Introduction

In this lesson, you will learn how to subtract negative numbers. Subtracting a negative number is the same as adding a positive number.

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

• Subtracting a Negative Number (03:34 mins) | Transcript

Subtracting a Negative Number

What does it mean to subtract a negative number?

Example 1
\(1 - -3\)

First you need to understand that \(1 - -3\) is the same as \(1 - (-3)\). If you use a number line to demonstrate the answer, you will start at 1. Head left because of the subtraction sign, but then go in the opposite direction (to the right) because of the negative in front of the 3 (see Figure 1).

Figure 1

Again, this example demonstrates that two negatives next to each other make a positive. \(-(-3)\) becomes \(+3\): So \(1-(-3)=4\) is the same as \(1 + 3 = 4\).

Figure 2

Example 2
\(-5-(-2)\)

On a number line, start at -5. The subtraction sign directs you to go left but the negative in front of the number 2 redirects you to go the opposite direction. So you will move 2 units to the right (see Figure 3).

Figure 3

\(-5 - (-2)\) is the same as \(-5 + 2\), so both give the same answer: -3.

This shows how subtracting a negative number is the same as adding a positive number.

Things to Remember

• Subtracting a negative number is the same as adding a positive number.

Practice Problems

1. \(6 - (- 3) = ?\) (
   Solution

   x

   Solution: 9
   Details:
   Explore the patterns:
   
   \(6 - (1) = 5\)
   
   \(6 - (0) = 6\)
   
   \(6 - (-1) = 7\)
   
   \(6 - (-2) = 8\)
   
   \(\color{red} 6 - (-3) = 9\)
   
   Subtracting a negative number from a positive number results in a positive answer. This problem can also be rewritten as \(6 + 3 = 9\).
   )
2. \(4 - (- 4) = ?\) (
   Solution

   x

   Solution: 8
   Details:
   Explore the patterns:
   
   \(4 - (1) = 3\)
   
   \(4 - (0) = 4\)
   
   \(4 - (-1) = 5\)
   
   \(4 - (-2) = 6\)
   
   \(4 - (-3) = 7\)
   
   \(\color{red} 4 - (-4) = 8\)
   
   Subtracting a negative number from a positive number results in a positive answer. This problem can also be rewritten as \(4 + 4 = 8\).
   )
3. \(3 - (- 5) = ?\) (
   Video Solution

   x

   Solution: 8
   Details:
   

   
   (What Does it Mean to Subtract a Negative Number #3 | Transcript)
   | Transcript)
4. \(4 - (- 8) = ?\) (
   Video Solution

   x

   Solution: 12
   Details:
   

   
   (What Does it Mean to Subtract a Negative Number #4 | Transcript)
   )
5. \(10 - (- 19) = ?\) (
   Solution

   x

   Solution:
   29
   )
6. \(48 - (- 16) = ?\) (
   Solution

   x

   Solution:
   64
   )

Need More Help?

1. Study other Math Lessons in the Resource Center.
2. Visit the Online Tutoring Resources in the Resource Center.
3. Contact your Instructor.
4. If you still need help, Schedule a Tutor.