Basic Mathematics for College Students

Solve application problems by multiplying fractions.

The key word ofoften appears in application problems involving fractions. When a
fraction is followed by the word of,such as of or of,it indicates that we are to find
a part of some quantity using multiplication.

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4

1

2

4

3.2 Multiplying Fractions 225

Self Check 6

Evaluate each expression:

a.

b.

c.

Now TryProblem 43

 a

3

4

b

2

a

3

4

b

2

a

2

5

b

3

EXAMPLE 6

Evaluate each expression: a. b. c.

StrategyWe will write each exponential expression as a product of repeated
factors, and then perform the multiplication. This requires that we identify the base
and the exponent.

WHYThe exponent tells the number of times the base is to be written as a factor.

Solution
Recall that exponents are used to represent repeated multiplication.

a.We read as “one-fourth raised to the third power,” or as “one-fourth,
cubed.”

Since the exponent is 3, write the base,

as a factor 3 times.

b.We read as “negative two-thirds raised to the second power,” or as
“negative two-thirds, squared.”
Since the exponent is 2, write the base,
as a factor 2 times.

c.We read as “the opposite of two-thirds squared.” Recall that if the

symbol is not within the parantheses, it is not part of the base.

Since the exponent is 2, write the base, as

a factor 2 times.

 

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9

Multiply the numerators.

  (^) Multiply the denominators.

2  2

3  3

2

a^23 ,

3

b

2



2

3



2

3

 1232

2



4

9

The product of two fractions with like signs is positive:

Drop the signs. Multiply the numerators. Multiply

the denominators.



2  2

3  3

 32 ,

a

2

3

b

2

a

2

3

ba

2

3

b

1 ^232

2



1

64

Multiply the numerators.

 Multiply the denominators.

1  1  1

4  4  4

1

a^14 ,

4

b

3



1

4



1

4



1

4

1142

3

a

2

3

b

2

a

2

3

b

2

a

1

4

b

3

ƒ T

Self Check 7

HOW A BILL BECOMES LAWIf only

96 Senators are present and cast a

vote, how many of their votes

does it takes to override a

Presidential veto?

Now TryProblems 45 and 87

EXAMPLE (^7) How a Bill Becomes LawIf the President vetoes (refuses
to sign) a bill, it takes of those voting in the House of Representatives (and the
Senate) to override the veto for it to become law. If all 435 members of the House
cast a vote, how many of their votes does it take to override a presidential veto?
Analyze

• It takes ofthose voting to override a veto. Given


• All 435 members of the House cast a vote. Given


• How many votes does it take to override a Presidential veto? Find

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2

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