Equivalent Fractions & Mixed Numbers
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22-9 Equivalent Fractions & Mixed Numbers
Equivalent Fractions:
Different fractions can name the same number. Equivalent fractions are
different expressions for the same nonzero number.
3
6
15
=
=
5
10
25
To create fractions equivalent to a given fraction, multiply or divide the numerator and denominator by
the same number.
14
Example: List two equivalent fractions of
: ________________________
16
Simplest Form:
A fraction is in simplest form when the numerator and denominator are relatively
prime. Relatively prime numbers have no common factors other than 1.
Example: Write the fractions in simplest form
18
15
=
=
___________
___________
24
45
Determining whether fractions are equivalent:
Method 1: To determine if two fractions are equivalent, find a common denominator and compare the
numerators.
6
20
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Both fractions can be written with a denominator of 50.
10
25
6
20
The numerators are ___________, so the fractions are ______________.
=
=
10
50
25
50
Method 2: Simplify each fraction and compare.
4
28
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Find the simplest form of each fraction.
6
42
4
28
The fractions are ____________________.
=
=
6
42
Method 3: You can use cross products to determine if two fractions are equivalent.
8
12
?
8 • 15
10 • 12
8
12
10
15
120
and
are equivalent. Their cross products are equal.
120
10
15
9
2
?
_________
_________
9
2
and
are _______________________________.
15
3
15
3
_________
_________
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