Work out 14 of 28
Fraction of an amount — Notes & Worked Examples Show / Hide
Explanation:
To find a fraction of an amount without a calculator, remember the rule: “Divide by the bottom (denominator), then multiply by the top (numerator)”. Dividing first keeps the numbers small and easy to work with.
In multi-step word problems, pay close attention to whether the question asks for the fraction itself or for the amount remaining (subtract your answer from the starting total).
Example 1: Work out 38 of £72
Solution:
Step 1: Divide by the denominator (8) to find 18:
• £72 ÷ 8 = £9
Step 2: Multiply by the numerator (3) to find 38:
• £9 × 3 = £27
Answer: £27
Example 2: Of 420 pupils, 37 walk to school, 25 catch the bus, and the rest cycle. How many pupils cycle?
Solution:
• Walk: (420 ÷ 7) × 3 = 60 × 3 = 180 pupils
• Bus: (420 ÷ 5) × 2 = 84 × 2 = 168 pupils
• Walk + Bus: 180 + 168 = 348 pupils
• Cycle: 420 − 348 = Answer: 72 pupils
Work out
45 of a number is 32
Find the number.
45 of a number is 32
Find the number.
Worked Solution & Answer
7 12 out of 16 squares shaded. What fraction of the shape is shaded in its simplest form?
What fraction of the shape is shaded?
Give your answer in its simplest form.
Give your answer in its simplest form.
Worked Solution & Answer
Daniel has a piece of rope.
58 of the total length of the rope is 240 cm.
58 of the total length of the rope is 240 cm.
Calculate the total length of the rope.
Worked Solution & Answer
58 of length = 240 cm. M1
18 of length = 240 ÷ 5 = 48 cm M1
Total length (88) = 48 × 8 = 384 cm. A1
18 of length = 240 ÷ 5 = 48 cm M1
Total length (88) = 48 × 8 = 384 cm. A1
Answer: 384 cm (or 3.84 m)
208 bars of chocolate were sold from a shop.
14 of these bars of chocolate were large bars.
The rest of the bars of chocolate were small bars.
All the large bars of chocolate were sold for £1 each.
All the small bars of chocolate were sold for 60p each.
Work out the total amount of money for which the 208 bars of chocolate were sold.
Give your answer in pounds.
14 of these bars of chocolate were large bars.
The rest of the bars of chocolate were small bars.
All the large bars of chocolate were sold for £1 each.
All the small bars of chocolate were sold for 60p each.
Work out the total amount of money for which the 208 bars of chocolate were sold.
Give your answer in pounds.
£
Worked Solution & Answer
Large = 208 ÷ 4 = 52 bars (£52) M1
Small = 208 – 52 = 156 bars (156 × £0.60 = £93.60) M1
Total = £52 + £93.60 = £145.60 A1
Small = 208 – 52 = 156 bars (156 × £0.60 = £93.60) M1
Total = £52 + £93.60 = £145.60 A1
Answer: £ 145.60
Here is the gauge for the fuel tank of a car.
The fuel tank holds 52 litres of fuel when the tank is full.
The tank is 14 full of fuel.
Work out how many more litres of fuel are needed to fill the tank.
The tank is 14 full of fuel.
Work out how many more litres of fuel are needed to fill the tank.
litres
Worked Solution & Answer
Raymond sells 80 burgers for a total of £176
15 of the burgers are large.
Each large burger costs £3
The remaining burgers are small.
Work out the cost of one small burger.
15 of the burgers are large.
Each large burger costs £3
The remaining burgers are small.
Work out the cost of one small burger.
£
Worked Solution & Answer
Large burgers = 1/5 × 80 = 16 M1
cost of large = 16 × £3 = £48 M1
Small burgers = 80 − 16 = 64 M1
total cost of small = 176 − 48 = £128
Cost of 1 small burger = 128 ÷ 64 = £2. A1
cost of large = 16 × £3 = £48 M1
Small burgers = 80 − 16 = 64 M1
total cost of small = 176 − 48 = £128
Cost of 1 small burger = 128 ÷ 64 = £2. A1
Answer: £ 2
Here is a rectangle.
The rectangle has been divided into two strips, A and B.
The strips have the same width.
25 of strip A is shaded.
58 of strip B is shaded.
The rectangle has been divided into two strips, A and B.
The strips have the same width.
25 of strip A is shaded.
58 of strip B is shaded.
The length of the rectangle is 40 cm.
What fraction of the rectangle is not shaded?
What fraction of the rectangle is not shaded?
Worked Solution & Answer
Shaded in A = 16/40, shaded in B = 25/40 M2
Total shaded = 41/80 M1
Unshaded = 39/80. A1
Total shaded = 41/80 M1
Unshaded = 39/80. A1
Answer: 3980
Here is a rectangle.
The rectangle has been divided into two strips, A and B.
The strips have the same width.
25 of strip A is shaded.
58 of strip B is shaded.
The length of the rectangle is 40 cm.
What fraction of the rectangle is not shaded?
The strips have the same width.
25 of strip A is shaded.
58 of strip B is shaded.
The length of the rectangle is 40 cm.
What fraction of the rectangle is not shaded?
Worked Solution & Answer
In strip A (40 units): 2/5 of 40 = 16 shaded M1
In strip B (40 units): 5/8 of 40 = 25 shaded M1
Total shaded = 41/80 M1
Not shaded = 39/80. A1
In strip B (40 units): 5/8 of 40 = 25 shaded M1
Total shaded = 41/80 M1
Not shaded = 39/80. A1
Answer: 3980
A shop sells two brands of battery.
Determine which brand is better value.
Brand A: Pack of 8, Price £3.60. One brand A battery powers a toy for 5 hours.
Brand B: Pack of 6, Price £2.94. One brand B battery powers the same toy for 512 hours.
Which brand is better value?
You must show your working.
Brand B: Pack of 6, Price £2.94. One brand B battery powers the same toy for 512 hours.
Which brand is better value?
You must show your working.
Answer
Worked Solution & Answer
Method: Compare cost per hour of power M1
Brand A total hours = 8 × 5 = 40 hours M1
Brand A cost per hour = £3.60 ÷ 40 = £0.09 = 9p per hour M1
Brand B total hours = 6 × 5.5 = 33 hours M1
Brand B cost per hour = £2.94 ÷ 33 = £0.08909... ≈ 8.91p per hour
Since 8.91p < 9p, Brand B is better value. A1
Brand A total hours = 8 × 5 = 40 hours M1
Brand A cost per hour = £3.60 ÷ 40 = £0.09 = 9p per hour M1
Brand B total hours = 6 × 5.5 = 33 hours M1
Brand B cost per hour = £2.94 ÷ 33 = £0.08909... ≈ 8.91p per hour
Since 8.91p < 9p, Brand B is better value. A1
Answer: Answer Brand B