# Subtracting Integers

When subtracting integers, use a number line to help you think through problems. We illustrate with some examples below.

For example: 4 − 6

6 is positive, so 4 − 6 = 4 −(+6)

Here, you are subtracting a positive from a positive, so the result is less positive.

Therefore, you will start at 4 and you have to move to the left.

In this case, you will move 6 units to the left.

You end up at -2, so the answer is -2.

Take a look at the number line below to see how this is done.

Find -5 − -6

Before you do this problem, it is important to lay down some foundation.

In mathematics, whenever you subtract something from the same thing you get 0. Mathematically speaking

x − x = 0

7 − 7 = 0

15 − 15 = 0

Would it make sense then to say -4 − -4 = 0 ?

Of course it would because you are subtracting negative 4 from negative 4.

Since the answer is 0 and you started at -4, you had to move to the right to end up at zero. This is crucial information I am giving you here.

In general, subtracting a negative from a negative makes the result less negative or more positive and you have to move to the right to get the answer. Where else can you get a deep understanding of math, if not right here?

Having said that, to find -5 − -6, you have to start at -5 and move 6 units to the right.

If you do that, you will end up at 1, so the answer is 1.

If you subtract a negative from a positive, you will have to move to the right too. In fact, whenever, you subtract a negative from anything, you have to move to the right for the same reason we explained above.

Find 1 −-7

Start at 1 and move 7 units to the right. You end up at 8, so the answer is 8.

In practice, it is convenient to do the following when subtracting a negative from anything:

-2 − - 3 = -2 + + 3 = 1

4 − - 5 = 4 + +5 = 9

Finally, subtracting a positive from a negative makes the result less positive, so you will move to the left to get the answer.

Find -1 − 8

Start at -1 and move 8 units to the left. You end up at -9, so the answer is -9

Here is a summary for subtracting integers:

4 − (+5) = 4 + (-5) = -1

-5 −(-6) = -5 + 6 = 1

5 − (-7) = 5 + (+7) = 12

-6 − (+8) = -6 + (-8) = -14

Here is the rule:

When subtracting integers, add the opposite.

3 − 5 = 3 + (-5) = -2

3 −-5 = 3 + + 5 = 8

Use this subtracting integers calculator to practice

Other popular topics related to integers are modeling integers with chips and

integers and inductive reasoning

## Recent Articles

1. ### Optical Illusions with Geometry

Oct 22, 18 04:14 PM

Take a good look at these optical illusions with geometry

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

## Recent Lessons

1. ### Optical Illusions with Geometry

Oct 22, 18 04:14 PM

Take a good look at these optical illusions with geometry

Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Everything you need to prepare for an important exam!

K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.