Multiplying and dividing fractions · Usually met around P5
From a part to the whole (unitary method)
Find one part, then the whole.
How to do it
Method
Find one part, then the whole
3 parts 18 → 1 part 6 → 4 parts 24
Another way
Divide by the fraction
18 ÷ 34 = 18 × 43 = 24
In full
34 of a number is 18: find the number. Way 1 (unitary method): 3 parts are 18, so 1 part is 18 ÷ 3 = 6, and 4 parts are 6 × 4 = 24. Way 2: the number × 34 = 18, so the number = 18 ÷ 34 = 18 × 43 = 24. Both agree; a bar model shows it too: the whole in 4 parts, 3 of them 18. Check: 24 × 34 = 18.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
19 of a number is 22. What is 29 of the number?
Show the answer and working
Answer: 44
1 part is 22, so 2 parts are 22 × 2 = 44.
Example 2
16 kg of sugar costs $3. How much does 23 kg cost?
Show the answer and working
Answer: 12 dollars
Find 1 kg first: 3 ÷ 16; then × 23: $12.
Example 3
29 of a number is 20. Which working finds the number?
- A. 20 × 9
- B. 20 ÷ 2
- C. 20 × 29
- D. 20 ÷ 29
Choose the right answer
Show the answer and working
Answer: D. 20 ÷ 29
The number × 29 = 20, so the number = 20 ÷ 29 (that is, 20 ÷ 2 × 9).
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