Basic Mathematics for College Students

Chapter 3 Summary and Review 299

Multiplying signed fractions

The product of two fractions with the same
(like) signs is positive. The product of two
fractions with different (unlike) signs is
negative.

Multiply and simplify, if possible:

Multiply the remaining factors in the

numerator: 1 1 1.

Multiply the remaining factors in the

denominator: 1 2  1  3  3 18.



1

18

Prime factor 4 and 27. Then simplify, by

removing the common factors of 2 and

3 from the numerator and denominator.



3

1

 2

1

2

1

 2  3

1

 3  3

Multiply the numerators.

Multiply the denominators.

Since the fractions have unlike signs,

make the answer negative.

 

3

4



2

27



3  2

4  27



3

4



2

27

The base of an exponential expressioncan be a
positive or a negative fraction.

The rule for multiplying two fractions can be
extended to find the product of three or more
fractions.

Evaluate:

Write the base, , as a factor 3 times.

 This fraction is in simplified form.

8

27

Multiply the numerators.

 Multiply the denominators.

2  2  2

3  3  3

2

a 3

2

3

b

3



2

3



2

3



2

3

a

2

3

b

3

When a fraction is followed by the wordof,it
indicates that we are to find a part of some
quantity using multiplication.

To find of 35, we multiply:

The word ofindicates multiplication.

Write 35 as a fraction:.

Any number divided by 1 is

 (^14) equal to that number.
Multiply the remaining factors in the
 numerator and in the denominator.

14

1

Prime factor 35. Then simplify by

removing the common factor of 5 from

the numerator and denominator.



2  5

1

 7

5

1

 1

Multiply the numerators.

 Multiply the denominators.

2  35

5  1

 35 ^351

2

5



35

1

2

5

of 35 

2

5

 35

2

5

The formula for the area of a triangle

Area of a triangle  (base)(height)

or

h

b

A

1

2

bh

1

2

Find the area of the triangle shown on the right.

A (base)(height)

 ( 8 )( 5 )

 Write 5 and 8 as fractions.

The area of the triangle is 20 ft^2.

 20

Prime factor 8. Then simplify, by

removing the common factor of 2 from

the numerator and denominator.



1  5  2

1

 2  2

2

1

 1  1

Multiply the numerators.

 Multiply the denominators.

1  5  8

2  1  1

1

2

a

5

1

ba

8

1

b

Substitute 8 for the base

and 5 for the height.

1

2

1

2 5 ft

8 ft