Fractions

You already know about halves and quarters. In Key Stage 2 you go much further — working with any fraction, comparing them, adding and subtracting them, multiplying them, and converting between mixed numbers and improper fractions.

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Equivalent Fractions

Equivalent fractions have the same value, even though they look different.

1/2 = 2/4 = 3/6 = 4/8 = 5/10 ...

To find an equivalent fraction, multiply (or divide) both the numerator and denominator by the same number.

• 1/3 x 4/4 = 4/12 (multiply top and bottom by 4)
• 6/9 / 3/3 = 2/3 (divide top and bottom by 3 — this is called simplifying)

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Simplifying Fractions

A fraction is in its simplest form when the numerator and denominator share no common factor other than 1.

To simplify, divide both numbers by their highest common factor (HCF).

Example: Simplify 12/18

• HCF of 12 and 18 = 6.
• 12 / 6 = 2, and 18 / 6 = 3.
• Simplest form: 2/3

Example: Simplify 15/20

• HCF of 15 and 20 = 5.
• 15 / 5 = 3, and 20 / 5 = 4.
• Simplest form: 3/4

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