# Positive and Negative Numbers

Positive and negative numbers are often used to represent quantities like temperature. For example, in winter, a temperature of ℃ is ℃ below zero.

When working with arithmetic, it can be helpful to think of positive numbers as something we possess and negative numbers as a debt we owe.

Negative numbers have a minus sign in front of them, such as ℃. Positive numbers can be written with or without the positive sign in front of the number.

In , we treat 10 as something we possess and the as something else we possess. So in total, we have . Therefore, .

In , we treat as a debt and the as something we have. After settling the account, we still have a debt. So, .

In , we regard as a debt and the as another debt. So in total, we have a debt. Therefore, .

Calculating sums and differences can also be visualised on a number line. We move to the right if we are adding and to the left if we are subtracting.

For , start at on the number line and move steps to the right. This gives us . For , start at and move steps to the right. For , start at and move steps to the left. This takes us to . Hence, . For , we start at and move steps to the right. This takes us to , so . Keep these rules in mind:

• • • • With larger numbers, using a number line becomes impractical. Instead, visualise what is happening on the number line. For example, consider .

Start at on the number line and move steps to the right. This takes us to . So, .

To calculate , start at and move steps to the left. This takes us to on the number line. Now, . Therefore, .

With practice, calculations become easier, and visualising the number line may no longer be necessary.

When multiplying numbers (positive, negative), remember these rules:

• Positive positive positive
• Positive negative negative
• Negative positive negative
• Negative negative positive

## Examples

• • • • The same rules apply for division:

• • • • 