Fractions: All Four Operations - Worksheets, Questions and Revision

18 original exam-style questions - 4 pages of questions with a full mark scheme - free printable PDF.

Download PDF Jump to mark scheme (page 5)Fractions: All Four Operations revision guide

This topic is chapter 5 of KS2 Maths: Fractions, Ratio and proportion, and Algebra Practice Book.

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4.9 Fractions: All Four Operations

Calculators not allowed · about 45 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Calculate 3/8 + 2/8.

(1)

Subtract 5/6 from 2. Give your answer as a mixed number if needed.

(2)

Find the missing numerator: ?/16 = 5/8. Write your answer as a whole number.

(2)

Which is larger, 7/10 or 3/4? Explain your answer showing any working.

(2)

Write 11/4 as a mixed number.

(1)

A bottle is 3/5 full of juice. You add another 4/7 of the bottle. Is the bottle more than full? Work out the total and give your answer in simplest form.

(3)

Is 2/3 + 1/4 greater than 1? Explain your answer clearly.

(2)

Calculate (6/9) x (3/8). Simplify your answer.

(2)

Work out 5 1/2 - 2 7/10. Give your answer in simplest form.

(2)

Sam has a pizza. He eats 2/5 of it. His friend eats 1/3 of the remaining pizza. How much of the whole pizza have they eaten altogether? Show your working and give the answer in simplest form.

(3)

Work out 4 1/3 - 2 2/3. Show any subtraction of the fractional parts.

(2)

Add 7/12 and 1/4. Give your answer in simplest form.

(2)

Write 12/18 in its simplest form.

(1)

Calculate 5 x 3/10.

(1)

Work out 2/3 x 3/5. Give your answer in simplest form.

(2)

Divide 3/4 by 3. Show your method.

(2)

Work out 2/5 ÷ 4/15. Give your answer in simplest form.

(2)

A cake recipe needs 3/4 of a cup of sugar and 2/3 of a cup of flour. How many cups of these two ingredients are needed in total? Give your answer in fractions and simplest form.

(3)

Mark scheme · 4.9 Fractions: All Four Operations

Question 1

B1 5/8 cao
Answer: 5/8

Question 2

M1 correct conversion or subtraction: 2 = 1 6/6, 1 6/6 - 5/6 = 1 1/6
A1 1 1/6 cao
Answer: 1 1/6

Question 3

M1 understands scaling: 8 -> 16 is x2 so numerator 5 x 2 = 10, or uses equivalent fraction method
A1 10 cao
Answer: 10

Question 4

M1 correct method to compare, e.g. convert to common denominator 7/10 = 28/40, 3/4 = 30/40 or convert to decimals
A1 3/4 is larger with correct reason (30/40 > 28/40) cao
Answer: 3/4 is larger

Question 5

B1 2 3/4 cao
Answer: 2 3/4

Question 6

M1 correct common denominator or conversion, e.g. 3/5 = 21/35, 4/7 = 20/35 then add to 41/35
A1 41/35 or 1 6/35 cao
B1 explicit yes, the bottle is more than full
Answer: 1 6/35

Question 7

M1 shows correct addition to a common denominator, e.g. 2/3 = 8/12, 1/4 = 3/12, total 11/12
A1 11/12 < 1 so answer is No, with reason cao
Answer: No, it is 11/12

Question 8

M1 correct multiplication with cancellation, e.g. cancel 6/9 to 2/3 then 2/3 x 3/8 = 2/8
A1 1/4 cao
Answer: 1/4

Question 9

M1 convert to improper fractions or to common denominator: 5 1/2 = 11/2, 2 7/10 = 27/10, convert to twentieths: 11/2 = 110/20, 27/10 = 54/20, then subtract
A1 56/20 = 14/5 or 2 4/5 cao
Answer: 2 4/5

Question 10

M1 correctly finds remaining pizza after Sam: 1 - 2/5 = 3/5, then finds 1/3 of 3/5 = 1/5
M1 adds amounts eaten: 2/5 + 1/5 = 3/5
A1 3/5 cao
Answer: 3/5

Question 11

M1 correct conversion or borrowing for the mixed-number subtraction, e.g. 4 1/3 = 3 4/3 then 3 4/3 - 2 2/3 = 1 2/3
A1 1 2/3 cao
Answer: 1 2/3

Question 12

M1 correct common denominator work, e.g. 1/4 = 3/12 and 7/12 + 3/12 = 10/12
A1 5/6 cao
Answer: 5/6

Question 13

B1 2/3 cao
Answer: 2/3

Question 14

B1 15/10 or 3/2 accepted; 3/2 cao
Answer: 3/2

Question 15

M1 correct multiplication of numerators and denominators, or cancellation first, e.g. 2/3 x 3/5 = (2x3)/(3x5)
A1 2/5 cao
Answer: 2/5

Question 16

M1 method using reciprocal or dividing numerator by 3, e.g. 3/4 x 1/3 or (3/4) ÷ 3 = 3/12
A1 1/4 cao
Answer: 1/4

Question 17

M1 correct use of reciprocal: 2/5 x 15/4 or equivalent cancellation
A1 3/2 or 1 1/2 cao
Answer: 3/2

Question 18

M1 correct common denominator work, e.g. 3/4 = 9/12, 2/3 = 8/12, then add to 17/12
A1 1 5/12 cao
B1 answer expressed in simplest form or as mixed number
Answer: 1 5/12

Fractions: All Four Operations - Worksheets, Questions and Revision

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4.9 Fractions: All Four Operations

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