Calculate 3/4 x 2/5, giving your answer in simplest form.
(1)
4
Work out 1 2/5 x 5/3. Show your method.
(2)
5
Write down the reciprocal of 5/9.
(1)
6
A box contains 90 sweets. Maya eats 3/10 of the sweets. How many sweets does she eat?
(2)
7
Calculate 2/3 divided by 1/6, giving your answer as a whole number.
(1)
8
Work out 7 divided by 3/5. Give your answer in simplest form.
(2)
9
Calculate and simplify: 5/8 x 12/15.
(2)
10
Find 5/6 of 42. Show how you work this out.
(2)
11
Calculate 3 1/3 divided by 1/6. Show your method.
(2)
12
Ben has 5/6 of a litre of paint. He uses 2/5 of it on a fence. How much paint does he use? Give your answer as a fraction of a litre in simplest form.
(2)
13
Simplify 3/7 divided by 9/14. Show your working and give your answer in simplest form.
(2)
14
A cake recipe needs 2 1/4 cups of flour. A baker makes 2/3 of the recipe. How many cups of flour are needed? Give your answer as a mixed number in simplest form.
(3)
15
A length of ribbon is 4 1/6 metres long. It is cut into pieces each 3/4 metre long. Work out how many full pieces can be cut, and how much ribbon (as a fraction of a metre) is left over.
(3)
16
Solve for y: y multiplied by 5/6 = 15/4. Show your method and give y in simplest form.
(3)
17
A tank is 5/8 full of water. This is equivalent to 30 litres. Work out the full capacity of the tank, and hence how many litres are needed to fill it completely.
(3)
18
Two thirds of a school's students walk to school. Of those who walk, 3/8 arrive before 8:30am. What fraction of the whole school arrives before 8:30am having walked to school? Give your answer in simplest form.
(3)
19
Stretch question. A recipe for lemonade needs 1 1/4 litres of water for every 3/8 litre of lemon juice. A chef has 4 3/8 litres of water. Work out how much lemon juice is needed to keep the same ratio, giving your answer as a mixed number in its simplest form.
(4)
Mark scheme · KS3.M-N10D Fractions: Multiplying and Dividing: Fluency and Exam Drill
Question 1
B1 1/15 cao
Answer: 1/15
Question 2
B1 4 cao
Answer: 4
Question 3
B1 3/10 cao
Answer: 3/10
Question 4
M1 converts 1 2/5 to the improper fraction 7/5
A1 7/3 or 2 1/3 cao
Answer: 7/3 (2 1/3)
Question 5
B1 9/5 cao
Answer: 9/5
Question 6
M1 uses 90 x 3/10
A1 27 cao
Answer: 27
Question 7
B1 4 cao
Answer: 4
Question 8
M1 multiplies 7 by the reciprocal of 3/5: 7 x 5/3
A1 35/3 or 11 2/3 cao
Answer: 35/3 (11 2/3)
Question 9
M1 multiplies numerators and denominators: (5x12)/(8x15) = 60/120
A1 1/2 cao
Answer: 1/2
Question 10
M1 uses 42 x 5/6
A1 35 cao
Answer: 35
Question 11
M1 converts 3 1/3 to the improper fraction 10/3, then multiplies by 6
A1 20 cao
Answer: 20
Question 12
M1 uses 5/6 x 2/5
A1 1/3 of a litre cao
Answer: 1/3 of a litre
Question 13
M1 multiplies by the reciprocal: 3/7 x 14/9
A1 2/3 cao
Answer: 2/3
Question 14
M1 converts 2 1/4 to the improper fraction 9/4
M1 multiplies 9/4 x 2/3 = 18/12
A1 1 1/2 cups cao
Answer: 1 1/2 cups
Question 15
M1 converts 4 1/6 to the improper fraction 25/6
M1 divides: 25/6 divided by 3/4 = 50/9
A1 5 full pieces, with 5/12 metre left over cao
Answer: 5 full pieces; 5/12 metre left over
Question 16
M1 sets up y = (15/4) divided by (5/6)
M1 y = 15/4 x 6/5 = 90/20
A1 y = 9/2 or 4 1/2 cao
Answer: 9/2 (4 1/2)
Question 17
M1 sets up (5/8) x capacity = 30
M1 capacity = 30 divided by 5/8 = 48 litres
A1 18 litres are needed cao
Answer: Capacity 48 litres; 18 litres needed
Question 18
M1 uses 2/3 x 3/8
M1 = 6/24
A1 1/4 cao
Answer: 1/4
Question 19
M1 converts 1 1/4 to 5/4 and 4 3/8 to 35/8
M1 finds the scale factor: (35/8) divided by (5/4) = 7/2
M1 multiplies the juice amount by the scale factor: 3/8 x 7/2 = 21/16