#### CHECK OUT SHMOOP'S FREE STUDY TOOLS: Essay Lab | Math Shack | Videos

# Basic Operations

# Subtracting Integers

**Subtraction** is the mirror opposite of addition. The most important thing to know is that

*subtracting a positive = adding a negative*

and

*subtracting a negative = adding a positive*

Got it? Don't worry, we'll explain.

**Try to visualize this by looking at the example (-3) - (-7). **

- Start with three minuses (- - -).
- Now, try to take away (subtract) seven negatives. Oops, there are only three available.
- So, we'll need to add pairs of pluses and minuses (Zero Pairs). They'll cancel each other out.
- In order to have seven negatives to take away, we must add at least four zero pairs.

Now we can take away seven negatives. Four positives remain and that's your answer, +4. Do not worry if you added too many zero pairs. If you have extra pairs remaining, just remember that each pair of positives and negatives make zero.

The basics of addition use integers. What are integers? Well here's a video to help explain them.

## Examples

## Subtracting Using a Number Line

Since subtraction is the *opposite* of addition, move in the *opposite* direction.

- To subtract a positive, move left
- To subtract a negative, move to the right

For the example 4 – 7, start at the +4. Now jump 7 places to the left, in the negative direction. We land on (-3).

## Examples

6 – (-2)Start at 6. Jump 2 places to the right. You land on the answer, +8. | -4 – (-4)Start at –4. Jump 4 places to the right. You land on the answer, 0. |

-5 – (3)Start at -5. Jump 3 places to the left. You land on the answer, -8. | 4 – 10Start at +4. Jump 10 places to the left. You land on the answer, -6. |

## Rule of Subtraction: Add the Opposite

Add The Opposite. Change the subtraction sign to addition and change the second number to the opposite sign. | |

Then follow the rules of addition. |

**Look Out**: many students make the mistake of changing the sign of the first number in the problem. This will result in an incorrect answer, so be sure to always change the sign of the second number.

This video might just make everything a little bit more complicated, but if you think you have additition down, give it a try.