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Study Guide

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**Subtraction** is the opposite of addition. Here's a little mantra to help us remember how it works when we're dealing with integers:

*subtracting a positive = adding a negative*

*subtracting a negative = adding a positive*

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

Let's say we're trying to solve (-6) – 3. We're subtracting a positive 3, which means we can rewrite things a bit and think of it as *adding* a *negative*. Check it out.

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

Then follow the rules of addition. |

On the other hand, we can think of subtracting a negative as adding a positive, because two negative signs cancel each other out. If we want to solve something like (-9) – (-4), all we need to do is turn those double negatives into a positive, like so:

(-9) – (-4) =

(-9) + 4

Now we can use the rules of addition like normal.

(-9) + 4 = -5

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

There are also a couple other ways to visualize subtraction when negative numbers are involved. They all give the exact same answers, so go with whichever method fits your brain best.

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, or
**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 our answer: +4. Don't 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.

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

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

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

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. |

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