Basic Mathematics for College Students

(Nandana) #1
Use the following steps to simplify a fraction.

Simplifying Fractions

To simplify a fraction,remove factors equal to 1of the form and so
on, using the following procedure:


  1. Factor (or prime factor) the numerator and denominator to determine their
    common factors.

  2. Remove factors equal to 1 by replacing each pair of factors common to the
    numerator and denominator with the equivalent fraction

  3. Multiply the remaining factors in the numerator and in the denominator.


Negative fractions are simplified in the same way as positive fractions. Just
remember to write a negative sign in front of each step of the solution. For example,
to simplify we proceed as follows:

ANSWERS TO SELF CHECKS


  1. a.numerator: 7; denominator: 9 b.numerator: 21; denominator: 20 2. a. b.

  2. a. 1 b. 51 c.undefined d. 0 4. 5. 6. a.yes b.no 7. a. b.

  3. a.^59 b.in simplest form9.^94


1
3
2
5
30
3
15
24

20
31
11
31




5


11





15


33





3


1
 5
3
1

 11


^1533


1
1.

2


2


,


3


3


,


4


4


,


5


5


,


216 Chapter 3 Fractions and Mixed Numbers


Fill in the blanks.


  1. A describes the number of equal parts of a
    whole.

  2. For the fraction the is 7 and the
    is 8.

  3. If the numerator of a fraction is less than its
    denominator, the fraction is called a fraction.
    If the numerator of a fraction is greater than or equal
    to its denominator it is called an fraction.

  4. Each of the following fractions is a form of.


...


  1. Two fractions are if they represent the
    same number.

  2. fractions represent the same portion of a
    whole.


1


1





2


2





3


3





4


4





5


5





6


6





7


7





8


8





9


9





7
8 ,

VOCABULARY 7. Writing a fraction as an equivalent fraction with a
larger denominator is called the fraction.


  1. A fraction is in form, or lowest terms, when
    the numerator and denominator have no common
    factors other than 1.

  2. What concept studied in this
    section is shown on the right?

  3. What concept studied in this section does the
    following statement illustrate?


...

1


2





2


4





3


6





4


8





5


10





CONCEPTS


SECTION 3.1 STUDY SET

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