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 \(-1+(-4)=-5\)

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 \(-3+(-5)=-8\)

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

1. \(-2 - 3 = ?\) (
   Solution

   x

   Solution: -5
   Details:
   For this solution, observe the pattern:
   
   \(-2 - 0 = -2\) (zero has no value, therefore the answer is -2)
   
   \(-2 - 1 = -3\)
   
   \(-2 - 2 = -4\)
   
   \(\color{green} -2 - 3 = -5\)
   
   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.
   )
2. \(-4 - 4 = ?\) (
   Solution

   x

   Solution: -8
   Details:
   For this solution, observe the pattern:
   
   \(-4 - 0 = -4\) (zero has no value, therefore the answer is -4)
   
   \(-4 - 1 = -5\)
   
   \(-4 - 2 = -6\)
   
   \(-4 - 3 = -7\)
   
   \(\color{green} -4 - 4 = -8\)
   
   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.
   )
3. \(-5 - 2 = ?\) (
   Solution

   x

   Solution:
   -7
   )
4. \(-17 - 2 = ?\) (
   Video Solution

   x

   Solution: -19
   Details:
   

   
   
   | Transcript)
5. \(-10 - 15 = ?\) (
   Solution

   x

   Solution:
   -25
   )
6. \(-46 - 15 = ?\) (
   Video Solution

   x

   Solution: -61
   Details:
   

   
   
   | Transcript)