# 5.2.9 Calculator Exploration—Negative Numbers

In this exploration, you will learn to use the calculator for negative numbers.

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

To enter a negative number on the calculator, use the key. This is between the 0 and the decimal point. Find this on the calculator now.

To enter a negative number like ^{−}3, you must use
parentheses. The key sequence for ^{−}3 is:

Notice that the parentheses appear in the white window of the calculator but not in the black window; the calculator takes some short cuts in calculations with negative numbers, as you will see.

To work out calculations including negative numbers, follow exactly the same method as for positive numbers, but remember that negative numbers must always be enclosed by parentheses.

Here are some calculations for you to try. Work out the answer in your head (or using a number line) first to get some more practice, then check that it is correct on the calculator.

## Activity: Adding and Subtracting Negative Numbers Using the Calculator

**Remember to put negative numbers in
parentheses**

(a)

### Discussion

Did you remember to include parentheses round each negative number?

### Answer

(a) The key sequence is

When you have entered the calculation but before you click on “equals,” the calculator looks like this:

Notice that the full calculation is shown in the white window, but the calculator gives a shorter version in the black window. It is using the rule:

- Adding a negative number is the same as subtracting the corresponding positive number.

Watch the windows on the calculator as you enter the calculation and this should help you remember the rule.

The answer is .

(b)

### Answer

(b)

(c)

### Answer

(c) Entering the calculation, with parentheses round
(^{−}5), the calculator looks like
this:

This time the calculator is using the rule:

- Subtracting a negative number is the same as adding the corresponding positive number.

So, .

(d)

### Answer

(d)

(e)

### Answer

(e)

You may be wondering which key to use on your keyboard for negative numbers. There is no direct equivalent of the button, but the minus key performs the same task. Try this if you want to. Be careful, though—you must still enclose the negative number in parentheses.

Mathematical operation | Calculator button | Keyboard key |
---|---|---|

Negative number | The − key | |

Remember to enclose negative numbers in parentheses. |

You know that practice makes perfect! Here is a link to a game [Tip: hold Ctrl and click a link to open it in a new tab. (Hide tip)] that is fun
and shows you more examples about **adding and subtracting** positive and
negative numbers. Show how great your skills are and make the teacher walk
the plank! (Click on each pirate to see which one is proposing the correct
answer.)

Working with negative numbers can be quite confusing, so well done for getting this far. Get as much practice as you can to reinforce your learning. Try making up your own examples again or asking for some help from friends or family.

Here is what you’ve already learnt:

- Adding a negative number is the same as subtracting the corresponding positive number.
- Subtracting a negative number is the same as adding the corresponding positive number.
- Use parentheses to enter negative numbers on the calculator.
- To add the sign, use the key on the calculator, or the “minus” key on your keyboard.
- Calculations involving negative numbers are carried out as usual (remembering the parentheses).

Now let’s turn to multiplication and division with negative numbers.

5.2.8 Rules for Negatives