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Numbers, units and arithmetic
Numbers, units and arithmetic

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3.5.2 With or without brackets

Brackets are not always given in a calculation, and there are rules which tell you in which order to do the calculations in the absence of brackets. The following is the order that scientific calculators normally use.

Calculations are performed in the following order:

Brackets;

Powers (e.g. squaring or cubing a number);

Division and Multiplication (performed in the order written, left to right);

Addition and Subtraction (performed in the order written, left to right).

If you have a calculator handy, check that it follows these rules.

Example 16

Calculate 10 + 3 × 7.

Answer

Multiplication is done before addition (unless brackets tell you otherwise) so

  10 + 3 × 7 = 10 + 21 = 31.

Sometimes brackets are implied in division. For example,