OCR GCSE Mathematics: Percentages and ordering fractions, decimals and percentages (J560)

This guide teaches sections 2.03 and 2.04 of the OCR GCSE (9-1) Mathematics (J560) specification, Version 2.1 (August 2026): percentages, percentage change and simple interest, and ordering fractions, decimals and percentages. All of it is Foundation and Higher tier content, and none of it is Higher tier only. The specification lists a Paper 2 (Foundation) and a Paper 5 (Higher) where a calculator is not permitted, so the by-hand methods below matter. Pair it with the revision notes and the practice questions. For wider fraction work see the fractions, decimals and percentages overview. The OCR GCSE Mathematics hub and the printable checklist show the rest of the course, and the free diagnostics help you find weak spots first.

What this unit covers

Ref	What you must be able to do	Tier
2.03a	Convert between fractions, decimals and percentages	Both
2.03b	Know a percentage is parts per hundred; find a percentage of a quantity; write one quantity as a percentage of another	Both
2.03c	Increase or decrease by a percentage using decimal or fractional multipliers; percentage change; original-value problems; simple interest	Both
2.04a	Order integers, fractions, decimals and percentages	Both
2.04b	Use the symbols <, >, ≤, ≥, =, ≠	Both

Compound interest and growth and decay sit in section 5.03a, so they are not taught here.

2.03a Converting between forms

“Percent” means “out of 100”. So 35% means 35 parts per hundred, which is 35/100 and 0.35. Every conversion moves between those three forms.

From	To	Method
Percentage	Decimal	Divide by 100
Decimal	Percentage	Multiply by 100
Percentage	Fraction	Write over 100 and simplify
Fraction	Decimal	Divide the numerator by the denominator
Fraction	Percentage	Convert to a decimal, then multiply by 100

Worked example 1. Write 7/20, 3/8 and 1¾ as percentages.

7/20 = 0.35         → 35%
3/8  = 3 ÷ 8 = 0.375 → 37.5%
1¾   = 1.75         → 175%

A fraction with denominator 20 scales to hundredths: 7/20 = 35/100. A value above 1 gives a percentage above 100%.

Worked example 2. Write 45% as a fraction in its simplest form, and 0.4% as a decimal.

45% = 45/100 = 9/20      (divide top and bottom by 5)
0.4% = 0.4 ÷ 100 = 0.004

Keep the decimal point moving two places each time. A small percentage such as 0.4% is far smaller than 0.4.

2.03b Percentage of a quantity

To find a percentage of a quantity without a calculator, build it from 10%, 5% and 1%.

Worked example 3. Find 15% of £84.

10% of 84 = 8.40
 5% of 84 = 4.20   (half of 10%)
15% of 84 = 8.40 + 4.20 = £12.60

Worked example 4. Find 7% of 350 kg.

1% of 350 = 3.5
7% of 350 = 7 × 3.5 = 24.5 kg

With a calculator, multiply by the decimal: 15% of 84 is 0.15 × 84.

One quantity as a percentage of another

Write a fraction “part over whole”, then multiply by 100. Both quantities need the same units.

Worked example 5. A film lasts 2 hours. Mia watches 45 minutes. What percentage is that?

2 hours = 120 minutes
45/120 × 100 = 37.5%

The whole is the quantity after “of”. Here it is 120 minutes, so 120 goes underneath.

2.03c Increase and decrease with multipliers

Adding 10% to a price keeps 100% and adds 10%, giving 110%. As a decimal that is 1.1, or 110/100. Multiplying by 1.1 does the whole job in one step.

Change	Percentage kept	Multiplier
Increase by 8%	108%	1.08
Decrease by 18%	82%	0.82
Increase by 1/5	6/5	6/5 or 1.2
Decrease by 3/8	5/8	5/8 or 0.625

Increase multipliers are greater than 1. Decrease multipliers are less than 1.

Worked example 6. A coat costs £720. It is reduced by 18%. Find the sale price.

multiplier = 1 − 0.18 = 0.82
720 × 0.82 = £590.40

By hand, you can find 18% as 10% + 5% + 3%, then subtract: 72 + 36 + 21.60 = 129.60, and 720 − 129.60 = 590.40. Both routes agree.

Worked example 7. A mass of 35 kg is increased by 1/5. Find the new mass.

multiplier = 1 + 1/5 = 6/5
35 × 6/5 = 42 kg

Percentage change

Percentage change compares the change with the original value.

percentage change = (new − original) ÷ original × 100

Worked example 8. A bus fare rises from £48 to £60. Find the percentage increase.

change = 60 − 48 = 12
12/48 × 100 = 25% increase

The multiplier route gives the same result: 60 ÷ 48 = 1.25, which is a 25% increase.

Worked example 9. The price of a bag falls from £80 to £68.

change = 68 − 80 = −12
−12/80 × 100 = −15%

State the direction: a 15% decrease.

Original-value (reverse percentage) problems

Here you know the value after a change and must work back to the start. Treat the original as 100%, find the percentage the new value represents, and divide by the multiplier.

Worked example 10. After a 20% rise, a gym fee is £90. Find the original fee.

new = 120% of original → multiplier 1.2
original = 90 ÷ 1.2 = £75

Worked example 11. A population of 2,800 is 1.4 times last year’s. Find last year’s population.

2800 ÷ 1.4 = 2000

Check by going forwards. £75 × 1.2 = £90. Always do this check. Taking 20% off £90 gives £72, which is not £75, so that tempting shortcut is wrong.

Simple interest

Simple interest is a fixed sum added each year, always calculated on the original deposit.

interest per year = amount × rate ÷ 100
total interest = interest per year × number of years

Worked example 12. Find the simple interest on £1,500 at 3% per year for 4 years, and the total amount.

per year: 1500 × 3/100 = £45
4 years: 4 × 45 = £180
total = 1500 + 180 = £1,680

Worked example 13. £800 earns £96 simple interest in 3 years. Find the yearly rate.

per year = 96 ÷ 3 = £32
rate = 32/800 × 100 = 4%

2.04a Ordering fractions, decimals and percentages

Convert everything to one form, usually decimals. Then compare digit by digit after writing the same number of decimal places. Finally, write the answer in the original forms.

Worked example 14. Put 13/20, 0.66, 64%, 2/3 and −0.7 in order, smallest first.

13/20 = 0.65
0.66  = 0.66
64%   = 0.64
2/3   = 0.6667 (to 4 d.p.)
−0.7  = −0.70

Negatives are smaller than positives, so −0.7 is first. Then 0.64 < 0.65 < 0.66 < 0.6667.

Answer: −0.7, 64%, 13/20, 0.66, 2/3.

When fractions are compared directly, use a common denominator. For 3/4, 5/7 and 7/10, use 140:

3/4 = 105/140    5/7 = 100/140    7/10 = 98/140

Smallest first: 7/10, 5/7, 3/4.

For negatives, a larger digit means a smaller number. So −2.5 is smaller than −2.05.

2.04b Inequality symbols

Symbol	Meaning
<	is less than
>	is greater than
≤	is less than or equal to
≥	is greater than or equal to
=	is equal to
≠	is not equal to

The small end of < and > points at the smaller number.

Worked example 15. Insert a symbol.

3/8 ... 0.4      3/8 = 0.375, so 3/8 < 0.4
45% ... 9/20     both are 0.45, so 45% = 9/20
−2.5 ... −2.05   −2.5 is further below zero, so −2.5 < −2.05

Worked example 16. List the integers n with −2 ≤ n < 3.

The ≤ includes −2. The < excludes 3. So n is −2, −1, 0, 1, 2.

Common errors

• Writing 0.4% as 0.4 or 40%. Divide by 100 to get 0.004.
• Using the wrong whole in “a as a percentage of b”. The whole goes underneath.
• Using 0.18 as the multiplier for an 18% decrease. That finds 18% of the amount, not the new price.
• Working backwards by subtracting the percentage from the final figure. The correct step is to divide the final figure by its multiplier.
• Treating 20% off and 20% on as cancelling. The second change works on a different amount.
• Comparing 0.5 with 0.45 by thinking 45 is bigger than 5. Pad both to two decimal places first.
• Ordering negatives as if the larger digit were larger.

A mixed example

A shop buys a chair for £60 and sells it for £81. Find the percentage profit, then find the sale price if the chair is later reduced by 20% from £81.

profit = 81 − 60 = £21
percentage profit = 21/60 × 100 = 35%
reduced price = 81 × 0.8 = £64.80

The profit is compared with the buying price, because that is the original value. The reduction is compared with the selling price, because that is the value being changed. Always ask which amount the percentage belongs to before you divide or multiply.

Exam skills

Write the multiplier you use, as this shows your method even if the arithmetic slips. Give money to two decimal places. Write “increase” or “decrease” after a percentage change. In a “show that” question, show every step.

Official syllabus

OCR GCSE (9-1) Mathematics (J560), Version 2.1 (August 2026), first assessment 2017, published by OCR. Sections 2.03a-2.03c and 2.04a-2.04b.