Discover Mathematics P5: Term 2, Unit 9, Lessons 9–13
GoalDivide a unit fraction by a whole number with a model, and see the link with multiplication.
New words
unit fraction · a fraction with 1 on top, such as 1/2 or 1/5equal parts · pieces that are exactly the same sizereciprocal · a number turned upside down: the reciprocal of 3 is 1/3
Explanation
To divide a unit fraction by a whole number, cut the fraction into that many equal parts. Take 1/2 and share it among 3. Cut every half into 3 equal pieces. Then the whole has 2 × 3 = 6 equal pieces, and each piece is 1/6. So 1/2 ÷ 3 = 1/6. In the same way 1/2 ÷ 4 = 1/8 and 1/4 ÷ 3 = 1/12. The rule is: keep the 1 on top and multiply the denominator by the whole number, 1/b ÷ n = 1/(b × n). This is the same as multiplying by 1/n, because dividing by 3 is the same as taking 1/3 of it: 1/2 ÷ 3 = 1/2 × 1/3 = 1/6. Check by multiplying back: 3 × 1/6 = 3/6 = 1/2.
Worked examples
Dina has 1/2 kg of cheese and shares it equally among 3 sandwiches. 1/2 ÷ 3 = 1/6, so each sandwich gets 1/6 kg. The bars show that 3 of the small pieces fill the half.
Work out 1/4 ÷ 3. Cut each quarter into 3 equal pieces. The whole now has 4 × 3 = 12 pieces, so 1/4 ÷ 3 = 1/12. As a multiplication: 1/4 × 1/3 = 1/12.
A path is 1/5 km long. Four friends clean it, each the same length. 1/5 ÷ 4 = 1/20, so each cleans 1/20 km. Check: 4 × 1/20 = 4/20 = 1/5.
Class activity
Fold a half. Fold a sheet of paper in half and colour one half. Now fold the coloured half into 3 equal strips. How many strips would fill the whole sheet? Write 1/2 ÷ 3 = 1/6. Then repeat with a new sheet: 1/2 ÷ 4.
Practice
1
Work out 1/3 ÷ 4.
1/12.
2
Work out 1/5 ÷ 2.
1/10.
3
Work out 1/8 ÷ 3.
1/24.
4
Youssef has 1/2 kg of dates and shares them equally among 5 children. How much does each child get?
