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Chapter 2—Integers

 When you complete the work for this section, you should be able to: Cite the rule for adding integers that have the same sign. Cite the rule for adding integers that have opposite signs. Demonstrate your ability to add signed integers. Procedure The procedure for adding signed integers depends upon whether the addends have the same sign or opposite signs. When the addends have the same sign (both + or both – ): Step 1: Add the absolute values of the addends Step 2. Give the result the sign that is common to the addends When the addends have opposite signs (one is + and the other is –): Step 1: Subtract the absolute values of the addends Step 2. Give the result the sign of the addend that has larger absolute value

Adding Integers That Have the Same Sign

Adding integers that have  the same sign means that both integers are positive or both are negative. For example:

 Adding two positive integers: ( +2 ) + ( +4 ) = ________ Adding two negative integers: ( –2 ) + ( –4 ) = ________

 Procedure To add integers that have the same sign (both positive or both negative): Step 1: Add the absolute values of the addends Step 2. Give the result the sign that is common to the addends Example

 Problem (+12) + (+7) =_____ Procedure Add the absolute values of the addends. |+12 | + | +7 | = 12 + 7 12 + 7 = 19 Give the result the sign that is common to the addends Both addends are positive, so the result is positive, +19 Solution (+12) + (+7) = ( +19 )  or  12 + 7 = 19

 Note There is no significant difference between adding a pair of positive integers and adding a pair of whole numbers. A problem such as ( +6 ) + ( + 4) = ( +10 ) can always be simplified to look like this: 6 + 4 = 10. And that looks exactly like a whole-number addition problem.

Examples and Exercises

 Adding Positive Integers Use these interactive examples and exercises to strengthen your understanding and build your skills:

The rule for adding negative integers is the same as the rule for adding positive integers:

2. Give the result the sign that is common to the addends

In this case, the common sign is a negative sign. Example

 Problem ( –12 ) + ( –7 ) =_____ Procedure Add the absolute values of the addends. | –12 | + | –7 | = 12 + 7 2 + 7 = 19 Give the result the sign that is common to the addends Both addends are negative, so the result is negative, –19 Solution ( –12 ) + ( –7 ) = ( –19 )  or  –12 + ( –7 ) =  –19

 Notes This is an addition problem. Although the addends both have negative values, you still add their absolute values. Adding negative integers will always produce a negative sum. A problem stated as ( –6 ) + ( –18 ) = ( –24 ) can be simplified a little bit:  –6  + ( –18 ) =  –24. It is not a good idea to remove the parentheses around the –18, because the result would be confusing: –6  +  –18  =  –24.

Examples and Exercises

 Adding Negative Integers Use these interactive examples and exercises to strengthen your understanding and build your skills:

Adding Integers That Have Opposite Signs

Adding integers that have opposite signs means that one is positive and the other is negative. For example:

 Adding a positive integer to a negative integer ( +2 ) + ( –4 ) = ________ Adding a negative integer to a positive integer ( –2 ) + ( +4 ) = ________

 Procedure To add integers that have opposite signs: Step 1: Subtract the absolute values. Step 2. Write the sum with the sign of the larger number.

Example

 Problem ( +6 ) + ( –4 ) = ________ Procedure Subtract the absolute values of the addends | +6 |   –  | –4 | =  6  – 4 Write the sum with the sign of the larger number. In this case, | +6 |  is larger than  | –4 |, so the result is positive + 2 Solution ( +6 ) + ( –4 ) = ( + 2) or 6 – 4 = 2

Example

 Problem ( –5 ) + ( +3 ) = ________ Procedure Subtract the absolute values. | –5 |  –  | +3 | =  5  – 3 Write the sum with the sign of the larger number. | –5 |  is larger than  | +3 |, so the result is negative. – 2 Solution ( –5 ) + ( +3 ) = ( – 2) or –5 + 3 = – 2

Examples and Exercises

 Adding Integers Having Opposite Signs Use these interactive examples and exercises to strengthen your understanding and build your skills:

Lesson Summary

To add integers that have the same sign (both positive or both negative):