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Students often find it difficult to add or subtract negative numbers. They rarely seem to get the right answer and it gets frustrating (I know from experience!

Broadly speaking, there are three scenarios where you will have to add or subtract negative numbers:

- Both numbers are negative (e.g. – 4 – 5 = – 9). This can also include when you are adding two negative numbers together (e.g. – 4 + (- 5) = – 9). This is basically the same equation as the first one, as the positive and the negative (+ -) in front of the 5 becomes a – .
- One number is positive, and is larger in value & the other is negative, and is smaller in value (e.g. – 4 + 5 = 1)
- One number is positive, and is smaller in value & the other is negative, and is larger in value (e.g. – 5 + 4 = – 1)

When Both Numbers are Negative

If the equation contains both negative numbers, then your answer will be negative, so you can write the negative sign down. Then simply add the values of the two numbers (assuming they are positive) and write it down following the negative sign. And there you have it – your answer. Let’s go through an example:

- Both numbers are negative so we can write down the negative sign.

2. Now, we are going to add the two numbers (as we would if they were positive) on the side.

3. Then we will write the answer to this equation (16) after the negative sign to get our final answer, which is – 16.

When one number is positive, and is larger in value & the other is negative, and is smaller in value

If the equation contains one number that is positive, and is larger in value & the other is negative, and is smaller in value, then you need to rearrange the equation so that the larger positive number comes first, followed by the smaller negative number. Once you do this, the equation will look much easier (in fact, it will be a normal subtraction question!). Let’s go through an example:

- One number is negative, and the other is positive. As the positive one is larger, we will rearrange the equation so that it comes first.

2. Now, the equation looks much more solvable (like an ordinary subtraction question).

When one number is positive, and is smaller in value & the other is negative, and is larger in value

If the equation contains one number that is positive, and is smaller in value & the other is negative, and is larger in value, then your answer will be negative as the negative number has a higher value. You can write the negative sign down. Next you will subtract the smaller number from the larger number, and write down this answer after the negative sign. And voila!

- The equation has both a negative number and a positive number. As the negative number is larger in value than the positive number, we can write down the negative sign.

2. Now, we are going to subtract the smaller number from the larger number (as we would if they were both positive).

3. Then we will write the answer to this equation (4) after the negative sign to get our final answer, which is – 4.

So that’s how you can add or subtract negative numbers. Even though it may take some time getting used to, once you master it you will never get another equation involving negative numbers wrong!

If you have another way that you use to solve equations that involve adding or subtracting negative numbers or have any questions about how to master these methods, then let me know in the comments below. As always, if you have any ideas or requests for future *How to* articles that you’d like to read, let me know in the comments below as well.

Happy Mathing!