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Addition and Subtraction with Positive and Negative Numbers
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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.


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
\(1+5=6\)

A number line from -2 to 7. 1 is highlighted orange, with an arrow above it moving to the right 5 places and pointing to the 6, which is also highlighted orange. 

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

A number line from -7 to 2. -2 is highlighted orange, with an arrow above it moving to the left 3 places and pointing to -5, which is also highlighted orange. 

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.

A number line from -7 to 2. 1 is highlighted orange, with an arrow above it moving to the left 6 places and pointing to -5, which is also highlighted orange. 

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. \(6-1=5\)

A number line from -2 to 7. 6 is highlighted orange, with an arrow above it moving to the left 1 place and pointing to 5, which is also highlighted orange. 

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.

An equation showing 6 above negative 1, with the answer of 5. 

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

An equation showing negative 6 above 4, with the answer of negative 2. 

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

Evaluate the following expressions:
  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. \(7 + (-9) = ?\) ( 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. \(-8 + 4 = ?\) ( )
  5. \(-4 + (-4) = ?\) (
    Solution
    x
    Solution:
    -8
    )
  6. \(-8 - (-4) = ?\) (
    Solution
    x
    Solution:
    -4
    )

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