Equivalent Fractions: Simplifying And Building With Answers
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
163.2 Equivalent Fractions: Simplifying and Building
Two fractions are said to be equivalent if they have the same value. Naturally, one approach we
could use to determine if two fractions are equivalent is to convert each fraction to a decimal. For
3
15
3
15
= 0.6 and
= 0.6 , the fractions
example, since
and
are equivalent, and we could
5
25
5
25
3
15
=
write
. Alternatively, consider the following forms of the number 1:
5
25
2
3
4
100
n
1 =
=
=
= ... =
=
2
3
4
100
n
Clearly 2 parts out of 2 is equal to 1, as is 100 parts out of 100, or n parts out of n. Now consider
the following property (the Fundamental Property of Fractions):
a
a • c
=
If a, b, and c are nonzero:
b
b • c
This statement is saying if both the numerator and denominator of a fraction have the same factor
(called a common factor), then that factor can be eliminated resulting in an equivalent fraction.
a
a
c
a • c
a
c
=
=
It is true because
•
, so we are multiplying the fraction
by
(a form of 1) to
b
b
c
b • c
b
c
a • c
result in the fraction
. Recall that multiplying a number by 1 does not change its value (the
b • c
3
15
Identity Property of Multiplication). Using our fractions
and
, note that:
5
25
15
3 • 5
3
=
=
25
5 • 5
5
15
3
15
3
=
Thus
and
are equivalent fractions, or
.
25
5
25
5
145
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education