Page 412 - Basic College Mathematics with Early Integers

S E C T I O N 5.4 I LENGTH: U.S. AND METRIC SYSTEMS OF MEASUREMENT 389

Objective Performing Operations on U.S. System
Units of Length

Finding sums or differences of measurements often involves converting units, as
shown in the next example. Just remember that, as usual, only like units can be
added or subtracted.

Example 6 Add 3 ft 2 in. and 5 ft 11 in.
PRACTICE 6
Solution: To add, we line up the similar units. Add 4 ft 8 in. to 8 ft 11 in.
3 ft 2 in.
+ 5 ft 11 in.
8 ft 13 in.
Since 13 inches is the same as 1 ft 1 in., we have

8 ft 13 in.=8 ft+1 ft 1 in.
=9 ft 1 in.

Work Practice 6

Concept Check How could you estimate the following sum?
7 yd 4 in.
+ 3 yd 27 in.

Example 7 Multiply 8 ft 9 in. by 3. PRACTICE 7
Multiply 4 ft 7 in. by 4.
Solution: By the distributive property, we multiply 8 ft by 3 and 9 in. by 3.
8 ft 9 in.
* 3
24 ft 27 in.
Since 27 in. is the same as 2 ft 3 in., we simplify the product as

24 ft 27 in.=24 ft+2 ft 3 in.
=26 ft 3 in.

Work Practice 7

We divide in a similar manner as above.

Example 8 Finding the Length of a Piece of Rope PRACTICE 8
A carpenter cuts 1 ft 9 in. from
A rope of length 6 yd 1 ft has 2 yd 2 ft cut from one end. Find the length of the
a board of length 5 ft 8 in. Find
remaining rope.
the length of the remaining
board.
Solution: Subtract 2 yd 2 ft from 6 yd 1 ft.
beginning length : 6 yd 1 ft Answers

- amount cut : - 2 yd 2 ft 6. 13 ft 7 in. 7. 18 ft 4 in.
remaining length 8. 3 ft 11 in.
We cannot subtract 2 ft from 1 ft, so we borrow 1 yd from the 6 yd. One yard is Concept Check Answer
converted to 3 ft and combined with the 1 ft already there. round each to the nearest yard:
Continued on next page 7 yd + 4 yd = 11 yd