The distributive property and mixed operations · Usually met around P4
Taking out a common factor; square brackets
Take the common factor outside; work from the innermost bracket.
How to do it
Method
Take the common factor outside; work from the innermost bracket
36 + 8 = 4 × (9 + 2)
Another way
Open the brackets to check
4 × (9 + 2) = 36 + 8 = 44
In full
If two numbers share a factor, you can take it out and write a multiplication: 36 + 8, where 36 = 4 × 9 and 8 = 4 × 2. Both parts have a 4, so 36 + 8 = 4 × (9 + 2). Take out the highest common factor and the numbers left in the brackets share no factor. With two layers of brackets, the round brackets ( ) sit inside the square brackets [ ]: work out the innermost round brackets first, then the square brackets, then what is outside: [20 − (3 + 5)] × 4 = [20 − 8] × 4 = 12 × 4 = 48. Another way: check by opening the brackets with the distributive property: 4 × (9 + 2) = 4 × 9 + 4 × 2 = 36 + 8, and both sides are 44.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
[(12 + 12) × 4 − 5] ÷ 7 = □
Show the answer and working
Answer: 13
12 + 12 = 24, 24 × 4 = 96, 96 − 5 = 91, 91 ÷ 7 = 13.
Example 2
28 + 12 = 4 × (7 + 4)
True or false?
Show the answer and working
Answer: False
28 ÷ 4 = 7 and 12 ÷ 4 = 3: the bracket should be 7 + 3.
Example 3
35 + 10 + 45 = 5 × □
Show the answer and working
Answer: 18
35 = 5 × 7, 10 = 5 × 2, 45 = 5 × 9: 5 × (7 + 2 + 9) = 5 × 18.
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