Basic Mathematics for College Students

Chapter 3 Summary and Review 301

The sign rules for dividing fractionsare the
same as those for multiplying fractions.

Divide and simplify:

Multiply by the reciprocal of ,

which is.

Multiply the remaining factors in the

numerator: 1  3  1 3.

Multiply the remaining factors in the

denominator: 16  1 16.



3

16

To simplify, factor 9 as 3 3. Then

remove the common factor of 3 from

the numerator and denominator.



3

1

 3  1

16  3

1

Multiply the numerators.

Multiply the denominators.

Since the fractions have unlike signs,

make the answer negative.



9  1

16  3

 31

169 ^3

9

16

(3)

9

16

a

1

3

b

9

16

(3)

Problems that involve forming equal-sized
groupscan be solved by division.

SEWING How many Halloween costumes, which require yard of

material, can be made from 6 yards of material?

Since 6 yards of material is to be separated into an unknown number

of equal-sized -yard pieces, division is indicated.

Write 6 as a fraction:.

Multiply by the reciprocal of , which is.

Any number divided by 1 is the same number.

The number of Halloween costumes that can be made from 6 yards of

material is 8.

 8

Multiply the remaining factors in the numerator.

 Multiply the remaining factors in the denominator.

8

1

To simplify, factor 6 as 2 3. Then

remove the common factor of 3 from

the numerator and denominator.



2  3

1

 4

1  3

1

Multiply the numerators.

 Multiply the denominators.

6  4

1  3

4

3

3

4

6

1

6 ^61

6 

3

4



6

1



4

3

3

4

3

4

39. Find the reciprocal of each number.

a.

b.

c. 5

d.

40. Fill in the blanks: To divide two fractions,
    the first fraction by the of the second
    fraction.

8

7



11

12

1

8

Divide. Simplify the quotient, if possible.

41. 
    
    
    
    42. 
        
    
    
    
    


42. 
    
    
    
    44. 
        
    
    
    
    


43. 
    
    
    
    46. 
        
    
    
    
    


44. 
    
    
    
    48. 
        
    
    
    
    


45. MAKING JEWELRY How many -ounce silver
    angel pins can be made from a -ounce bar of
    silver?


46. SEWING How many pillow cases, which require
    yard of material, can be made from 20 yards of
    cotton cloth?

2

3

3

4

1

16

7

15



7

15

2

3

(120)

4

5



1

2



3

8



1

4

54 

63

5



39

25

a

13

10

b



7

32



1

4

1

6



11

25

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