146 Chapter 2 The Integers
The Language of Mathematics When writing additions that involve
integers, write negative integers within parentheses to separate the negative
sign from the plus symbol.
9 (4) 9 4 and 9 (4) 9 4EXAMPLE (^1) Add: a. b. c.
StrategyWe will use the rule for adding two integers that have the same sign.
WHYIn each case, we are asked to add two negative integers.
Solution
a.To add two negative integers, we add the absolute values of the integers and
make the final answer negative. Since and , we have
b.Find the absolute values: and
c.Find the absolute values: and
4
1
5
1
6
177
633
Add their absolute values, 456 and 177, to
get 633. Then make the final answer negative.
456 (177) 633
0 4560 456 0 1770 177
21
6
65
91Add their absolute values, 26 and 65, to
get 91. Then make the final answer negative.26 (65) 91
0 260 26 0 650 65
Add their absolute values, 3 and 5, to get 8.
Then make the final answer negative.3 (5) 8
0 30 3 0 50 5
3 (5) 26 (65) 456 (177)
Self Check 1
Add:
a.
b.
c.
Now TryProblems 19, 23, and 27325 (169)
25 (48)
7 (2)
The Language of Mathematics Two negative integers, as well as two positive
integers, are said to have likesigns.2 Add two integers that have different signs.
To find on a number line, we begin at 0 and draw an arrow 4 units long that
points to the right. This represents positive 4. From the tip of that arrow, we draw a
second arrow, 3 units long, that points to the left. It represents. Since we end up at
1, it follows that 4 (3) 1.3
4 (3)
In terms of money, if you won $4 and then lost $3 , overall, you would have
$1 left.
To find on a number line, we begin at 0 and draw an arrow 4 units long
that points to the left. It represents 4. From the tip of that arrow, we draw a second4 3
(3)
4 (3) 1End− 8 − 7 − 6 − 5 − 4 − 3 − 2 − 1Begin01 2 34 5 6 7 84− 3Success Tip Calculations that you cannot perform in your head should be
shown outside the steps of your solution.