Page 148 - Basic College Mathematics with Early Integers

2.3 ADDING INTEGERS Objectives

Add Integers.

Objective Adding Integers Evaluate an Algebraic Expression
by Adding.
Adding integers can be visualized using a number line. A positive number can be
represented on the number line by an arrow of appropriate length pointing to the Solve Problems by Adding
right, and a negative number by an arrow of appropriate length pointing to the left. Integers.
2 2
Both arrows represent 2 or +2.
They both point to the right and they are
both 2 units long. 5 4 3 2 1 0 1 2 3 4 5
3 3
Both arrows represent -3.
They both point to the left and they are
5 4 3 2 1 0 1 2 3 4 5
both 3 units long.
Example 1 Add using a number line: 5 + 1-22 PRACTICE 1
Add using a number line:
Solution: To add integers on a number line, such as 5 + 1-22, we start at 0 on the 5 + 1-12
number line and draw an arrow representing 5. From the tip of this arrow, we draw
another arrow representing -2. The tip of the second arrow ends at their sum, 3. 3 2 1 0 1 2 3 4 5 6 7

Start End
2
5
5 4 3 2 1 0 1 2 3 4 5
5 + 1-22 = 3
Work Practice 1

Example 2 Add using a number line: -1 + 1-42 PRACTICE 2
Add using a number line:
Start at 0 and draw an arrow representing -1. From the tip of this arrow, we draw
-6 + 1-22
another arrow representing -4. The tip of the second arrow ends at their sum, -5.
Solution: End Start 9 8 7 6 5 4 3 2 1 0 1
4 1 PRACTICE 3

5 4 3 2 1 0 1 2 3 4 5 Add using a number line:
-8 + 3
-1 + 1-42 =-5
Work Practice 2 9 8 7 6 5 4 3 2 1 0 1

Answers
Example 3 Add using a number line: -7 + 3
1. Start End
5
Solution: End Start 1
3
7 3 2 1 0 1 2 3 4 5 6 7
5 (1) 4
2. End Start
7 6 5 4 3 2 1 0 1 2 3
2 6
Work Practice 3
9 8 7 6 5 4 3 2 1 0 1
6 (2) 8
Using a number line each time we add two numbers can be time consuming.
3. End Start
Instead, we can notice patterns in the previous examples and write rules for adding 8
signed numbers. 3
Rules for adding signed numbers depend on whether we are adding numbers 9 8 7 6 5 4 3 2 1 0 1
with the same sign or different signs. When adding two numbers with the same sign, 8 3 5
as in Example 2, notice that the sign of the sum is the same as the sign of the addends.
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