Introduction

In this lesson, you will learn about addition and subtraction with positive and negative numbers. The key to knowing whether to add or subtract is to know what kind of numbers you are working with: positive or negative. It is up to you to determine what you’re working with, and practicing multiple types of problems is important in becoming familiar with the different kinds of numbers.

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

• Summary Addition and Subtraction with Positive and Negative Numbers (08:49 mins) | Transcript

Adding Positive Numbers

First, identify what kind of numbers you have: positive or negative. If you have two positive numbers to combine, use addition.

Example 1
\(1+5=6\)

Figure 1

In this example, the positive number became more positive, or became a greater positive number.

Adding Negative Numbers

Similarly, when adding two negative numbers together, start in a negative position and make the number even more negative. The number will become a greater negative number.

Example 2
\(-2+(-3)=-5\)

Figure 2

The same would be true if you rewrote this example as a negative number subtracting a number: \(-2-(3)=-5\)

If you want to combine two negative numbers, use addition.

Subtracting Positive and Negative Numbers

The only time subtraction is used is when you have both a positive and negative number.

Example 3
\(1-6\)

Start at 1 and go the left 6 times.

Figure 3

Notice that the answer is negative: -5.

Example 4
Similarly, if you started with a bigger number, you would still be counting in the negative direction.

\(6-1\) will still make you go toward the negative side of the number line. \(6-1=5\)

Figure 4

It is sometimes helpful to stack the numbers when adding and subtracting. When you do this, simply look at which number is bigger. If the bigger number is positive, your answer will be positive. If the bigger number is negative, your answer will be negative.

Figure 5

In this example, 6 is a positive number and 1 is a negative number. Because 6 is the bigger number in the equation, the answer will be positive. In this case, the answer is positive 5.

Example 5

Figure 6

In this example, 6 is a negative number and 4 is a positive number. Because 6 is the bigger number in the equation, the answer is negative 2.

Things to Remember

• If you have two positive numbers to combine, perform addition.
• If you have two negative numbers, or a negative number subtracting another negative number, perform addition. The answer will be negative.
• If you’re combining a positive and a negative number, or a negative and a positive number, perform subtraction.

Practice Problems

1. \(4 - 9 = ?\) (
   Solution

   x

   Solution: -5
   Details:
   Subtraction can be rewritten as the addition of the opposite.
   
   You can change this problem to addition by turning -9 into \(+(-9)\).
   
   \(4 - 9 = -5\) is the same as \(4 + ( - 9) = -5\)
   )
2. \(7 + (-9) = ?\) (
   Video Solution, 01:18 mins

   x

   Solution: -2
   Details:
   

   
   
   | Transcript)
3. \(10 - (-7) = ?\) (
   Solution

   x

   Solution: 17
   Details:
   Subtraction can be rewritten as the addition of a negative number.
   
   To solve this problem, you can turn the subtraction to addition by adding the opposite of -7 which is 7.
   
   The problem \(10 - ( -7 )\) becomes: \(10 + ( 7 ) = 17\)
   )
4. \(-8 + 4 = ?\) (
   Video Solution, 01:00 mins

   x

   Solution: -4
   Details:
   

   
   
   | Transcript)
5. \(-4 + (-4) = ?\) (
   Solution

   x

   Solution:
   -8
   )
6. \(-8 - (-4) = ?\) (
   Solution

   x

   Solution:
   -4
   )