Basic Mathematics for College Students

252 Chapter 3 Fractions and Mixed Numbers

Fill in the blanks.

1. Because the denominators of and are the same
   number, we say that they have a
   denominator.


2. The common denominator for a set of
   fractions is the smallest number each denominator
   will divide exactly (no remainder).


3. Consider the solution below. To an equivalent
   fraction with a denominator of 18, we multiply by a
   1 in the form of.


4. Consider the solution below. To the fraction
   we factor 15 and 27, and then remove the common
   factor of 3 from the and the
   .

Fill in the blanks.

5. To add (or subtract) fractions that have the same
   denominator, add (or subtract) their and
   write the sum (or difference) over the
   denominator. the result, if possible.


6. To add (or subtract) fractions that have different
   denominators, we express each fraction as an
   equivalent fraction that has the for its
   denominator. Then we use the rule for adding
   (subtracting) fractions that have the
   denominator.


7. When adding (or subtracting) two fractions with
   different denominators, if the smaller denominator is
   a factor of the larger denominator, the
   denominator is the LCD.

CONCEPTS



5

9

15

27



3

1

 5

3

1

 3  3

15

27 ,



8

18

4

9



4

9



2

2

4

9

7

8

3

8

VOCABULARY 8.Write the subtraction as addition of the opposite:

9. Consider By what form of 1 should we multiply the
   numerator and denominator to express it as an
   equivalent fraction with a denominator of 36?


10. The denominatorsof two fractions are given. Find the
    least common denominator.
    a. 2 and 3 b. 3 and 5
    c. 4 and 8 d. 6 and 36


11. Consider the following prime factorizations:

For any one factorization, what is the greatest number

of times

a. a 5 appears?

b. a 3 appears?

c. a 2 appears?

12. The denominatorsof two fractions have their prime-
    factored forms shown below. Fill in the blanks to find
    the LCD for the fractions.


13. The denominatorsof three fractions have their prime-
    factored forms shown below. Fill in the blanks to find
    the LCD for the fractions.


14. Place a or symbol in the blank to make a true
    statement.

a.

b. 

11

17



13

17

31

35

32

35

 

¶LCD     

20  2  2  5

30  2  3  5

90  2  3  3  5

fLCD    

20  2  2  5

30  2  3  5

90  2  3  3  5

24  2  2  2  3

3

4.



1

8

a

5

8

b

SECTION 3.4 STUDY SET