Basic Mathematics for College Students

238 Chapter 3 Fractions and Mixed Numbers

Analyze

• The surfboard is to have a -inch-thick fiberglass finish. Given


• Each layer of fiberglass is of an inch thick. Given


• How many layers of fiberglass need to be applied? Find
  Form Think of the -inch-thick finish separated into an unknown number of
  equally thick layers of fiberglass. This indicates division.
  We translate the words of the problem to numbers and symbols.

is equal to divided by

The number of

layers of fiberglass 

that are needed

SolveTo find the quotient, we will use the rule for dividing two fractions.

Multiply by the reciprocal of which is

Any whole number divided by 1 is the same number.

StateThe number of layers of fiberglass needed is 6.

CheckIf 6 layers of fiberglass, each of an inch thick, are used, the finished

thickness will be of an inch. If we simplify we see that it is equivalent to the

desired finish thickness:

The result checks.

6

16



2

1

 3

2

1

 8



3

8

6

16 ,

6

16

1

16

 6

Multiply the remaining factors in the numerator.

 (^) Multiply the remaining factors in the denominator.

6

1

To simplify, factor 16 as 2 8. Then remove the common

 (^) factor of 8 from the numerator and denominator.

3  2  8

1

8

1

 1

Multiply the numerators.

Multiply the denominators.



3  16

8  1

16

1.

1

16 ,

3

(^8)

3

8



1

16



3

8



16

1

1

16



3

8

the thickness

of 1 layer of

fiberglass.

the thickness

of the finish

The number of

layers of fiberglass

that are needed

3

8

1

16

3

8

Self Check 7

COOKINGA recipe calls for

4 cups of sugar, and the only

measuring container you have

holds cup. How many cups of

sugar would you need to add to

follow the recipe?

Now TryProblem 77

1

3

1

3

1. a. 35 b. 56 c. 81 2.^1621 3.^52 4. 44 5. 47 6. 165 7. 12

ANSWERS TO SELF CHECKS