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

These notes condense sections 2.03 and 2.04 of the OCR GCSE (9-1) Mathematics (J560) specification, Version 2.1 (August 2026). Everything here is Foundation and Higher tier content; nothing in this unit is Higher tier only. Read the full study guide for explanations, then test yourself with the practice questions. Course links: the OCR GCSE Mathematics hub, the printable checklist, the fractions, decimals and percentages overview and the free diagnostics.

Key facts

Idea	Rule
Percent	“parts per hundred”: 1% = 1/100 = 0.01
Percentage to decimal	Divide by 100
Decimal to percentage	Multiply by 100
Fraction to decimal	Numerator ÷ denominator
Part as a percentage of whole	part/whole × 100, same units
Increase by r%	Multiply by 1 + r/100
Decrease by r%	Multiply by 1 − r/100
Percentage change	(new − original)/original × 100
Original value	New value ÷ multiplier
Simple interest	Same amount each year, on the original sum

2.03a Conversion table to learn

Percentage	As a decimal	As a fraction
20%	0.2	1/5
12.5%	0.125	1/8
75%	0.75	3/4
33.3…%	0.333…	1/3
50%	0.5	1/2
150%	1.5	1 1/2
25%	0.25	1/4

Method for any fraction: divide, then multiply by 100.

17/40 = 0.425 → 42.5%
0.07 = 7/100 → 7%

2.03b Percentage of a quantity

Build the answer from 10%, 5% and 1%.

24% of 150:
10% = 15, so 20% = 30
 1% = 1.5, so 4% = 6
24% = 30 + 6 = 36

One quantity as a percentage of another:

30 of 120 → 30/120 × 100 = 25%

Steps in order:

1. Put both amounts in the same unit.
2. Write part over whole.
3. Multiply by 100.

2.03c Multipliers

Change	Multiplier
+5%	1.05
+30%	1.3
+150%	2.5
−6%	0.94
−12%	0.88
+1/4	5/4
−2/5	3/5

Fractional multipliers work the same way as decimal ones. A multiplier of 110/100 is the same as 1.1.

Increase £200 by 6%:  200 × 1.06 = £212
Decrease 60 kg by 15%: 60 × 0.85 = 51 kg

Percentage change in steps

1. Work out the change: new − original.
2. Divide by the original.
3. Multiply by 100.
4. Write “increase” or “decrease”.

150 → 135: change −15; −15/150 × 100 = −10%, a 10% decrease

Original value in steps

1. Write the multiplier for the change.
2. Divide the new value by it.
3. Check by multiplying forwards.

After a 12% decrease a price is £74.80.
multiplier 0.88; original = 74.80 ÷ 0.88 = £85
Check: 85 × 0.88 = £74.80

Simple interest in steps

1. Interest per year = amount × rate ÷ 100.
2. Multiply by the number of years.
3. Add to the starting amount if the question asks for the total.

£600 at 4% for 3 years:
per year = £24; 3 years = £72; total = £672

To find a missing rate or time, work backwards: total interest ÷ years gives interest per year, and that divided by the amount, times 100, gives the rate.

2.04a Ordering

1. Convert every value to a decimal.
2. Pad to the same number of decimal places.
3. Put negatives first, the most negative being the smallest.
4. Write the answer in the original forms.

0.4, 3/8, 38%, −1/2
0.400, 0.375, 0.380, −0.500
Smallest first: −1/2, 3/8, 38%, 0.4

For fractions only, a common denominator is a quick alternative: 2/3 and 5/8 become 16/24 and 15/24, so 2/3 is larger.

2.04b Symbols

Symbol	Read as	Does it include the end value?
<	less than	No
>	greater than	No
≤	less than or equal to	Yes
≥	greater than or equal to	Yes
=	equal to	Not applicable
≠	not equal to	Not applicable

List integers n with −1 < n ≤ 3:  0, 1, 2, 3

Worked reminders

Fraction and decimal to percentage in both directions. 0.35 = 35/100 = 7/20. In reverse, 5/8 = 0.625 = 62.5%.

Fractional multiplier. A £36 ticket is reduced by 1/4. The multiplier is 3/4, so 36 × 3/4 = £27.

Original value with a fraction. A length is increased by 1/4 and is now 45 cm. The multiplier is 5/4, so the original is 45 ÷ 5/4 = 45 × 4/5 = 36 cm.

Percentages above 100. 130% of 40 is 1.3 × 40 = 52. A multiplier above 1 always gives a larger result.

Two changes in a row. Increase by 25%, then decrease by 20%: 1.25 × 0.8 = 1. The end value equals the start value, so the overall change is 0%. Equal percentages up and down do not cancel, but these two do, because 5/4 × 4/5 = 1.

Missing time in simple interest. £500 earns £60 at 2% per year. Interest per year is 500 × 2/100 = £10, so the time is 60 ÷ 10 = 6 years.

Percentage profit. An item bought for £40 is sold for £56. The profit is £16, so the percentage profit is 16/40 × 100 = 40%. Equivalently, 56 ÷ 40 = 1.4, a 40% increase.

Shortcut check. To check an answer to a 12.5% question, divide by 8. To check 75%, find 25% and multiply by 3.

Shortcut percentages

Some percentages are quick to find by dividing. Learn these before the exam, using 96 as the quantity.

Percentage	Same as	Of 96
50%	÷ 2	48
25%	÷ 4	24
20%	÷ 5	19.2
12.5%	÷ 8	12
10%	÷ 10	9.6
1%	÷ 100	0.96

Thirds do not give exact decimals. 1/3 is 0.333… and 33.3…%, and 2/3 is 0.666… and 66.6…%. Write the recurring digits or round sensibly, and say which you have done.

Choosing a method

If the question says	Use
“Find x% of”	Multiply by x/100, or build from 10%, 5%, 1%
“What percentage is a of b”	a/b × 100
“Increase” or “decrease by x%”	Multiply by 1 + x/100 or 1 − x/100
“Percentage profit”, “percentage rise”	Change ÷ original × 100
“Before the sale”, “original price”	Divide by the multiplier
“Simple interest”	Amount × rate ÷ 100, times years
“Put in order”	Convert to decimals and compare

Paper facts

The specification shows Paper 2 on Foundation tier and Paper 5 on Higher tier as papers where a calculator is not permitted. Practise the 10%, 5% and 1% route, simple fractions to percentages, and decimal comparisons by hand. On any paper, write the multiplier or fraction you use, so your method is visible.

Must-know distinctions

• Percentage of a quantity gives an amount. Percentage change gives a rate.
• Increase by 20% (multiply by 1.2) is different from “20% of” (multiply by 0.2).
• Percentage change divides by the original. A reverse percentage divides by the multiplier.
• Simple interest adds a fixed sum each year. Compound interest changes, and is taught under section 5.03a.
• Fraction answers stay as fractions in the original forms when ordering.

Quick self-test

1. Write 17/40 as a percentage.
2. Write 0.07 as a fraction and as a percentage.
3. Find 24% of 150 without a calculator.
4. Write 30 out of 120 as a percentage.
5. Give the multiplier for a 6% increase, and increase £200 by 6%.
6. Give the multiplier for a 12% decrease.
7. A value goes from 150 to 135. Find the percentage change.
8. After a 12% decrease a price is £74.80. Find the original price.
9. Find the simple interest on £600 at 4% per year for 3 years.
10. Order 0.4, 3/8, 38% and −1/2, smallest first.
11. Insert a symbol: 1/8 … 12%.
12. List the integers n with −1 < n ≤ 3.

Answers

1. 42.5%
2. 7/100 and 7%
3. 36
4. 25%
5. 1.06; £212
6. 0.88
7. 10% decrease
8. £85
9. £72
10. −1/2, 3/8, 38%, 0.4
11. 1/8 = 0.125, so 1/8 > 12%
12. 0, 1, 2, 3

Where marks are usually lost

• Choosing the final figure as the divisor in a percentage change, when the starting figure is needed.
• Writing 0.12 as the multiplier for a 12% decrease, when it should be 0.88.
• Multiplying, not dividing, in an original-value question.
• Leaving money as £74.8 instead of £74.80.
• Writing “15%” with no word for increase or decrease when the question asks for the change.
• Mixing minutes and hours in a percentage of another quantity.
• Calling 0.4% equal to 0.4.
• Putting −0.5 above −0.3 in an ordering question.
• Reading ≤ as strictly less than and leaving out an end value.
• Giving rounded decimals in an ordering answer instead of the original forms.
• Dropping working in a multi-step question, so a slip in the arithmetic leaves nothing to credit.
• Forgetting the units of the answer, such as £, kg or years.

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.