The distributive property and mixed operations · Usually met around P4
The distributive property
Take out the shared factor; add (or subtract) the rest first.
How to do it
Method
Take out the shared factor; add (or subtract) the rest first
37 × 6 + 37 × 4 = 37 × (6 + 4) = 37 × 10 = 370
Another way
Split off the hundred
102 × 15 = 100 × 15 + 2 × 15 = 1530
In full
Start with chairs set out in 3 rows, each row 5 red chairs and 2 blue. Count each row as 5 + 2 = 7 and 3 × 7 = 21; or count the colours apart, 3 × 5 = 15 red and 3 × 2 = 6 blue, 15 + 6 = 21. Both ways give the same, so 3 × (5 + 2) = 3 × 5 + 3 × 2. A number times a sum equals the number times each part, added: a × (b + c) = a × b + a × c, and the same with take away. It is handiest the other way round: in 37 × 6 + 37 × 4 both parts are times 37, so add 6 and 4 first: 37 × (6 + 4) = 37 × 10 = 370. To multiply by a number near a hundred, split it: 102 × 15 = 100 × 15 + 2 × 15 = 1500 + 30 = 1530, and 98 × 15 = 100 × 15 − 2 × 15 = 1470. Or check by working each part: 37 × 6 = 222, 37 × 4 = 148, 222 + 148 = 370, the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
6 × (50 + 8) = 6 × 50 + 6 × □ = □
Fill in each box
Show the answer and working
Answer: 8，348
6 times 50 and times 8, added: 300 + 48 = 348.
Example 2
46 × 9 + 46 × 91 = 46 × □
Show the answer and working
Answer: 100
Both parts are times 46, so add 9 and 91 first: 9 + 91 = 100.
Example 3
44 × 63 − 44 × 12 = 44 × 75
True or false?
Show the answer and working
Answer: False
Both parts are times 44 with a take away between, so it is 44 × (63 − 12) = 44 × 51.
Practise it in the game →The distributive property and mixed operations · Free to start, unlimited questions, no download