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
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