SECTION 1.5 Adding and Subtracting Real Numbers^37
OBJECTIVES
Adding and Subtracting Real Numbers
1.5
1 Add two numbers
with the same sign.
2 Add two numbers
with different signs.
3 Use the definition
of subtraction.
4 Use the rules for
order of operations
with real numbers.
5 Translate words and
phrases involving
addition and
subtraction.
6 Use signed numbers
to interpret data.OBJECTIVE 1 Add two numbers with the same sign. Recall that the answer
to an addition problem is called a sum.A number line can be used to add real
numbers.
Adding Numbers on a Number LineUse a number line to find each sum.
(a)
Step 1 Start at 0 and draw an arrow 2 units to the right. See FIGURE 12.
Step 2 From the right end of that arrow, draw another arrow 3 units to the right.
The number below the end of this second arrow is 5, so 2+ 3 =5.
2 + 3
EXAMPLE 1
–2 –1 0 1 2 3 4 5 62 32 3 5
FIGURE 12(b)
(We put parentheses around due to the and next to each other.)
Step 1 Start at 0 and draw an arrow 2 units to the left. See FIGURE 13.
Step 2 From the left end of the first arrow, draw a second arrow 4 units to the left
to represent the addition of a negativenumber.
The number below the end of this second arrow is -6,so - 2 + 1 - 42 =-6.
- 4 + -
- 2 + 1 - 42
–2–7 –6 –5 –4 –3 –2 –1 0 1–4 2 (4) 6
FIGURE 13 NOW TRYIn Example 1(b),the sum of the two negative numbers and is a negative
number whose distance from 0 is the sum of the distance of from 0 and the dis-
tance of from 0. That is, the sum of two negative numbers is the negative of the
sum of their absolute values.
- 2 + 1 - 42 =- 1 |- 2 |+ |- 4 | 2 =- 12 + 42 =- 6
- 4
- 2
- 2 - 4
NOW TRY
EXERCISE 1
Use a number line to find
each sum.
(a) 3 + 5 (b) - 1 + 1 - 32
NOW TRY ANSWERS
- (a) 8 (b)- 4