Multiplying and dividing by two digits; divisibility · Usually met around P4
Reordering and regrouping factors
Pair up first: 25 × 4, 125 × 8.
How to do it
Method
Pair up first: 25 × 4, 125 × 8
25 × 53 × 4 = 25 × 4 × 53 = 100 × 53 = 5300
Another way
Split, then regroup
25 × 36 = 25 × 4 × 9 = 100 × 9 = 900
In full
When several numbers are multiplied, you may change their order (the commutative property) or multiply any two of them first (the associative property): the answer stays the same. So look for a pair that makes a round ten, hundred or thousand: 25 × 4 = 100, 5 × 2 = 10, 125 × 8 = 1000. For 25 × 53 × 4, put 25 and 4 together: 25 × 4 × 53 = 100 × 53 = 5300. If no pair is there, split a number into two factors first: 25 × 36 = 25 × 4 × 9 = 100 × 9 = 900. Or check by multiplying left to right: 25 × 53 = 1325 and 1325 × 4 = 5300, the same answer.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Work out: 2 × 43 × 5 = □
Show the answer and working
Answer: 430
Change the order and multiply 5 and 2 first: 5 × 2 = 10. Then times 43 gives 430.
Example 2
To work out 125 × 37 × 8, which two numbers are handiest to multiply first?
- A. 37 × 8
- B. Only left to right, one at a time
- C. 125 × 37
- D. 125 × 8
Choose the right answer
Show the answer and working
Answer: D. 125 × 8
125 × 8 = 1000, a round number, and then times 37 is easy.
Example 3
Work out: 25 × 152 = □
Show the answer and working
Answer: 3800
Split 152 into 4 × 38: 25 × 4 × 38 = 100 × 38 = 3800.
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