Adding, subtracting and multiplying fractions – Year 5 maths lesson to download as PDF

Example 1

Work out \(\frac{5}{6}\) + \(\frac{4}{6}\) and give the answer as a mixed number.

5 + 4 = 9, so the sum is \(\frac{9}{6}\). This is an improper fraction. 9 ÷ 6 = 1 remainder 3, so \(\frac{9}{6}\) = \(1\frac{3}{6}\) = \(1\frac{1}{2}\) after simplifying.

Example 2

Work out \(\frac{3}{4}\) + \(\frac{5}{8}\).

The common denominator is 8, because 4 goes into 8. \(\frac{3}{4}\) = \(\frac{6}{8}\). Now \(\frac{6}{8}\) + \(\frac{5}{8}\) = \(\frac{11}{8}\) = \(1\frac{3}{8}\).

Example 3

Work out \(\frac{5}{6}\) − \(\frac{1}{3}\).

The common denominator is 6, because 3 goes into 6. \(\frac{1}{3}\) = \(\frac{2}{6}\). Now \(\frac{5}{6}\) − \(\frac{2}{6}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\).

Example 4

Work out \(2\frac{3}{5}\) + \(1\frac{4}{5}\).

Whole numbers: 2 + 1 = 3. Fractions: \(\frac{3}{5}\) + \(\frac{4}{5}\) = \(\frac{7}{5}\) = \(1\frac{2}{5}\). Add: 3 + \(1\frac{2}{5}\) = \(4\frac{2}{5}\).

Example 5

Work out \(5\frac{1}{2}\) − \(2\frac{3}{4}\).

Write \(5\frac{1}{2}\) as \(5\frac{2}{4}\). The fraction \(\frac{2}{4}\) is smaller than \(\frac{3}{4}\), so borrow 1 from the 5: \(5\frac{2}{4}\) = \(4\frac{6}{4}\). Now \(4\frac{6}{4}\) − \(2\frac{3}{4}\) = 2 and \(\frac{3}{4}\) = \(2\frac{3}{4}\). Check: \(2\frac{3}{4}\) + \(2\frac{3}{4}\) = 5 and \(\frac{6}{4}\) = \(5\frac{1}{2}\). ✓

Example 6

Work out 4 × \(\frac{3}{8}\).

4 × 3 = 12, so the answer is \(\frac{12}{8}\). Divide top and bottom by 4: \(\frac{3}{2}\) = \(1\frac{1}{2}\).

Example 7

Work out 3 × \(2\frac{1}{4}\).

3 × 2 = 6. 3 × \(\frac{1}{4}\) = \(\frac{3}{4}\). Add: 6 + \(\frac{3}{4}\) = \(6\frac{3}{4}\).