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2- 6 Combining Integer Addition and Subtraction

Most of the examples and exercises in these lessons deal with only two terms at a time. However, you don't have to advance much further in your study of mathematics until you encounter situation where you must add or subtract strings of three or more signed integers. For instance:

(+ 4) + (+  5) + (+ 12) + (+ 6) = ?

(+ 12) + (– 14) + (– 8) = ? 

(+ 2) – (+ 15) + (– 22) = ?

(+ 17) – (+ 24) + (– 1) – (+ 6) = ?

Performing Combinations of Addition and Subtraction

Example

The Problem: (+ 4) + (+  5) + (+ 12) + (+ 6) = ?

Add the terms:

• Two at a time
• From left to right

(+ 4) + (+  5) + (+ 12) + (+ 6) = (+ 9) + (+ 12) + (+ 6)
(+ 9) + (+ 12) + (+ 6) = (+ 21) + (+ 6)
(+ 21) + (+ 6) = (+ 27)

The Solution: (+ 4) + (+  5) + (+ 12) + (+ 6) = (+ 27)

Example

The Problem: (+ 12) + (– 14) + (– 8) = ?

Add the terms:

• Two at a time
• From left to right

(+ 12) + (– 14) + (– 8)  = (– 2) + (– 8)
(–2) + (– 8) = (– 10)

The Solution: (+ 12) + (– 14) + (– 8) =  (– 10)

Example

The Problem: (+ 2) – (+ 15) + (– 22) = ?

Step 1: Change the subtraction signs (–) to addition (+).
Step 2: Switch the sign attached to the term that follows the operation.

(+ 2) – (+ 15) + (– 22) = (+ 2) + (– 15) + (– 22)

Step 3: Complete the addition of all terms.

(+ 2) + (– 15) + (– 22) = (– 13) + (– 22)
(– 13) + (– 22) = (– 35)

The Solution: (+ 2) – (+ 15) + (– 22) = (– 35)

You might also write this solution as: 2 – 15 – 22 = – 35

Example

The Problem: (+ 17) – (+ 24) + (– 1) – (+ 6) = ?

Step 1: Change the subtraction signs (–) to addition (+).
Step 2: Switch the sign attached to the term that follows the operation.

(+ 17) – (+ 24) + (– 1) – (+ 6) = (+ 17) + (– 24) + (– 1) + (– 6)

Step 3: Complete the addition of all terms.

(+ 17) + (� 24) + (– 1) + (� 6) = (� 7) + (– 1) + (– 6)
(– 7) +  (– 1) + (– 6)  = (– 8) + (– 6)
(– 8) + (– 6) = (– 14)

The Solution:  (+ 17) – (+ 24) + (– 1) – (+ 6) = (– 14)

You might also write this solution as: 17 – 24 – 1– 6 = – 14

Exercises

Complete the following addition and subtraction problems.
Click the  ?  symbol to see the correct answer.

Simplifying Signed-Integer Expressions for Addition and Subtraction

You have been seeing a lot of parentheses in this lesson. Pre-algebra teachers and textbooks tend to "overuse" the parentheses in order to clearify the different ways plus and minus signs are used. An expression such as ( + 8) – ( + 6) + (– 2) is really very cumbersome, but it clearly say + 6 is to be subracted from + 8, and the result is added to – 2. Once you have mastered the concepts of adding and subtracting positive and negative numbers, you can simplify these expressions—and without changing their meaning.

Here are some simple examples of removing unnecessary parentheses:

(+ 2) is the same as 2

(– 2) is the same as – 2

(+ 2) + (+ 3) is the same as  2 + 3

(+ 2) –  (+ 3) is the same as  2 –  3

(– 2) –  (+ 3) is the same as  –2 –  3

(+ 2) –  (– 3) is the same as  2 +  3

Copyright � 2006, David L. Heiserman
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