Basic Mathematics for College Students

264 Chapter 3 Fractions and Mixed Numbers

Solution

Alw This is the formula for the area of a rectangle.

Substitute for land for w.

Write and as improper fractions.

Write the improper fraction as a mixed number.

The area of the screen of an Etch-a-Sketch is 28 18 in.^2.

225

 28 8

1

8

28

8  225

 16

65

 64

1

Since there are no common factors to remove,

perform the multiplication in the numerator and in

the denominator. The result is an improper fraction.



225

8

Multiply the numerators.

 Multiply the denominators.

25  9

4  2

 6 41 4 21

25

4



9

2

 6 6 14 4 21

1

4

 4

1

2

EXAMPLE (^8) Government Grants If million is to be split equally
among five cities to fund recreation programs, how much will each city receive?
Analyze

• There is million in grant money. Given


• 5 cities will split the money equally. Given


• How much grant money will each city receive? Find
  Form The key phrase split equallysuggests division.
  We translate the words of the problem to numbers and symbols.

is equal to divided by

 5

SolveTo find the quotient, we will express and 5 as fractions and then use the

rule for dividing two fractions.

Write as an improper fraction, and write 5 as a fraction.

Multiply by the reciprocal of , which is.

Write the improper fraction as a mixed number

by dividing 5 by 2. The units are in millions of dollars.

5

 2 1 2

2

Multiply the remaining factors in the numerator.

 (^) Multiply the remaining factors in the denominator.

5

2

To simplify, factor 25 as 55. Then remove the common

 (^) factor of 5 from the numerator and denominator.

5

1

 5  1

2  5

1

Multiply the numerators.

 (^) Multiply the denominators.

25  1

2  5

1

5

5

 1

25

2



1

5

12 12 21

1

2

 5 

25

2



5

1

12 12

12 

1

2

The amount of

money that each

city will receive (in

millions of dollars)

the number of

cities receiving

money.

the total amount

of grant money

(in millions

of dollars)

The amount of

money that each

city will receive (in

millions of dollars)

$12 12

$12 12

Self Check 8

TV INTERVIEWSAn -minute

taped interview with an actor

was played in equally long

segments over 5 consecutive

nights on a celebrity news

program. How long was each

interview segment?

Now TryProblem 107

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