The distributive property and mixed operations · Usually met around P4
Unitary method: finding one first
Find one, then as many as you need.
How to do it
Method
Find one, then as many as you need
3 for $27 → 1 for 27 ÷ 3 = $9 → 5 for 9 × 5 = $45
Another way
Scale by a multiple
6 is 2 times 3: 27 × 2 = $54
In full
When every part is the same size, the total grows in step with the number of parts. Find one first, then as many as you need: 3 pens cost $27, so 1 costs 27 ÷ 3 = $9 and 5 cost 9 × 5 = $45. The other way round, to find how many from the money, divide by the price of one: $90 buys 90 ÷ 9 = 10. When the numbers are a neat multiple, you can scale directly: 6 pens are 2 times 3 pens, so the price is 2 times too, 27 × 2 = $54. Careful: 2 more pens doesn't mean $2 more, it means 2 more pens' worth.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
8 ballpoint pens cost $152. One costs $□, and 2 cost $□.
Fill in each box
Show the answer and working
Answer: 19，38
Find one first: 152 ÷ 8 = 19; then 2 of them: 19 × 2 = 38.
Example 2
3 notebooks cost $75. How much do 8 cost?
Show the answer and working
Answer: 200 dollars
One: 75 ÷ 3 = $25; 8: 25 × 8 = $200.
Example 3
3 storybooks cost $18, so 7 cost $22.
True or false?
Show the answer and working
Answer: False
One costs 18 ÷ 3 = $6, so 7 cost 6 × 7 = $42. 4 more items is 4 more items' worth, not $4 more.
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