Step by step
The question
Question: work out 35 × 7 × 2 in your head.
35 × 7 × 2
1 Find the easy pair
Look for two numbers that make a round number.
35 times 2 is 70.
That is easy.
2 Change the order
We move 2 next to 35.
= 35 × 2 × 7
In multiplying, the order does not matter.
This is the commutative property.
a × b = b × a
commutative: the order does not matter
3 Group the easy pair
We put brackets round the easy pair, so we do it first.
= (35 × 2) × 7
With only multiplying, we can group the numbers any way we like.
This is the associative property.
(a × b) × c = a × (b × c)
associative: brackets can move
Careful!
This works for multiplying only.
With minus or divide, moving the brackets changes the answer.
Careful: only with ×: not with − or ÷
4 Work it out
35 times 2 is 70.
= 70 × 7
70 times 7 is 490.
= 490
5 Check
Let's check the long way, from left to right: 35 times 7 is 245.
245 times 2 is 490.
The same.
So the answer is right!
35 × 7 = 245, 245 × 2 = 490
Let's look back.
First: find the easy pair.
Then: change the order.
Then: group the easy pair.
Then: work it out.
Last: check.
Answer
= 490