Step by step
The question
Question: work out 25 × 7 × 4 in your head.
25 × 7 × 4
1 Find the easy pair
Look for two numbers that make a round number.
25 times 4 is 100.
That is easy.
2 Change the order
We move 4 next to 25.
= 25 × 4 × 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.
= (25 × 4) × 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, the order matters.
Careful: only with ×: not with − or ÷
4 Work it out
25 times 4 is 100.
= 100 × 7
100 times 7 is 700.
= 700
5 Check
Let's check the long way, from left to right: 25 times 7 is 175.
175 times 4 is 700.
The same.
So the answer is right!
25 × 7 = 175, 175 × 4 = 700
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
= 700