When we subtract a positive number from a negative number, we move towards the left on the number line.
For example, let's consider the following subtraction problem:
To subtract from we start at on the number line and move places to the left.
When we do this, we land at Therefore,
To subtract from , we start at on the number line and move places to the left.
$-12-8=$
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a
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$-20$ |
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b
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$4$ |
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c
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$-4$ |
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d
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$-16$ |
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e
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$20$ |
It is impractical to use number lines to subtract large numbers.
However, a neat trick makes subtracting a positive number from a negative number very easy!
As an example, let's consider the following subtraction problem:
The answer will be negative since is negative, and we're subtracting from it.
We start by solving an easier problem: adding their absolute values. In other words, we need to figure out
Carrying out the addition gives the following:
So, we have
However, since our answer must be negative, we need to change the sign of the answer above.
Therefore, we conclude that
And that's it!
Let's use this technique to solve a problem with three-digit numbers.
The answer will be negative since is negative, and we're subtracting from it.
We start by solving an easier problem:
Next, we carry out the addition:
So, we have
However, since our answer must be negative, we need to change the sign of the answer above.
Therefore, we conclude that
$-36 - 24 = $
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a
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b
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c
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d
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e
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$-100 - 25 = $
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a
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$75$ |
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b
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$-75$ |
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c
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$-125$ |
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d
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$25$ |
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e
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$125$ |
$-112 - 241=$
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a
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$-333$ |
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b
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$-129$ |
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c
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$353$ |
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d
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$-353$ |
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e
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$129$ |