Calculate 2/3 × 3/4 and give your answer in simplest form.
(1)
4
Work out 1 1/3 × 3/2. Show your method.
(2)
5
A box contains 60 sweets. Tom eats 2/5 of the sweets. How many sweets does he eat?
(2)
6
Write down the reciprocal of 4/7.
(1)
7
Calculate 3/4 ÷ 1/2. Give your answer as a fraction and as a mixed number if appropriate.
(2)
8
Work out 5 ÷ 2/3. Give your answer in simplest form.
(2)
9
Calculate and simplify: (3/7) × (14/9).
(2)
10
Find 3/8 of 56. Show how you work this out.
(2)
11
Calculate 2 1/2 ÷ 1/4. Show your method.
(2)
12
Sally has 3/4 of a litre of juice. She pours away 2/3 of it. How much juice does she pour away? Give your answer in litres.
(2)
13
Simplify (2/5) ÷ (4/15). Show your working and give your answer in simplest form.
(2)
14
A cake recipe needs 1 2/3 cups of flour. If a baker makes 1/3 of the recipe, how many cups of flour are needed? Give your answer as a fraction in simplest form.
(2)
15
Solve for x: x × 3/4 = 9/8. Show your method and give x in simplest form.
(3)
16
A length of ribbon is 2 1/2 metres long. It is cut into pieces each 3/5 metre long. How many full pieces can be cut from the ribbon and how much ribbon is left over? Give the leftover length as a fraction in simplest form.
(3)
Mark scheme · KS3.M-N10 Fractions: Multiplying and Dividing
Question 1
B1 1/8 cao
Answer: 1/8
Question 2
B1 6 cao
Answer: 6
Question 3
B1 1/2 cao
Answer: 1/2
Question 4
M1 convert mixed number to improper fraction and multiply: 4/3 × 3/2 or equivalent method
A1 2 cao
Answer: 2
Question 5
M1 method to find 2/5 of 60, e.g. 60 × 2/5 or 60 ÷ 5 × 2
A1 24 cao
Answer: 24
Question 6
B1 7/4 cao
Answer: 7/4
Question 7
M1 use reciprocal: 3/4 × 2/1 or equivalent
A1 3/2 or 1 1/2 cao
Answer: 3/2 = 1 1/2
Question 8
M1 rewrite as 5 × 3/2 or equivalent method
A1 15/2 or 7 1/2 cao
Answer: 15/2 = 7 1/2
Question 9
M1 multiply numerators and denominators or cancel first: 3×14 and 7×9 or cancel 7 with 14 etc
A1 2/3 cao
Answer: 2/3
Question 10
M1 method to find fraction of amount, e.g. 56 × 3/8 or 56 ÷ 8 × 3
A1 21 cao
Answer: 21
Question 11
M1 convert 2 1/2 to improper fraction 5/2 and use reciprocal: 5/2 × 4/1
A1 10 cao
Answer: 10
Question 12
M1 method: 3/4 × 2/3 or equivalent
A1 1/2 litre cao
Answer: 1/2 litre
Question 13
M1 use reciprocal: 2/5 × 15/4 or show equivalent method
A1 3/2 or 1 1/2 cao
Answer: 3/2 = 1 1/2
Question 14
M1 convert 1 2/3 to improper fraction 5/3 and multiply by 1/3
A1 5/9 cao
Answer: 5/9
Question 15
M1 isolate x by dividing both sides by 3/4 or multiply by reciprocal: x = 9/8 × 4/3
M1 attempt to multiply numerators and denominators to get 36/24 or equivalent
A1 3/2 or 1 1/2 cao
Answer: 3/2 = 1 1/2
Question 16
M1 method to divide: convert to improper fractions and divide 5/2 ÷ 3/5 = 5/2 × 5/3
M1 calculate 25/6 and identify 4 full pieces with remainder 1/6 of a piece (since 25/6 = 4 1/6)
A1 convert remainder to a length: 1/6 × 3/5 = 1/10, so 4 full pieces and leftover 1/10 metre cao