2
Review: multiplying and dividing fractions
Discover Mathematics P5: Term 2, Units 7–12, Review
GoalReview multiplying fractions and mixed numbers, and dividing with unit fractions and whole numbers.
New words
improper fraction · a fraction whose numerator is bigger than or equal to its denominatorproduct · the answer to a multiplicationunit fraction · a fraction with numerator 1, like 1/4
Explanation
To multiply fractions, multiply the numerators and multiply the denominators, then simplify: 2/3 × 3/4 = 6/12 = 1/2. For mixed numbers, first change each one into an improper fraction: 2 1/2 × 1 1/5 = 5/2 × 6/5 = 30/10 = 3. To divide a fraction by a whole number, make the denominator that many times bigger: 3/4 ÷ 3 = 3/12 = 1/4. To divide a whole number by a unit fraction, count how many of those pieces fit: 4 ÷ 1/2 = 8, because every whole has 2 halves and 4 × 2 = 8.
| Operation | Method | Answer |
|---|---|---|
| 2/3 × 3/4 | 6/12 | 1/2 |
| 2 1/2 × 1 1/5 | 5/2 × 6/5 | 3 |
| 3/4 ÷ 3 | 3/(4 × 3) | 1/4 |
| 4 ÷ 1/2 | 4 × 2 | 8 |
Worked examples
3/5 × 10 = 3/5 × 10/1 = 30/5 = 6.
1 1/3 × 2 1/4 = 4/3 × 9/4 = 36/12 = 3.
A ribbon is 3 1/2 m long. Mona cuts it into pieces of 1/2 m each. Each metre gives 2 pieces, so 3 m give 3 × 2 = 6 pieces, and the last 1/2 m gives 1 more: 7 pieces.
Class activity
Paper strips. Take a strip of paper as 1 whole. Fold it into quarters and shade 3 of them. Fold again to show 1/2 of 3/4 and check that 1/2 × 3/4 = 3/8. Then cut a strip of 2 wholes into halves and count how many halves there are.
Practice
1
5 ÷ 1/4 = ?
5 × 4 = 20.
2
2/3 ÷ 4 = ?
2/(3 × 4) = 2/12 = 1/6.
3
A garden is 2 1/2 m wide and 3 1/5 m long. Find its area.
5/2 × 16/5 = 80/10 = 8 square metres.
4
Youssef has 1/2 of a litre of juice and pours it equally into 4 cups. How much is in each cup?
1/2 ÷ 4 = 1/(2 × 4) = 1/8 litre.
5
3/8 of the 24 children in a class wear glasses. How many is that?
3/8 × 24 = 72/8 = 9 children.