Numbers, units and arithmetic

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3.5 Several calculations and using brackets

Sometimes you may want to make several calculations in succession, and the order in which the calculations are performed may or may not be significant. For example, if you want to add 12 + 7 + 13, it makes no difference which of these two processes you adopt:

add the 12 and 7 first, to give 19, and then the 13, to give 32;

or

add the 7 and 13 first, to give 20, and then add this to 12 to give 32 again.

Brackets can be used in a calculation to mean ‘do this first’.

Although (7 + 13) + 12 is the same as 7 + (13 + 12), sometimes the order of calculation does make a difference:

(7 − 12) + 13 is not the same as 7 − (12 + 13).

Example 15

Calculate (7 + 3) × 2 and 7 + (3 × 2).

To find (7 + 3) × 2, first do the calculation in brackets to get 7 + 3 = 10.

Then multiply by 2 to get 10 × 2 = 20.

For the second calculation, to find 7 + (3 × 2), first calculate 3 × 2 to give 6.

Then add to 7 to give 13. So (7 + 3) × 2 ≠ 7 + (3 × 2).

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