# 5.5.4 Placement of Parentheses

Below are the screens from the two different calculations we carried out.

The first calculation was and the calculator shows exactly this with the answer 25.

The second calculation was . The calculator has added parentheses around 5, squared
this to give 25, then made it negative. So, the answer is ^{−}25.

## Activity: What’s Up with the Calculator?

Why has the calculator given the answer
^{−}25 this time, while it gave 25 for the earlier
calculation?

### Discussion

The calculator is using the PEMDAS code.

### Answer

For :

In the PEMDAS code, parentheses are evaluated first. The cannot be simplified, so the calculator moves to the exponent, which operates on whatever is inside the parentheses. So, it carries out .

A negative number is the same thing as multiplying the corresponding
positive number by ^{–}1. For example, . This is sometimes called finding the
opposite.

In the second calculation, the calculator thinks you meant the “opposite of” five squared, since you did not place parentheses around the negative 5. Because of this, it places parentheses around the 5 only, so the calculator carries out , because exponents come before multiplication in the PEMDAS code.

Be careful when you work with negative numbers on the calculator, and remember to enclose them in parentheses to make sure that the calculator does what you want it to do.

## To recap:

- Don’t try to take short cuts when you enter negative numbers on the calculator; negative numbers must be enclosed in parentheses.

5.5.3 Role of Parentheses