Fraction Problem Solving (A) Worksheet | Cazoom Maths Worksheets - Free Printable

I will solve the problems step by step.

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Problem 1a:
A father brings £55. He spends 3/5 on tickets.

Step 1: Find 1/5 of £55 → 55 ÷ 5 = 11
Step 2: Multiply by 3 → 11 × 3 = 33

✔ He spent £33 on tickets.

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Problem 1b:
He spends £15 on snacks. What fraction of the money was spent on snacks?

Total money = £55
Spent on snacks = £15

Fraction = 15/55

Simplify: divide numerator and denominator by 5 → 3/11

✔ The fraction is 3/11.

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Problem 1c:
His wife wanted him to bring 2/11 more to the cinema. How much did his wife want him to bring?

This means: add 2/11 of the original amount (£55) to the original amount.

Step 1: Find 2/11 of £55 → (55 ÷ 11) × 2 = 5 × 2 = 10
Step 2: Add to original → 55 + 10 = 65

✔ His wife wanted him to bring £65.

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Problem 2a:
Perimeter of USB port (rectangle): length = 9/10 cm, width = 3/4 cm

Perimeter = 2 × (length + width)

Step 1: Add length and width → 9/10 + 3/4
Find common denominator: 20
→ 9/10 = 18/20, 3/4 = 15/20
Sum = 18/20 + 15/20 = 33/20

Step 2: Multiply by 2 → 2 × 33/20 = 66/20

Step 3: Simplify → 66 ÷ 2 = 33, 20 ÷ 2 = 10 → 33/10
Convert to mixed fraction: 33 ÷ 10 = 3 with remainder 3 → 3 3/10

✔ Perimeter = 3 3/10 cm

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Problem 2b:
Shaded area = outer rectangle minus inner rectangle

Outer rectangle: 9/10 cm × 3/4 cm
Inner rectangle: 1/2 cm × 1/3 cm

Step 1: Outer area = 9/10 × 3/4 = (9×3)/(10×4) = 27/40

Step 2: Inner area = 1/2 × 1/3 = 1/6

Step 3: Subtract → 27/40 - 1/6
Common denominator of 40 and 6 is 120

27/40 = (27×3)/120 = 81/120
1/6 = (1×20)/120 = 20/120

Subtract: 81/120 - 20/120 = 61/120

✔ Shaded area = 61/120 cm²

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Problem 3a (Section B):
1/3 of life is spent asleep. If someone lives 72 years, how much is spent asleep?

Step 1: 1/3 of 72 = 72 ÷ 3 = 24

✔ 24 years

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Problem 3b:
Baby sleeps:
- First month: 15 hours/day
- Next two months: 16 hours/day
Total time: 3 months = 3 × 4 weeks = 12 weeks = 84 days (since 1 week = 7 days → 12 × 7 = 84)

But let’s calculate total sleep hours and total possible hours.

First month: 30 days? Wait — problem says “1 month is equivalent to 4 weeks” → so 1 month = 28 days.

So:
- Month 1: 28 days × 15 hours = 420 hours
- Months 2 & 3: 2 × 28 = 56 days × 16 hours = 896 hours

Total sleep hours = 420 + 896 = 1316 hours

Total hours in 3 months: 3 × 28 days × 24 hours = 84 × 24 = 2016 hours

Fraction asleep = 1316 / 2016

Simplify:

Divide numerator and denominator by 4:
1316 ÷ 4 = 329
2016 ÷ 4 = 504

Check if 329 and 504 have common factors.

329 ÷ 7 = 47 → 7×47=329
504 ÷ 7 = 72 → 7×72=504

So 329/504 = 47/72

✔ Fraction = 47/72

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Problem 3c:
Julian gets 2/7 less sleep than recommended 8 hours/day.

How much sleep does he lose each week?

Step 1: Daily loss = 2/7 of 8 hours = (2×8)/7 = 16/7 hours per day

Step 2: Weekly loss = 7 days × 16/7 = 16 hours

✔ He loses 16 hours per week.

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Final Answer:
1a. £33
1b. 3/11
1c. £65
2a. 3 3/10 cm
2b. 61/120 cm²
3a. 24 years
3b. 47/72
3c. 16 hours