Problem

Add. See Examples 1 through 12.ExampleExample1 Add: −1 + (−2)Solution:Thinking of integers...

Add. See Examples 1 through 12.

Example

Example1 Add: −1 + (−2)
Solution:
Thinking of integers as money earned or lost might help make addition more meaningful. Earnings can be thought of as positive numbers. If $1 is earned and later another $3 is earned, the total amount earned is $4. In other words, 1 + 3 = 4.
On the other hand, losses can be thought of as negative numbers. If $1 is lost and later another $3 is lost, a total of $4 is lost. In other words, (−1) + (−3) = −4.
In Example, we added numbers with the same sign. Adding numbers whose signs are not the same can be pictured on a number line also.
Example 2 Add: −4 + 6
Solution:
Let’s use temperature as an example. If the thermometer registers 4 degrees below 0 degrees and then rises 6 degrees, the new temperature is 2 degrees above 0 degrees. Thus, it is reasonable that −4 + 6 = 2. (See the diagram in the margin.)
Example 3 Add: 4 + (−6)
Solution:
Using a number line the time we add two numbers can be time consuming, Instead, we can notice patterns in the previous examples and write rules for adding real numbers.
Example 4
Add without using a number line: (−7) + (−6)
Solution: Here, we are adding two numbers with the same sign.
Example 5 Add without using a number line: (−10) + 4
Solution: Here, we are adding two numbers with different signs.
Examples 6 Add without using a number line.
(−8) + (−11) = −19
Examples 7 Add without using a number line.
(−2) + 10 = 8
Examples 8 Add without using a number line.
0.2 + (−0.5) = −0.3
Examples 9 Add without using a number line.
Examples 10 Add without using a number line.
11.4 + (−4.7) = 6.7
Examples 11 Add without using a number line.
Examples 12 Find the sum.
a. 3 + (−7) + (−8)
b. [7 + (−10)] + [−2 + (−4)]
Solution:
a. Perform the additions from left to right.
b. Simplify inside the brackets first.
Examples Add.
−56 + 56 = 0
Examples Add.
17 + (−17) = 0