top

Chapter 2—Integers

2-4 Adding Signed 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.

fig020401.gif (2012 bytes)

Terminology for integer addition.

 

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

anim020401.gif (41214 bytes)
Animated example: Adding positive integers.

Adding Positive Integers

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:

Adding Negative Integers

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

1: Add the absolute values of the addends
2. Give the result the sign that is common to the addends

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

anim020402.gif (41925 bytes)
Animated example: Adding negative integers.

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):

Step 1: Add the absolute values of the addends
Step 2. Give the result the sign that is common to the addends

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.

Examples and Exercises

Adding Signed Integers

These examples and exercises will show you that you've mastered the whole idea of adding signed integers.

David L. Heiserman, Editor

Copyright   SweetHaven Publishing Services
All Rights Reserved

Revised: June 06, 2015