5.5.4 Placement of Parentheses

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

The first calculation was left parenthesis super minus times five right parenthesis squaredand the calculator shows exactly this with the answer 25.

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

Activity symbol 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?

Hint symbol


The calculator is using the PEMDAS code.

Solution symbol


For open five minus close squared:

In the PEMDAS code, parentheses are evaluated first. The open five minus close cannot be simplified, so the calculator moves to the exponent, which operates on whatever is inside the parentheses. So, it carries out equation sequence open five minus close squared equals open five minus close multiplication open five minus close equals 25.

A negative number is the same thing as multiplying the corresponding positive number by 1. For example, equation left hand side three minus equals right hand side one minus multiplication three. 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 equation sequence five minus squared equals open five minus close squared equals one minus multiplication open five multiplication five close equals one minus multiplication open 25 close equals two minus times five, 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

5.5.5 Home Improvement Project