Browse Fractions & decimals

52 questions at your level

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The four operations with fractions

21 questions

LessonNot started
Work out 25+15\dfrac{2}{5} + \dfrac{1}{5}
●●●●●Level 11 markStart
Work out 12+14\dfrac{1}{2} + \dfrac{1}{4}
●●●●●Level 12 marksStart
0.3750.375 written as a fraction in its simplest form is

Circle your answer.
  • A 35\dfrac{3}{5}
  • B 38\dfrac{3}{8}
  • C 37\dfrac{3}{7}
  • D 58\dfrac{5}{8}
●●●●●Level 11 markStart
Work out 34−25\dfrac{3}{4} - \dfrac{2}{5}

Give your answer as a fraction in its simplest form. (2 marks)
●●●●●Level 12 marksStart
Work out

(a) 25+14\dfrac{2}{5} + \dfrac{1}{4}

(b) 56−38\dfrac{5}{6} - \dfrac{3}{8}

Give each answer in its simplest form.
●●●●●Level 24 marksStart
Write these numbers in order of size, starting with the smallest.

0.454944%370.45 \qquad \dfrac{4}{9} \qquad 44\% \qquad \dfrac{3}{7}

(2 marks)
●●●●●Level 22 marksStart
Work out 123÷2121\frac{2}{3} \div 2\frac{1}{2}

Give your answer as a fraction in its simplest form. (3 marks)
●●●●●Level 23 marksStart
Work out 213×1152\dfrac{1}{3} \times 1\dfrac{1}{5}

Give your answer as a mixed number in its simplest form. [3]
●●●●●Level 23 marksStart
Work out 7.56÷0.247.56 \div 0.24

(3 marks)
●●●●●Level 23 marksStart
Work out

(a) 38+56\dfrac{3}{8} + \dfrac{5}{6} — give your answer as a mixed number in its simplest form.

(b) 710−215\dfrac{7}{10} - \dfrac{2}{15} — give your answer in its simplest form.
●●●●●Level 34 marksStart
Work out

(a) 49×310\dfrac{4}{9} \times \dfrac{3}{10} — give your answer in its simplest form.

(b) 58÷1516\dfrac{5}{8} \div \dfrac{15}{16} — give your answer in its simplest form.
●●●●●Level 34 marksStart
Work out 315−1343\tfrac{1}{5} - 1\tfrac{3}{4}

Give your answer as a mixed number in its simplest form.
●●●●●Level 33 marksStart
(a) Work out 416−1344\frac{1}{6} - 1\frac{3}{4}

Give your answer as a mixed number.

(2 marks)

Omar was asked to work out 423×564\frac{2}{3} \times \frac{5}{6}

Here is his working and his answer.

423×56=143×564\frac{2}{3} \times \frac{5}{6} = \frac{14}{3} \times \frac{5}{6}

=7018= \frac{70}{18}

=4218= 4\frac{2}{18}

Omar's answer is wrong.
(b) What mistake has Omar made?

(1 mark)
●●●●●Level 33 marksStart
Work out 234×1352\tfrac{3}{4} \times 1\tfrac{3}{5}

Give your answer as a mixed number in its simplest form.

You must show all your working.
●●●●●Level 43 marksStart
Work out 312÷1253\tfrac{1}{2} \div 1\tfrac{2}{5}

Give your answer as a mixed number in its simplest form.

You must show all your working.
●●●●●Level 43 marksStart
One batch of pancake mixture needs 34\dfrac{3}{4} of a litre of milk.

A jug holds 2252\tfrac{2}{5} litres of milk.

How many complete batches of mixture can be made from the jug?
●●●●●Level 43 marksStart
In a school, 23\dfrac{2}{3} of the students walk to school.

Of the students who walk, 38\dfrac{3}{8} walk with a friend.

(a) What fraction of the whole school walks with a friend?

(b) What fraction of the whole school walks alone?
●●●●●Level 44 marksStart
Show that (412−223)÷234=23\left(4\tfrac{1}{2} - 2\tfrac{2}{3}\right) \div 2\tfrac{3}{4} = \dfrac{2}{3}

You must show each stage of your working.
●●●●●Level 54 marksStart
Show that (123)2÷279=1\left(1\tfrac{2}{3}\right)^2 \div 2\tfrac{7}{9} = 1

You must show each stage of your working.
●●●●●Level 53 marksStart
Show that 0.4˙2˙+0.35˙7˙0.\dot{4}\dot{2} + 0.3\dot{5}\dot{7} can be written in the form m55\dfrac{m}{55} where mm is an integer.

(3 marks)
●●●●●Level 53 marksStart
x=0.7˙y=0.16˙3˙x = 0.\dot{7} \qquad y = 0.1\dot{6}\dot{3}

Work out the value of xyxy.

Give your answer as a fraction in its simplest form.

(5 marks)
●●●●●Level 55 marksStart

Fractions of amounts

19 questions

LessonNot started
Work out 14\dfrac{1}{4} of 3232.
●●●●●Level 11 markStart
Work out 35\dfrac{3}{5} of 4040.
●●●●●Level 12 marksStart
There are 150150 people at a cinema. 23\dfrac{2}{3} of them are adults. How many are adults?
●●●●●Level 12 marksStart
Work out 35\dfrac{3}{5} of 4545 kg.
●●●●●Level 22 marksStart
There are 720720 people at a concert.

38\dfrac{3}{8} of the people are children. 40%40\% of the children are girls.

Work out the number of girls at the concert. [3]
●●●●●Level 23 marksStart
Work out 47\dfrac{4}{7} of £322
●●●●●Level 32 marksStart
Which is larger: 23\dfrac{2}{3} of £8484, or 34\dfrac{3}{4} of £7676?

You must show your working.
●●●●●Level 33 marksStart
The amount of honey a beekeeper collected this year is 29\dfrac{2}{9} less than the amount she collected last year.

This year the beekeeper collected 15961596 kg of honey.

Work out the amount of honey the beekeeper collected last year.

(3 marks)
●●●●●Level 33 marksStart
There are 252252 tiles in a box.

There are only white tiles, grey tiles and black tiles.

29\frac{2}{9} of the 252252 tiles are white tiles.

number of grey tiles : number of black tiles =2:5= 2 : 5

number of black tiles : number of white tiles =n:1= n : 1
(a) Work out the value of nn.

You must show all your working.

(5 marks)

66 of the grey tiles are cracked and are taken out of the box.
(b) Does this affect your answer to part (a)?

Give a reason for your answer.

(1 mark)
●●●●●Level 36 marksStart
Dev has some small, medium and large candles.

He has a total of 500500 candles.

35\frac{3}{5} of the 500500 candles are scented.

For the scented candles,

number of small candles : number of medium candles =1:3= 1 : 3

number of medium candles : number of large candles =6:7= 6 : 7

Work out the percentage of Dev's candles that are small scented candles.

(5 marks)
●●●●●Level 35 marksStart
Freya, Tomasz and Ines share some beads in the ratio 3:4:113 : 4 : 11

Ines gives 311\frac{3}{11} of her beads to Freya.

Ines then gives 25%25\% of the rest of her beads to Tomasz.

Ines says,

"We each have the same number of beads now."

Is Ines correct?

You must show how you get your answer.

(4 marks)
●●●●●Level 34 marksStart
Kwame, Lena and Priya share some marbles in the ratio 3:4:93 : 4 : 9

Priya gives 13\frac{1}{3} of her marbles to Kwame.

Priya then gives 20%20\% of the rest of her marbles to Lena.

Priya says,

"We each have an equal share of the marbles now."

Is Priya correct?

You must show how you get your answer.

(4 marks)
●●●●●Level 34 marksStart
Lena is paid £540.

She puts 29\dfrac{2}{9} of the £540 into savings.

She then spends 37\dfrac{3}{7} of the remainder on rent.

How much of the £540 does Lena have left?
●●●●●Level 43 marksStart
38\dfrac{3}{8} of a number is 96.

(a) Find the number.

(b) Find 58\dfrac{5}{8} of the number.
●●●●●Level 43 marksStart
Write 35 minutes as a fraction of 2122\tfrac{1}{2} hours.

Give your answer in its simplest form.
●●●●●Level 42 marksStart
Keira spends 58\dfrac{5}{8} of her money on a coat.

She has £48.6048.60 left.

How much money did she have to start with?
●●●●●Level 43 marksStart
A plank of wood is 2.42.4 m long.

A carpenter cuts off 512\dfrac{5}{12} of the plank.

(a) Work out the length that is cut off. Give your answer in metres.

(b) Work out the length that remains. Give your answer in metres.
●●●●●Level 43 marksStart
At a cinema one evening, 35\dfrac{3}{5} of the tickets sold were adult tickets.

23\dfrac{2}{3} of the adult tickets were sold online.

348 adult tickets were sold online.

How many tickets were sold in total that evening?
●●●●●Level 53 marksStart
At a sports club, 25\dfrac{2}{5} of the members are juniors.

34\dfrac{3}{4} of the remaining members are seniors, and the rest are coaches.

There are 4545 coaches.

(a) Show that 320\dfrac{3}{20} of the members are coaches.

(b) Work out the total number of members.
●●●●●Level 55 marksStart

Recurring decimals and fractions

14 questions

LessonNot started
Prove algebraically that the recurring decimal 0.8˙0.\dot{8} can be written as 89\dfrac{8}{9}
●●●●●Level 32 marksStart
Without working out any division, decide whether each fraction is equal to a terminating decimal or a recurring decimal.

Give a reason for each answer.

(a) 940\dfrac{9}{40}

(b) 712\dfrac{7}{12}
●●●●●Level 32 marksStart
(a) Write the recurring decimal 0.4˙0.\dot{4} as a fraction.

(b) Hence write 5.4˙5.\dot{4} as an improper fraction.
●●●●●Level 33 marksStart
Write the recurring decimal 0.7˙2˙0.\dot{7}\dot{2} as a fraction in its simplest form. (3 marks)
●●●●●Level 33 marksStart
Write the recurring decimal 0.5˙4˙0.\dot{5}\dot{4} as a fraction in its simplest form.
●●●●●Level 42 marksStart
Write 0.38˙0.3\dot{8} as a fraction in its simplest form.
●●●●●Level 43 marksStart
Write the recurring decimal 0.2˙7˙0.\dot{2}\dot{7} as a fraction in its simplest form.
●●●●●Level 43 marksStart
Prove algebraically that 0.16˙=160.1\dot{6} = \dfrac{1}{6}
●●●●●Level 43 marksStart
(a) Write 0.6˙0.\dot{6} and 0.1˙0.\dot{1} as fractions.

(b) Hence work out 0.6˙+0.1˙0.\dot{6} + 0.\dot{1}, giving your answer as a fraction in its simplest form.
●●●●●Level 44 marksStart
Prove algebraically that the recurring decimal 0.2˙7˙0.\dot{2}\dot{7} can be written as 311\dfrac{3}{11} (3 marks)
●●●●●Level 43 marksStart
Prove algebraically that the recurring decimal 2.13˙6˙2.1\dot{3}\dot{6} can be written as 4722\dfrac{47}{22}
●●●●●Level 53 marksStart
Prove algebraically that the recurring decimal 1.2˙0˙7˙1.\dot{2}\dot{0}\dot{7} can be written as 134111\dfrac{134}{111}
●●●●●Level 53 marksStart
Show that 0.4˙2˙+0.35˙7˙0.\dot{4}\dot{2} + 0.3\dot{5}\dot{7} can be written in the form m55\dfrac{m}{55} where mm is an integer.

(3 marks)
●●●●●Level 53 marksStart
x=0.7˙y=0.16˙3˙x = 0.\dot{7} \qquad y = 0.1\dot{6}\dot{3}

Work out the value of xyxy.

Give your answer as a fraction in its simplest form.

(5 marks)
●●●●●Level 55 marksStart