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1.1.6 Multiple operations

Sometimes you may wish to perform several operations in one step (for example: 35 / 10−3).

When you enter a number of operations one after the other, before clicking the '=key', the Windows calculator will evaluate the combination of operations in a particular order. This corresponds to the order used for any calculation that involves several arithmetic operations. Multiplication and division are evaluated first, then addition and subtraction.

In the example given above, this would result in dividing 35 by 10 (giving 3.5) and then subtracting 3 from the result, giving an answer of 0.5.

But maybe this wasn't what was intended? Maybe you had wanted to subtract 3 from 10 (giving 7) first and then divide 35 by this result, giving an answer of 5.

To force the calculator to perform certain operations before others you can place these operations in brackets. (You can use the bracket keys '(' and ')' on your computer keyboard or on the calculator.)

Activity 1 (self-assessment)

Using the Windows calculator, evaluate:

  1. 35 / 10 – 3 =

  2. 35 / (10 – 3) =

Answer

You should have obtained different answers for these two calculations:

  1. 0.5

  2. 5

If you didn't then it is probably because you were not entering the brackets correctly. Perhaps you forgot the closing bracket or the equals sign after the bracket?

For the first calculation no brackets were needed, because division is always evaluated before subtraction. For the second calculation, the brackets force the calculator to carry out the subtraction first.

Activity 2 (self-assessment)

Write down how you would use brackets to do the following calculations, then carry out the calculation using the Windows calculator. (Remember to clear the previous calculation before entering a new one.)

  1. Add together 6 and 8 and multiply the result by 9.

  2. Add 8 to 56 then divide the result by 8.

  3. Subtract 81 from 129 and multiply the result by 16.

  4. Add together 8 and 15 and divide 46 by the result.

Answer

  1. (6+8)×9=126

  2. (8+56) / 8=8

  3. (129 – 81)×16=768

  4. 46 / (8+15)=2