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Subtracting integers


When subtracting integers, use a number line to help you think through problems.


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.

numberline-image

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.

numberline-image

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.

numberline-image

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

numberline-image

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

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






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