Step by step
The question
Question: work out 4 × 19 × 25 in your head.
4 × 19 × 25
1 Find the easy pair
Look for two numbers that make a round number.
4 times 25 is 100.
That is easy.
2 Change the order
We move 25 next to 4.
= 4 × 25 × 19
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.
= (4 × 25) × 19
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
4 times 25 is 100.
= 100 × 19
100 times 19 is 1900.
= 1900
5 Check
Let's check the long way, from left to right: 4 times 19 is 76.
76 times 25 is 1900.
The same.
So the answer is right!
4 × 19 = 76, 76 × 25 = 1900
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
= 1900