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Print Only after you! Or the true meaning of the Order of Precedence

Order of precedence

Only after you! Or the true meaning of the "Order of Precedence" 

We have been in touch with hundreds of psychometric test takers and job candidates who train hard to improve their numerical reasoning skills. One issue that keeps coming back is something that should be ingrained into everybody at a very early age but it is still causing a few problems for many: the order of precedence. 

You certainly know the order of precedence of operators when doing calculations but when you’re using a calculator you need to be dead sure.

Mental calculation vs Calculator operations

Indeed, it is very easy to do sums in your head such as:

12 + 3 * 5

but is the answer 75 or 27?

If you type it into your calculator, it should produce the answer 27 but is that what you meant in the first place?

The calculator will always process the calculation according to accepted rules of precedence of operators and so you have to make sure you type things in the order which you want them processed.

How calculators process your input

The generally accepted order of precedence that we need to concern ourselves with for the scope of these tests is:

) Close bracket

- Unary minus

*/ Multiply and divide

+- Addition and subtraction

( Open bracket

= Equals

What this means is that whenever you type in any of these operators which may be lower than anything waiting to be processed then the calculator will evaluate it and wait for it to be processed.

How it works in practice

In our above example, we type in 12 and then ‘+’. At this point there is nothing to evaluate and so the calculator will store the operator to use it later. We then type in ‘3’ followed by ‘*’. The multiply is higher in priority than the addition which is waiting and so the calculator stores this also. You then type in '5' and terminate the calculation with an ‘=’ which is the lowest priority operator and so the calculator evaluates the expression it is holding from right to left as 5*3+12=27.

Suppose we really wanted to do (12+3)*5, how would that work?

We start with the ‘(‘ operator which is very low priority but there is nothing waiting. We then type ‘12+’. The addition is higher than the open bracket and so the calculator stores the calculation. We type ‘3)’ and at this point the calculator will evaluate the expression from right to left as 3+12 and store the answer 15. We type ‘*’ which is the only operator outstanding and so it is stored for later use. Finally we type ‘5=’ which terminate the expressions and the calculator evaluates from right to left 15*5 and gets the answer 75.

Unary minus: what the heck is that?!

One other little point I want to mention here is about the unary minus operator. This is the operator used to denote negative numbers and it can wreak havoc in calculations if not treated correctly. If you multiply or divide by a negative number then the answer will also be negative. However, if you multiply or divide two negative numbers then you will end up with a positive number.

Similarly, if you subtract a negative number then you effectively do an addition. So:

12 - -3 = 15

And if you add a negative number then you effectively do a subtraction:

12 + -3 = 9

The take-away

To sum it up, you need to be aware of and careful with using the calculator even for relatively simple operations. As long as you know the order of precedence and you apply the right operations, you can avoid any unpleasant surprise.

Wish to practice more? Check our free psychometric tests to put theory into practice!


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