OCR GCSE Maths · OCR 2

Fractions, Decimals and Percentages

50 maths questions with worked answers with answers for OCR 2 Fractions, Decimals and Percentages in OCR GCSE Maths (spec J560). Practise with flashcards, a topic quiz, a random quiz across the course, 5 crosswords, or read every question and answer below.

All 50 questions and answers

Question 1 · Mixed numbers · OCR 2.01b
Calculate 213 + 134.
Answer:
Whole numbers: 2 + 1 = 3. Fractions: 13 + 34 = 412 + 912 = 1312 = 1112.
Total = 4112.
Question 2 · Fractions · OCR 2.01b
Calculate 56 ÷ 23.
Answer:
Multiply by the reciprocal: 56 × 32 = 1512.
Simplify: 54 = 114.
Question 3 · Fractions · OCR 2.01b
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 · OCR 2.01b
Write 114 as a mixed number.
Answer:
11 ÷ 4 = 2 remainder 3.
Therefore 114 = 2 34.
Question 5 · Fractions · OCR 2.01b
Write 2 25 as an improper fraction.
Answer:
Two wholes contain 10 fifths; add 2 fifths.
2 25 = 125.
Question 6 · Fraction of an amount · OCR 2.01c
Find 38 of 64.
Answer:
64 ÷ 8 = 8.
8 × 3 = 24.
Question 7 · Fractions · OCR 2.01c
Calculate 79 − 16.
Answer:
Common denominator 18: 1418 − 318.
1118.
Question 8 · Fractions to decimals · OCR 2.02a
Write 78 as a decimal.
Answer:
7 ÷ 8.
0.875.
Question 9 · Decimals to fractions · OCR 2.02a
Write 0.36 as a fraction in its simplest form.
Answer:
0.36 = 36100.
Divide by 4: 925.
Question 10 · Fractions to decimals · OCR 2.02a
Write 320 as a decimal and a percentage.
Answer:
320 = 15100.
0.15 = 15%.
Question 11 · Terminating decimals · OCR 2.02a
Does 740 give a terminating decimal? Explain.
Answer:
40 = 2³ × 5, which has only prime factors 2 and 5.
So yes, it terminates: 740 = 0.175.
Question 12 · Recurring decimals · OCR 2.02a · Higher only
Write 0.4̇ (0.444…) as a fraction.
Answer:
Let x = 0.444…, so 10x = 4.444….
Subtract: 9x = 4, so x = 49.
Question 13 · Ordering · OCR 2.02a
Which is larger, 47 or 0.57?
Answer:
47 = 0.5714….
47 is larger.
Question 14 · Converting · OCR 2.02a
Write 516 as a decimal.
Answer:
5 ÷ 16.
0.3125.
Question 15 · Written methods · OCR 2.02b
Calculate 3.6 × 0.4.
Answer:
36 × 4 = 144.
There are two decimal places in total, so 3.6 × 0.4 = 1.44.
Question 16 · Written methods · OCR 2.02b
Calculate 7.2 ÷ 0.08.
Answer:
Multiply both numbers by 100: 720 ÷ 8.
720 ÷ 8 = 90.
Question 17 · Addition · OCR 2.02b
Calculate 27 + 37.
Answer:
The denominators already match.
Add the numerators: 27 + 37 = 57.
Question 18 · Subtraction · OCR 2.02b
Calculate 56 − 14.
Answer:
Use denominator 12: 56 = 1012 and 14 = 312.
1012 − 312 = 712.
Question 19 · Division · OCR 2.02c
Calculate 35 ÷ 910.
Answer:
Divide by a fraction by multiplying by its reciprocal.
35 × 109 = 3045 = 23.
Question 20 · Percentages · OCR 2.03a
Write £18 as a percentage of £240.
Answer:
18240 × 100.
7.5%.
Question 21 · Percentages · OCR 2.03a
A school has 1200 pupils; 45% are boys. How many girls are there?
Answer:
55% are girls.
0.55 × 1200 = 660.
Question 22 · Percentages · OCR 2.03a
Increase £80 by 12.5%.
Answer:
12.5% = 18; 18 of £80 is £10.
£80 + £10 = £90.
Question 23 · Percentages · OCR 2.03a
Decrease 500 by 18%.
Answer:
An 18% decrease leaves 82%.
500 × 0.82 = 410.
Question 24 · Percentages · OCR 2.03a
A value changes from 80 to 100. Find the percentage increase.
Answer:
Increase = 100 − 80 = 20.
Percentage increase = 2080 × 100% = 25%.
Question 25 · Percentages · OCR 2.03a
After a 20% discount an item costs £48. Find the original price.
Answer:
A 20% discount leaves 80% of the original price.
Original price = £48 ÷ 0.80 = £60.
Question 26 · Error check · OCR 2.03a
A student says increasing then decreasing a price by 10% restores the original price. Is this true?
Answer:
Increase multiplier = 1.10; decrease multiplier = 0.90.
1.10 × 0.90 = 0.99, so the final price is 1% lower.
The statement is false.
Question 27 · Fractions · OCR 2.03b
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 28 · Multipliers · OCR 2.03b
What single multiplier increases an amount by 7.5%?
Answer:
100% + 7.5% = 107.5%.
1.075.
Question 29 · VAT · OCR 2.03b
A TV costs £350 before VAT at 20%. Find the price including VAT.
Answer:
350 × 1.2.
£420.
Question 30 · Reverse percentages · OCR 2.03b
After a 20% increase a coat costs £66. What was the original price?
Answer:
£66 is 120% of the original.
66 ÷ 1.2 = £55.
Question 31 · Reverse percentages · OCR 2.03b
After a 30% reduction a bike costs £245. Find the original price.
Answer:
£245 is 70% of the original.
245 ÷ 0.7 = £350.
Question 32 · Simple interest · OCR 2.03b
£800 is invested at 3% simple interest per year. Find the interest after 4 years.
Answer:
Interest per year = 800 × 0.03 = £24.
4 × 24 = £96.
Question 33 · Compound interest · OCR 2.03b
£2000 is invested at 5% compound interest per year. Find its value after 2 years.
Answer:
2000 × 1.05² = 2000 × 1.1025.
£2205.
Question 34 · Percentage of an amount · OCR 2.03b
Find 35% of 260.
Answer:
10% = 26, so 30% = 78 and 5% = 13.
78 + 13 = 91.
Question 35 · Percentage increase · OCR 2.03b
Increase 450 by 12%.
Answer:
Multiplier = 1.12.
450 × 1.12 = 504.
Question 36 · Percentage decrease · OCR 2.03b
Decrease 80 by 15%.
Answer:
Multiplier = 0.85.
80 × 0.85 = 68.
Question 37 · Percentages · OCR 2.03b
What percentage of 80 is 28?
Answer:
2880 × 100.
35%.
Question 38 · Percentages · OCR 2.03b
Write 0.035 as a percentage.
Answer:
Multiply by 100.
3.5%.
Question 39 · Percentage profit · OCR 2.03b
A trader buys a lamp for £25 and sells it for £32. Find the percentage profit.
Answer:
Profit = £7.
725 × 100 = 28%.
Question 40 · Percentage of an amount · OCR 2.03b
Find 2.5% of 640.
Answer:
1% = 6.4.
2.5 × 6.4 = 16.
Question 41 · Percentage change · OCR 2.03c
A price rises from £40 to £46. Find the percentage increase.
Answer:
Increase = £6.
640 × 100 = 15%.
Question 42 · Percentage change · OCR 2.03c
A car's value falls from £12 000 to £9 000. Find the percentage decrease.
Answer:
Decrease = £3 000.
300012000 × 100 = 25%.
Question 43 · Repeated change · OCR 2.03c · Higher only
A population of 5000 falls by 10% each year. Find the population after 3 years.
Answer:
5000 × 0.9³ = 5000 × 0.729.
3645.
Question 44 · Ordering · OCR 2.04a
Write these in order from smallest: 0.6, 58, 0.59, 23.
Answer:
Convert to decimals: 58 = 0.625 and 23 = 0.666…
Order: 0.59, 0.6, 58, 23.
Question 45 · Ordering · OCR 2.04a
Order from smallest: −3.2, −3.02, −3.5, −3.25.
Answer:
The most negative number is smallest.
−3.5, −3.25, −3.2, −3.02.
Question 46 · Order · OCR 2.04a
Put −7, 4, −2 and 0 in ascending order.
Answer:
Ascending means smallest first.
On a number line, −7 < −2 < 0 < 4.
Answer: −7, −2, 0, 4.
Question 47 · Order · OCR 2.04a
Which is greater: −0.3 or −0.35?
Answer:
Write −0.3 as −0.30.
−0.30 > −0.35, so −0.3 is greater.
Question 48 · Order · OCR 2.04a
Insert < or >: −6 __ −9.
Answer:
−6 is closer to zero and lies to the right of −9.
Therefore −6 > −9.
Question 49 · Inequality symbols · OCR 2.04b
Insert < or > between −7 and −4.
Answer:
−7 is further below zero than −4.
−7 < −4.
Question 50 · Inequality symbols · OCR 2.04b
What does the symbol ≠ mean?
Answer:
It means "is not equal to".
For example, 3 + 4 ≠ 8.

← OCR 1 Number Operations and Integers OCR 3 Indices and Surds →

Fractions, Decimals and Percentages

All 50 questions and answers

More OCR GCSE Maths topics

Cookies on Knowledge Noodles

Cookie settings