3
Dividing a whole number by a unit fraction
Discover Mathematics P5: Term 2, Unit 9, Lessons 9–13
GoalDivide a whole number by a unit fraction by counting how many pieces fit, and link it to multiplication.
New words
how many in · division can ask how many equal pieces fit into a numberinverse · opposite: dividing by 1/4 is the inverse of dividing by 4quarter · one of 4 equal parts, 1/4
Explanation
How many quarters are in 3 wholes? Each whole holds 4 quarters, so 3 wholes hold 3 × 4 = 12 quarters. That is the division 3 ÷ 1/4 = 12. In the same way 2 ÷ 1/3 = 2 × 3 = 6 and 5 ÷ 1/2 = 5 × 2 = 10. The rule: dividing a whole number by a unit fraction 1/b gives the whole number times b. The pieces are small, so there are many of them, and the answer is bigger than the starting number. Check by multiplying back: 12 × 1/4 = 3. A story helps: 6 litres of juice poured into cups of 1/4 litre fill 6 ÷ 1/4 = 24 cups.
Worked examples
How many 1/2-metre pieces can be cut from a 4 m ribbon? 4 ÷ 1/2 = 4 × 2 = 8 pieces. Check: 8 × 1/2 = 4.
A baker has 6 kg of flour and uses 1/4 kg for each small cake. 6 ÷ 1/4 = 6 × 4 = 24 cakes. If each cake sells for 15 LE, all 24 cakes bring 24 × 15 = 360 LE.
Work out 7 ÷ 1/3. Each whole has 3 thirds, so 7 ÷ 1/3 = 7 × 3 = 21. Notice that 21 is much bigger than 7: dividing by a small piece gives many pieces.
Class activity
Pour and count. Use a 1-litre bottle and a small cup that holds exactly 1/4 litre (or use a drawing). How many cups fill 1 litre? How many fill 3 litres? Write 3 ÷ 1/4 = 12 and check by multiplying 12 × 1/4.
Practice
1
Work out 2 ÷ 1/5.
2 × 5 = 10.
2
Work out 4 ÷ 1/3.
4 × 3 = 12.
3
Work out 7 ÷ 1/2.
7 × 2 = 14.
4
How many cups of 1/4 litre can be filled from 5 litres of water?
5 ÷ 1/4 = 5 × 4 = 20 cups.
5
Karim says 3 ÷ 1/2 = 3/2. Explain his mistake and give the correct answer.
There are 2 halves in each whole, so 3 wholes hold 6 halves: 3 ÷ 1/2 = 3 × 2 = 6. The answer must be bigger than 3.