AQA GCSE Maths · 3.1.2

Fractions, decimals and percentages

50 maths questions with worked answers with answers for 3.1.2 Fractions, decimals and percentages in AQA GCSE Maths (spec 8300). Practise with flashcards, a topic quiz, a random quiz across the course, 5 crosswords, or read every question and answer below. Not official AQA material.

All 50 questions and answers

Question 1 · Fractions · N10
Write 0.75 as a fraction in simplest form.
Answer:
0.75 = 75100.
Divide numerator and denominator by 25: 34.
Question 2 · Fractions · N10
Write 720 as a decimal.
Answer:
Multiply numerator and denominator by 5: 720 = 35100.
35100 = 0.35.
Question 3 · Fractions · N10
Write 1.375 as a mixed number in simplest form.
Answer:
1.375 = 1 + 3751000.
3751000 = 38, so the mixed number is 1 38.
Question 4 · Fractions · N10
Write 114 as a mixed number.
Answer:
11 ÷ 4 = 2 remainder 3.
Therefore 114 = 2 34.
Question 5 · Fractions · N10
Write 2 25 as an improper fraction.
Answer:
Two wholes contain 10 fifths; add 2 fifths.
2 25 = 125.
Question 6 · Fractions · N10
Put 0.6, 58 and 58% in ascending order.
Answer:
Convert to decimals: 58% = 0.58, 0.6 = 0.60 and 58 = 0.625.
Smallest first: 58%, 0.6, 58.
Question 7 · Equivalent fractions · N10
Simplify 1824.
Answer:
Divide numerator and denominator by 6.
1824 = 34.
Question 8 · Equivalent fractions · N10
Find the missing numerator: 35 = □40.
Answer:
5 × 8 = 40, so multiply the numerator by 8 as well.
3 × 8 = 24.
Question 9 · Addition · N2
Calculate 27 + 37.
Answer:
The denominators already match.
Add the numerators: 27 + 37 = 57.
Question 10 · Addition · N2
Calculate 13 + 14.
Answer:
Use denominator 12: 13 = 412 and 14 = 312.
412 + 312 = 712.
Question 11 · Subtraction · N2
Calculate 56 − 14.
Answer:
Use denominator 12: 56 = 1012 and 14 = 312.
1012 − 312 = 712.
Question 12 · Subtraction · N2
Calculate 2 − 35.
Answer:
Write 2 as 105.
105 − 35 = 75 = 1 25.
Question 13 · Multiplication · N2
Calculate 34 × 25.
Answer:
Multiply numerators and denominators: 34 × 25 = 620.
Simplify 620 = 310.
Question 14 · Multiplication · N12
Find 23 of 45.
Answer:
One third of 45 is 15.
Two thirds is 2 × 15 = 30.
Question 15 · Division · N2
Calculate 35 ÷ 910.
Answer:
Divide by a fraction by multiplying by its reciprocal.
35 × 109 = 3045 = 23.
Question 16 · Division · N2
Calculate 1 12 ÷ 34.
Answer:
Change the mixed number: 1 12 = 32.
32 ÷ 34 = 32 × 43 = 2.
Question 17 · Percentages · N12
Calculate 15% of £80.
Answer:
10% of £80 is £8; 5% is £4.
15% is £8 + £4 = £12.
Question 18 · Percentages · N12
Calculate 40% of 65.
Answer:
10% of 65 is 6.5.
40% = 4 × 6.5 = 26.
Question 19 · Percentages · N12
What is 20% off £50?
Answer:
20% of £50 = 0.20 × £50 = £10.
Sale price = £50 − £10 = £40.
Question 20 · Percentages · N12
What is 20% of £50?
Answer:
Convert 20% to 0.20.
0.20 × £50 = £10.
Question 21 · Percentages · N12
Increase 240 by 15%.
Answer:
An increase of 15% gives 115% of the original.
240 × 1.15 = 276.
Question 22 · Percentages · N12
Decrease 360 by 25%.
Answer:
A decrease of 25% leaves 75%.
360 × 0.75 = 270.
Question 23 · Percentages · N12
What multiplier increases an amount by 8%?
Answer:
An increase of 8% gives 100% + 8% = 108%.
108% as a decimal is 1.08.
Question 24 · Percentages · N12
What multiplier decreases an amount by 13%?
Answer:
A decrease of 13% leaves 100% − 13% = 87%.
87% as a decimal is 0.87.
Question 25 · Percentages · N12
A price rises from £60 to £75. Find the percentage increase.
Answer:
Increase = £75 − £60 = £15.
Percentage increase = 1560 × 100% = 25%.
Question 26 · Percentages · N12
A price falls from £90 to £72. Find the percentage decrease.
Answer:
Decrease = £90 − £72 = £18.
Percentage decrease = 1890 × 100% = 20%.
Question 27 · Percentages · N12
A jacket costs £84 after a 30% discount. Find its original price.
Answer:
After a 30% discount, 70% of the price is £84.
Original price = £84 ÷ 0.70 = £120.
Question 28 · Percentages · N12
After a 20% increase a value is 96. What was the original value?
Answer:
After a 20% increase, the new value is 120% of the original.
Original = 96 ÷ 1.20 = 80.
Question 29 · Ratio and fractions · N11
Red and blue beads are in the ratio 3:5. What fraction are red?
Answer:
Total parts = 3 + 5 = 8.
Red makes up 3 of the 8 parts: 38.
Question 30 · Ratio and fractions · N11
There are 4 red and 6 green counters. What fraction are green?
Answer:
Total counters = 4 + 6 = 10.
Green fraction = 610 = 35.
Question 31 · Ratio and fractions · N11
In a group the ratio of adults to children is 2:3. What fraction are children?
Answer:
Total parts = 2 + 3 = 5.
Children make up 3 parts, so the fraction is 35.
Question 32 · Ratio and fractions · N11
A class has 12 girls and 18 boys. Express girls as a fraction of boys.
Answer:
Girls as a fraction of boys = 1218.
Divide by 6 to get 23.
Question 33 · Proportions · N12
A jar is 38 full. What fraction is empty?
Answer:
A full jar is 88.
Empty fraction = 88 − 38 = 58.
Question 34 · Proportions · N12
Three-fifths of a group of 35 travel by bus. How many do not travel by bus?
Answer:
The fraction not travelling by bus is 1 − 35 = 25.
25 × 35 = 14 people.
Question 35 · Percentages · N12
Express 18 out of 24 as a percentage.
Answer:
1824 = 34 = 0.75.
0.75 × 100% = 75%.
Question 36 · Percentages · N12
Express 0.045 as a percentage.
Answer:
Multiply the decimal by 100 to convert to a percentage.
0.045 × 100% = 4.5%.
Question 37 · Percentages · N12
Write 32% as a fraction in simplest form.
Answer:
32% = 32100.
Divide numerator and denominator by 4: 825.
Question 38 · Percentages · R16
A salary of £400 is increased by 5%, then by a further 10%. Find the new salary.
Answer:
First increase: £400 × 1.05 = £420.
Second increase: £420 × 1.10 = £462.
Question 39 · Percentages · R16
A value is reduced by 10% twice. What single percentage decrease is this?
Answer:
Two decreases give a multiplier of 0.9 × 0.9 = 0.81.
81% remains, so the decrease is 19%.
Question 40 · Recurring decimals · N10 · Higher only
Express 0.333... as a fraction.
Answer:
Let x = 0.333...; then 10x = 3.333....
Subtract: 9x = 3, so x = 13.
Question 41 · Recurring decimals · N10 · Higher only
Express 0.777... as a fraction.
Answer:
Let x = 0.777...; then 10x = 7.777....
Subtract: 9x = 7, so x = 79.
Question 42 · Recurring decimals · N10 · Higher only
Express 0.121212... as a fraction in simplest form.
Answer:
Let x = 0.121212...; then 100x = 12.121212....
Subtract: 99x = 12.
x = 1299 = 433.
Question 43 · Recurring decimals · N10 · Higher only
Express 0.1666... as a fraction.
Answer:
Let x = 0.1666.... Then 10x = 1.666... and 100x = 16.666....
Subtract: 90x = 15, so x = 1590 = 16.
Question 44 · Recurring decimals · N10 · Higher only
Write 29 as a recurring decimal.
Answer:
Divide 2 by 9: the quotient is 0.222... .
The digit 2 continues to repeat.
Question 45 · Fraction problems · N12
A tank contains 34 of its 120-litre capacity. How many litres does it contain?
Answer:
One quarter of 120 litres is 30 litres.
Three quarters = 3 × 30 = 90 litres.
Question 46 · Fraction problems · N12
A recipe uses 23 of a 300 g bag of flour. How much flour remains?
Answer:
The remaining fraction is 1 − 23 = 13.
13 × 300 g = 100 g.
Question 47 · Fraction problems · N2
Calculate 49 + 56.
Answer:
Use denominator 18: 49 = 818 and 56 = 1518.
818 + 1518 = 2318 = 1 518.
Question 48 · Fraction problems · N2
Calculate 78 − 23.
Answer:
Use denominator 24: 78 = 2124 and 23 = 1624.
2124 − 1624 = 524.
Question 49 · Fraction problems · N12
A book costs £24. A voucher reduces it by one quarter. Find the sale price.
Answer:
One quarter of £24 is £6.
Sale price = £24 − £6 = £18.
Question 50 · Error check · N2
A student says 13 + 14 = 27. Correct the calculation.
Answer:
Use denominator 12: 13 = 412 and 14 = 312.
412 + 312 = 712, not 27.

← 3.1.1 Structure and calculation 3.1.3 Measures and accuracy →

Fractions, decimals and percentages

All 50 questions and answers

More AQA GCSE Maths topics

Cookies on Knowledge Noodles

Cookie settings