Fractions: Equivalence, Ordering and Calculation - Worksheets, Questions and Revision

20 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

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KS2 · Number

KS2.M-FRAC Fractions: Equivalence, Ordering and Calculation

NCETM National Curriculum (2014) Mathematics - KS2 Number: Fractions (Equivalence, Ordering and Calculation) · Calculators not allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Complete each equivalent fraction statement.

(a)2/5 = ?/20(1)

(b)Write 18/24 in its simplest form.(1)

Write these fractions in order of size, starting with the smallest: 5/8, 1/8, 6/8, 3/8

(2)

Which is greater, 3/4 or 5/6? Show working to justify your answer.

(2)

Convert between improper fractions and mixed numbers.

(a)Write 17/5 as a mixed number.(1)

(b)Write 4 3/7 as an improper fraction.(1)

Work out 3/8 of 96.

(2)

Add and subtract these fractions, giving each answer in its simplest form.

(a)3/10 + 4/10(1)

(b)5/6 - 1/4(2)

Work out 2 3/4 + 1 5/8. Give your answer as a mixed number in its simplest form.

(3)

Work out 5/6 x 4. Give your answer as a mixed number in its simplest form.

(2)

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

(2)

Work out 3/4 divided by 6. Give your answer in its simplest form.

(2)

Write these fractions in order of size, starting with the smallest: 2/3, 5/9, 7/12. Show your working.

(3)

Priya is baking scones. One batch of scones uses 2/5 of a bag of flour. Priya has 3/4 of a bag of flour.

(a)How many complete batches of scones can Priya make?(2)

(b)What fraction of a bag of flour will be left over after making the complete batches?(1)

Find the missing numbers in each equivalent fraction.

(a)3/7 = 12/?(1)

(b)?/40 = 7/8(1)

Which is greater, 4/7 or 5/9? Use cross multiplication to explain your answer, without using a calculator.

(2)

Work out 1/2 + 1/3 + 1/4. Give your answer as a mixed number in its simplest form.

(3)

Work out 5 1/6 - 2 5/6. Give your answer as a mixed number in its simplest form.

(3)

Show that 5/6 is greater than 7/9, without using a calculator.

(2)

There are 360 pupils at Hartfield Primary School. 5/8 of the pupils are girls. 2/3 of the girls walk to school.

(a)How many pupils are girls?(1)

(b)How many girls do not walk to school?(2)

A fraction in its simplest form is 3/4. Find two different fractions equivalent to 3/4, each with a denominator between 12 and 30.

(2)

The sum of two unit fractions is 7/12. One of the fractions is 1/3. Find the other fraction, giving your answer in its simplest form.

(2)

Mark scheme · KS2.M-FRAC Fractions: Equivalence, Ordering and Calculation

Question 1

(a) B1 8 cao
(a) Answer: 8
(b) B1 3/4 cao
(b) Answer: 3/4

Question 2

B1 smallest and largest correctly identified as 1/8 and 6/8
B1 fully correct order 1/8, 3/8, 5/8, 6/8 cao
Answer: 1/8, 3/8, 5/8, 6/8

Question 3

M1 correct common denominator working, e.g. 3/4 = 9/12 and 5/6 = 10/12
A1 5/6 is greater, with reason (10/12 > 9/12) oe
Answer: 5/6 is greater than 3/4

Question 4

(a) B1 3 2/5 cao
(a) Answer: 3 2/5
(b) B1 31/7 cao
(b) Answer: 31/7

Question 5

M1 96/8 = 12 seen (or equivalent method)
A1 36 cao
Answer: 36

Question 6

(a) B1 7/10 cao
(a) Answer: 7/10
(b) M1 common denominator of 12 used, e.g. 10/12 - 3/12
(b) A1 7/12 cao
(b) Answer: 7/12

Question 7

M1 2 3/4 converted to eighths, e.g. 2 6/8
M1 whole numbers and fractions combined correctly, e.g. 3 + 11/8
A1 4 3/8 cao
Answer: 4 3/8

Question 8

M1 20/6 oe seen
A1 3 1/3 cao
Answer: 3 1/3

Question 9

M1 6/15 oe seen
A1 2/5 cao
Answer: 2/5

Question 10

M1 3/24 oe seen
A1 1/8 cao
Answer: 1/8

Question 11

M1 common denominator of 36 used for at least two fractions
M1 all three fractions correctly converted, e.g. 24/36, 20/36, 21/36
A1 correct order 5/9, 7/12, 2/3 cao
Answer: 5/9, 7/12, 2/3

Question 12

(a) M1 correct comparison or division method, e.g. (3/4) / (2/5) = 15/8 oe
(a) A1 1 complete batch cao
(a) Answer: 1 complete batch
(b) B1 7/20 cao (ft from part a if one batch used)
(b) Answer: 7/20

Question 13

(a) B1 28 cao
(a) Answer: 28
(b) B1 35 cao
(b) Answer: 35

Question 14

M1 correct cross products found, e.g. 4 x 9 = 36 and 5 x 7 = 35
A1 4/7 is greater, because 36 > 35 oe
Answer: 4/7 is greater than 5/9

Question 15

M1 common denominator of 12 used
M1 6/12 + 4/12 + 3/12 = 13/12 seen
A1 1 1/12 cao
Answer: 1 1/12

Question 16

M1 recognises that 1/6 is less than 5/6 and regroups, e.g. 5 1/6 = 4 7/6
M1 4 7/6 - 2 5/6 = 2 2/6 oe seen
A1 2 1/3 cao
Answer: 2 1/3

Question 17

M1 both fractions correctly converted to a common denominator, e.g. 5/6 = 15/18 and 7/9 = 14/18
A1 correct conclusion stated (15/18 > 14/18) cso
Answer: 5/6 is greater than 7/9 (shown)

Question 18

(a) B1 225 cao
(a) Answer: 225
(b) M1 number of girls who walk found, e.g. 225 x 2/3 = 150 (ft from part a)
(b) A1 75 cao
(b) Answer: 75

Question 19

B1 one correct equivalent fraction with denominator between 12 and 30, e.g. 15/20, 18/24 or 21/28 oe
B1 a second, different correct equivalent fraction with denominator between 12 and 30 oe
Answer: e.g. 15/20 and 21/28 (any two of 15/20, 18/24, 21/28 accepted)

Question 20

M1 correct common denominator method, e.g. 7/12 - 4/12
A1 1/4 cao
Answer: 1/4

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