Negative numbers: Add, subtract, multiply, divide

In a nutshell

Negative numbers are numbers that are less than zero. It's possible to add, subtract, multiply and divide with them.

Adding and subtracting negative numbers

To add and subtract negative numbers, it is best done with a number line.

When adding and subtracting with negative numbers, you should be aware of the following facts: 

• Move to the left on a number line to subtract.
• Move to the right on a number line to add.
• Subtracting a negative number is the same as adding a positive number.

Example 1

What is $$-4+5$$?

Start off at $$-4$$ on the number line, then move $$5$$ steps to the right.

Moving $$5$$ steps to the right ends up at $$1$$.

​$$\underline{-4+5=1}$$​​

Example 2

What is $$10-(-5)$$?

Subtracting a negative number is the same as adding a positive number. Therefore:

​$$10-(-5)=10+5=15$$​​

​$$\underline{10-(-5)=15}$$​​

Multiplying and dividing negative numbers

To multiply and divide negative numbers, multiply them as if they were positive numbers. If the two numbers have different signs (so if one is positive and the other is negative), then add a negative symbol to the answer.

Example 3

What is $$-5\times-7$$?

Multiply the two numbers together as if they were both positive:

​$$5\times7=35$$​​

Since both numbers have the same sign (they are both negative), there is no need to change the sign of the answer.

​$$\underline{-5\times-7=35}$$​​

Example 4

What is $$100\div-10$$?

Divide the two numbers as if they were both positive:

​$$100\div10=10$$​​

The numbers have opposing signs - one is negative and one is positive. Hence, the answer will be negative.

$$\underline{100\div-10=-10}$$​​​​