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:
The same rules apply for division: