how far each friend cycled on a 24 kilometre route: Amara 3 quarters of the route, Ben 0.7 of the route, Chloe 80 percent of the route, Dev 17.5 kilometres.
Name	How far they cycled
Amara	3/4 of the route
Ben	0.7 of the route
Chloe	80% of the route
Dev	17.5 km

(a) Who cycled the furthest? [1]

Type the word or sentence exactly, with its spelling and punctuation.

(b) How much further did Chloe cycle than Ben? [1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(d) What fraction of the route did Dev cycle? Give your answer in its simplest form. [1]

Type fractions as 3/8 and mixed numbers as 2 1/4.

(e) The four friends raise £160 altogether. They give 45% of it to a hospital and

\frac{3}{8}

of it to an animal shelter. They spend the rest on a bike rack for the school. How much does the bike rack cost? [2]

Type fractions as 3/8 and mixed numbers as 2 1/4.