Step by step
The question
Question: work out 5 × 13 × 2 in your head.
5 × 13 × 2
1 Find the easy pair
Look for two numbers that make a round number.
5 times 2 is 10.
That is easy.
2 Change the order
We move 2 next to 5.
= 5 × 2 × 13
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.
= (5 × 2) × 13
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, the order matters.
Careful: only with ×: not with − or ÷
4 Work it out
5 times 2 is 10.
= 10 × 13
10 times 13 is 130.
= 130
5 Check
Let's check the long way, from left to right: 5 times 13 is 65.
65 times 2 is 130.
The same.
So the answer is right!
5 × 13 = 65, 65 × 2 = 130
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
= 130