(b)
Work inside brackets.
Add.
Add the additive inverse.
Work from left to right.= 1 NOW TRY
=- 5 + 6
=- 9 + 4 + 6
=- 9 - 3 - 44 + 6
=- 9 - 3 - 8 + 44 + 6
- 9 - 3 - 8 - 1 - 424 + 6
SECTION 1.2 Operations on Real Numbers 17
NOW TRY
EXERCISE 4
Perform the indicated
operation.
- 4 - 1 - 2 - 72 - 12
–8–7–6–5–4–3–2–1 0 1 2 3 4 5 6 7 8 910
FIGURE 16NOW TRY
EXERCISE 5
Find the distance between the
points and 12.- 7
DistanceThe distancebetween two points on a number line is the absolute value of the
difference between their coordinates.
To find the distance between the points 4 and 7, we subtract Since dis-
tance is always positive (or 0), we must be careful to subtract in such a way that the
answer is positive (or 0). To avoid this problem altogether, we can find the absolute
value of the difference. Then the distance between 4 and 7 is found as follows.
| 7 - 4 |= | 3 |= 3 or | 4 - 7 |= |- 3 |= 3
7 - 4 =3.
Finding Distance Between Points on the Number LineFind the distance between each pair of points. Refer to FIGURE 16.
(a)8 and
Find the absolute value of the difference of the numbers, taken in either order.
,or
(b) and
,or NOW TRY
OBJECTIVE 4 Multiply real numbers.Recall that the answer to a multiplica-
tion problem is called the product.
|- 4 - 1 - 62 | = 2 |- 6 - 1 - 42 |= 2
- 4 - 6
| 8 - 1 - 42 |= 12 |- 4 - 8 |= 12
- 4
EXAMPLE 5
Multiplying Real NumbersSame sign The product of two numbers with the samesign is positive.
Different signs The product of two numbers with differentsigns is negative.
OBJECTIVE 3 Find the distance between two points on a number line.
The number line in FIGURE 16shows several points.
NOW TRY ANSWERS
4.- 7 5. 19