Adding Integers: Rules & Examples

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  • 0:00 Absolute Value & the…
  • 0:45 Integers with Like Signs
  • 3:45 Integers with Unlike Signs
  • 6:45 Lesson Summary
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Lesson Transcript
Instructor: Betty Bundly

Betty has a master's degree in mathematics and 10 years experience teaching college mathematics.

In this lesson, we will learn about adding integers or signed numbers. Using the number line and idea of absolute value, we will see that the rules used to add them are simply an extension of the rules of basic arithmetic.

Absolute Value and the Number Line

First, we need to understand absolute value. Think about a walk from your house in a straight line without regard for the direction you are walking. Then, measure how far you walked. If you think of your house as being the point zero, then the measurement would be the absolute value of the distance you walked. Absolute value is the distance from zero without regard to sign or direction. Since the absolute value is distance, the absolute value of a number is always positive.

In mathematical notation, we represent the absolute value of a number with two vertical bars on either side of the number. For example, the absolute value of 5 is written like this | 5|.

To understand absolute value, a number line is often helpful.

Absolute Value on Number Line
Absolute Value Number Line

Integers With Like Signs

To add two integers with the same sign, let's start with what we already know. What is the value of 3 + 2? We know that 3 + 2 = 5. Now, let's see how this would be visualized on the number line.

3 + 2 on Number Line
3+2 on number line

Basically, the two arrows point in the same direction because both 3 and 2 have a positive sign. The final arrow ends up at the sum of the integers.

Now, let's look at a problem with two negative integers. What is -3 + -2?

- 3 + ( - 2 ) on Number Line
Adding -3 + -2

Similar to the sum of the positive integers, the arrows for the sum of the negative integers both point in the same direction. Now, however, since they both have a negative sign, they both point in the negative direction. The final arrow shows the sum of the integers to be -5.

Notice that both the (absolute value) of | 5 | = 5 and the (absolute value) of | -5 | = 5. Why? The answer is that even though the sums were on different sides of zero, they were both the same distance from zero. This idea is behind the first rule we will learn for adding integers.

  • To add two integers with the same sign, add their absolute values. The answer will have the same sign as the integers.

We do this every day to add positive integers. For example, we know that 4 + 7 = 11. We didn't learn to go through these steps:

  1. | +4 | = 4 and |+ 7| = 7
  2. +4 +7 = +11

Yes, that is actually what is happening behind the scenes to get the final answer.

Let's try a problem with two negative integers. What is the value for = -4+ -2?

  1. First, find the absolute value of each integer. | -4 | = 4 and | -2 | = 2
  2. Second, add the absolute values. 4 + 2 = 6
  3. Third, give the answer the common sign of the integers you added. -4 + -2 = -6. The answer is -6.

While some examples can be demonstrated with number lines, some cannot. You should not depend on number lines to add integers. Number lines are handy for visualizing the process of adding integers. Once you understand the general idea behind adding integers using the number line, you should rely on the rules to complete the calculation. Here is another example. What is -52 + -63?

  1. Find the absolute value for each integer: | -52 | = 52 and | -63 | = 63
  2. Add the absolute values: 52 + 63 = 115
  3. Give the answer the common sign of the integers you added: So, -52 + - 63 = -115

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