Grade 5 · Unit 2: Fractions, decimals and percentages

Multiplying and dividing fractions

Half of a half, and how many quarters fit.

Vegetable plots are often parts of a bigger garden.

Parts of parts

A part of a part is a multiplication. ¾ of ½ means ¾ × ½. Drawings help us see the answer.

Multiplying fractions

Multiply the tops: 3 × 1 = 3. Multiply the bottoms: 4 × 2 = 8. ¾ × ½ = 3/8. Of means multiply.

Mixed numbers

Change 2½ to an improper fraction: 5/2. 5/2 × 3 = 15/2. Change back: 15/2 = 7½.

Dividing by a fraction

3 ÷ ¼ asks: how many quarters fit into 3? 12. Shortcut: dividing by a fraction is multiplying by its reciprocal: 3 × 4/1 = 12. ¾ ÷ ½ = ¾ × 2/1 = 6/4 = 1½.

Order of operations with fractions

Multiply before adding: ½ + ¼ × 2 = ½ + ½ = 1. With brackets: (½ + ¼) × 2 = ¾ × 2 = 1½. Simplify each answer to its simplest form.

What I learnt