5.5.3 Role of Parentheses

Now we’ll investigate why parentheses need to be placed around negative numbers.

Let’s check what happens if you square 5. When you multiply a negative number by a negative number, the answer is positive. So, if you want to find the square of 5, you calculate left parenthesis super minus times five right parenthesis prefix multiplication of left parenthesis super minus times five right parenthesis and the answer is 25.

Calculator symbol The calculator can be accessed on the left-hand side bar under Toolkit.

Activity symbol Activity: Squaring 5

Use the calculator to find left parenthesis super minus times five right parenthesis squared.

Hint solution

Discussion

Remember that negative numbers must be enclosed in parentheses.

Solution symbol

Answer

You should indeed have found that left parenthesis super minus times five right parenthesis squared equals 25. The calculator screen looks like this:

Calculator screen showing opening parenthesis minus 5 closing parenthesis cubed or squared equals 25

Activity symbol Activity: Forgotten Parentheses

Now let’s suppose that you forget the rule about enclosing negative numbers in parentheses and you enter five minus squared with no parentheses. NOTE: You will have to do this using your keyboard because the calculator does not allow negative numbers created with the Plus and minus symbol button to be entered without parentheses.

Use the keyboard and type in − 5 ^ 2, then hit the return key. What happens?

Hint symbol

Discussion

Remember that you may have to clear the calculator by clicking on Cancel symbol before you can begin typing. Also, do NOT use the Plus and minus symbol button—use your keyboard.

Solution symbol

Answer

The calculator screen should look like this:

You see that the answer given is 25. We obtained a negative value instead of a positive value!

5.5.2 Calculator Exploration—Exponents with Negative Numbers

5.5.4 Placement of Parentheses