Multiplying and dividing fractions · Usually met around P5
Bar models for fraction problems
Which cells does the number cover? Find one cell.
How to do it
Method
Which cells does the number cover? Find one cell
5 cells left are 25 → 1 cell 5 → 7 cells 35
Another way
Work with the fraction
25 ÷ (1 − 27) = 25 ÷ 57 = 35
In full
Draw the problem as a bar model, then find what one cell is worth. Before and after: “27 of it was used and 25 is left”: draw the whole as one bar in 7 equal cells; 2 are used, so the 5 left are 25, one cell is 25 ÷ 5 = 5, and the whole is 5 × 7 = 35. Comparing: “A is 35 of B”: draw B as 5 cells and A as 3 of the same size; if B has 20 more than A, those 2 cells are 20, one cell is 10, A is 30 and B is 50; together they are 8 cells. The key is to see which cells the number you know covers. Another way, with fractions: what is left is 1 − 27 = 57, so the whole is 25 ÷ 57 = 35. Check: 27 of 35 is 10, and 35 − 10 = 25.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Ming spent 710 of the pocket money and has $9 left. How many dollars is each cell of the bar model worth?
Show the answer and working
Answer: 3 dollars
10 cells in all, 7 used (dashed), so the 3 left are 9: 9 ÷ 3 = 3.
Example 2
A is 13 of B, and B is 6 more than A. So A is 3.
True or false?
Show the answer and working
Answer: True
B is 3 cells and A 1; the 2 between them are 6, so 1 cell is 3: A is 1 × 3 = 3.
Example 3
Ming has some stickers, gives away 13 of them, then 35 of the rest, and has 8 left. How many stickers did Ming have to begin with?
Show the answer and working
Answer: 30 stickers
Work backwards: after the second gift, (5 − 3)/5 of the rest is left, so the rest was 20; 20 is (3 − 1)/3 of the whole, so the whole was 30.
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