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Year 7AC9M7N06

Multiplying and Dividing Fractions

Use the 4 operations with positive rational numbers including fractions, decimals and percentages to solve problems using efficient calculation strategies.

Multiplying fractions is easier than adding them — no common denominator needed. Dividing is the same job with one extra move at the start.

Builds onYr 7 · Adding and Subtracting Fractions

Method

To multiply, go straight across
ab×cd=a×cb×d\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}
No common denominator. This is the one time the bottoms do change.
To divide, flip the second fraction and multiply
ab÷cd=ab×dc\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}
Flip the second one only. Never the first.
‘Of’ means multiply
23 of 15=23×15\tfrac{2}{3} \text{ of } 15 = \tfrac{2}{3} \times 15
Whole numbers become fractions over 1.
Multiplying by a fraction under 1 makes it smaller
This surprises students. Half of a half is a quarter, not one.

Worked example

e.g. 34×25and34÷25\frac{3}{4} \times \frac{2}{5} \quad \text{and} \quad \frac{3}{4} \div \frac{2}{5}
  1. To multiply, cancel any common factors first to keep numbers small.34×25cancel 2 with 4\frac{3}{4} \times \frac{2}{5} \quad\text{cancel } 2 \text{ with } 4
  2. Multiply the tops.3×1=33 \times 1 = 3
  3. Multiply the bottoms.2×5=102 \times 5 = 10
  4. Write the answer.34×25=310\frac{3}{4} \times \frac{2}{5} = \frac{3}{10}
  5. Now to divide. Flip the second fraction.25 → 52\frac{2}{5} \ \rightarrow\ \frac{5}{2}
  6. Change the sign to multiply, then go across.34×52=158\frac{3}{4} \times \frac{5}{2} = \frac{15}{8}
  7. Write improper answers as mixed numbers if asked.158=178\frac{15}{8} = 1\frac{7}{8}

Practice

Cancel first where you can.

1
23×35\frac{2}{3} \times \frac{3}{5}
Answer25\frac{2}{5}
2
49×38\frac{4}{9} \times \frac{3}{8}
Answer16\frac{1}{6}
3
35 of 40\frac{3}{5} \text{ of } 40
Answer2424
4
12÷14\frac{1}{2} \div \frac{1}{4}
Answer12×41=2\frac{1}{2} \times \frac{4}{1} = 2
5
56÷23\frac{5}{6} \div \frac{2}{3}
Answer56×32=54=114\frac{5}{6} \times \frac{3}{2} = \frac{5}{4} = 1\frac{1}{4}
6
Why is 12÷14=2 and not 18?\text{Why is } \frac{1}{2} \div \frac{1}{4} = 2 \text{ and not } \frac{1}{8}?
AnswerYou are asking how many quarters fit into a half. Two do.\text{You are asking how many quarters fit into a half. Two do.}
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