Subtracting From a Negative Number

Introduction

In this lesson, you will learn how to subtract from a negative number. If subtraction is taking an amount away from another amount, what does it mean to take an amount away from a negative amount?

Remember, subtraction is the same as addition but it goes in the opposite direction. On a number line, subtraction is shown by moving to the left. If the starting number is already negative, then moving to the left makes the solution a larger negative number.

This video illustrates the lesson material below. Watching the video is optional.

Subtracting from a Negative Number (03:42 mins) | Transcript

Subtracting From a Negative Number

This concept is most familiar when it comes to temperature. If it is -5 degrees and the temperature gets 10 degrees colder, the temperature can be calculated as follows:
\begin{align*}
− 5 − 10 = − 5 + ( − 10 ) = − 15
\end{align*}

Another example is debt. If you are $1000 in debt and you spend another $500, you would subtract 500 from -1000. This is shown as follows:
\begin{align*}
− $1000 − $500 = − $1000 + ( − $500 ) = − $1500
\end{align*}

Note: If the starting number is negative and you subtract a number from it, you can simply add the numbers together and keep the negative sign, which means the answer will be a larger negative number.

Consider this example: $-1-4$. Start with -1 on the number line and add -4. This means that you will move 4 units to the left from -1. This puts you at -5. Remember, when subtracting from a negative number. it is the same as adding a negative number.

$-1-4=-5$ or $-1+(-4)=-5$

The figure shows a horizontal line that points on both sides with a yellow dot on negative one and an arrow above the line pointing to the left with a negative four above it. Negative five is encircled, with the following values under the image: -1 - 4 = -1 + (-4) = -5.

Figure 1

Consider an example with temperature. If it is -3 degrees and the temperature gets 5 degrees cooler, the temperature can be calculated as follows:

$-3-5=-8$ or $-3+(-5)=-8$

This figure shows a horizontal line with zero at the middle with positive number from 1-9 on its right, and negative numbers from 1-9 on its left. A yellow dot is on point -3, with a yellow arrow pointing to the left and a -5 above it. -8 is encircled with the following values below the image: -3 - 5 = -3 + (-5) = -8.

Figure 2

Things to Remember

Subtraction is the same as adding a negative number.
If both numbers are negative, the answer will remain negative.

Practice Problems

$-2 - 3 = ?$ (
Solution

x

Solution: -5
Details:
For this solution, observe the pattern:

$-2 - 0 = -2$ (zero has no value, therefore the answer is -2)

$-2 - 1 = -3$

$-2 - 2 = -4$

$\color{red} -2 - 3 = -5$

When you subtract a positive number from a negative number your answers are always negative. The above pattern shows how increasing the value of the positive number results in a decreasing solution. The answer becomes more negative.

)
$-4 - 4 = ?$ (
Solution

x

Solution: -8
Details:
For this solution, observe the pattern:

$-4 - 0 = -4$ (zero has no value, therefore the answer is -4)

$-4 - 1 = -5$

$-4 - 2 = -6$

$-4 - 3 = -7$

$\color{red} -4 - 4 = -8$

This same problem could be re-written as $-4 + (-4)$; negative four plus negative four results in negative eight. It is the same idea as adding positive numbers, except going in the negative direction.

)
$-5 - 2 = ?$ (
Solution

x

Solution:
-7

)
$-17 - 2 = ?$ (
Video Solution

x

Solution: -19
Details:

(Subtracting from a Negative Number #4 (01:00 mins) | Transcript)

| Transcript)
$-10 - 15 = ?$ (
Solution

x

Solution:
-25

)
$-46 - 15 = ?$ (
Video Solution

x

Solution: -61
Details:

(Subtracting from a Negative Number #6 (02:06 mins) | Transcript)

| Transcript)

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