FRACTIONS & PERCENTAGES Revision

What does “of” mean in maths?

👉 Multiply

How do you find a fraction of an amount?

Multiply the fraction by the number.

Work out: ⅔ of 9

⅔ × 9 = 6

What does increase by 25% mean?

Multiply by 1.25

Work out: 6 increased by 25%

6 × 1.25 = 7.5

What multiplier increases an amount by 50%?

👉 1.5

Do you need to convert decimals to fractions in GCSE maths?

❌ No
✔ Decimals are accepted

Convert 1.25 to a fraction.

1.25 = 5/4

How do you convert a decimal to a fraction?

Write it over 100, then simplify.

Why does 1.25 mean “increase by 25%”?

100% + 25% = 125%
125% = 1.25

What is an improper fraction?

A fraction where the top number is bigger than the bottom.
Example: 7/4

What is a mixed number?

A whole number and a fraction together.
Example: 1 ¾

Convert 7/4 to a mixed number.

7 ÷ 4 = 1 remainder 3
So: 1 ¾

Convert 1 ¾ to an improper fraction.

1 × 4 + 3 = 7
So: 7/4

Why do we convert mixed numbers to improper fractions?

To make multiplying and dividing easier.

How do you divide by a fraction?

👉 Multiply by the reciprocal

What is the reciprocal of a fraction?

Flip the fraction upside down.
Example: ⅔ → 3/2

Work out: 6 ÷ ⅔

6 × 3/2 = 18/2 = 9

Why does dividing by a fraction become multiplying?

Division by a fraction is the same as multiplying by its reciprocal.

GCSE fraction rule for division (one line)

Keep – Flip – Multiply