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Rounding and estimation
Rounding and estimation

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3.2 Have I used the correct order for my calculation?

When calculating an answer it is important that you give careful consideration to the order of operations used in the calculation. If you are using a mixture of operations remember that certain operations take priority in a calculation. Consider the following, apparently, simple sum.

   1 + 2 × 3 = ?

What answer would you give?

Did you give 7 as your response, or 9?

The correct answer is 7 but can you explain why?

If you have a calculator handy, check that it follows the correct order. Some basic calculators do not, but scientific calculators should do so.

Brackets come first, then powers, and then multiplication and division (working from left to right), and finally addition and subtraction (working from left to right).

Consider this sum:

   10 − 5 + 3 = ?

What answer would you give?

Did you provide 2 as your response, or 8?

The correct answer is 8 but can you explain why?

The operations of addition and subtraction belong to the same group, and so you perform the calculation from left to right. Addition does not have priority over subtraction.

Consider these calculations:

   (1 + 2) × 3 = ?

   10 − (5 + 3) = ?

These calculations are similar to earlier ones but this time involve the use of brackets, which take priority over the other operations. The correct answers here are 9 and 2 respectively.