Basic Mathematics for College Students

Chapter 3 Summary and Review 297

There are four special fraction forms that

involve 0 and 1.

Each of these fractions is a form of 1:

1  ...

1

1



2

2



3

3



4

4



5

5



6

6



7

7



8

8



9

9



Simplify each fraction:

is undefined

20

20

 1

5

1

 5

7

0

0

8

 0

Two fractions are equivalentif they represent

the same number. Equivalent fractions

represent the same portion of a whole.

, , and are equivalent fractions. They represent the same shaded

portion of the figure.

(^2) –
3 =
(^4) –
6 =
––^8
12
8
12
4
6
2
3
To build a fraction,we multiply it by a factor of
1 in the form 22 ,^33 ,^44 ,^55 ,and so on.
Write as an equivalent fraction with a denominator of 36.
1
We must multiply the denominator of by 9 to obtain a
denominator of 36. It follows that should be the form
of 1 that is used to build.
(^2736) is equivalent to. (^34)



27

36

Multiply the numerators.

 Multiply the denominators.

3  9

4  9

3

4

9

9

3

3 4

4



3

4



9

9

3

4

A fraction is in simplest form,or lowest terms,

when the numerator and denominator have no

common factors other than 1.

Is in simplest form?

The factors of the numerator, 6, are: 1 , 2 ,3,6.

The factors of the denominator, 14, are: 1 , 2 ,7,14.

Since the numerator and denominator have a common factor of 2, the

fraction is 146 notin simplest form.

6

14

To simplify a fraction,we write it in simplest

form by removing a factor equal to 1:

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.

1

1

Simplify:

Prime factor 12 and 30.

Since 2 and 5 have no common factors other than 1, we say that is in

simplest form.

2

5

Multiply the remaining factors in the numerator:

1  2  1 2.

Multiply the remaining factors in the denominator:

1  1  5 5.



2

5

Remove the common factors of 2 and 3

 from the numerator and denominator.

2

1

 2  3

1

2

1

 3

1

 5

12

30



2  2  3

2  3  5

12

30

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

Proper fractions: and Proper fractions are less than 1.

Improper fractions: and

Improper fractions are greater

than or equal to 1.

15

15

3

2

,

41

16

,

999

1,000

1

5

,

7

8

,