How to tell if fractions are equivalent
1) Simplify all fractions. If they “reduce” to be the same fraction, then the
fractions are equivalent.
2) Cross multiply. We do this by making a “heart” shape. If the two products
are equal, then the fractions are equivalent.
3) Get a common denominator and compare numerators.
Example: Find out if the fractions
6
10
and
are equivalent.
15
50
Way #1: Simplify both fractions completely:
6 2 • 3/ 2
=
=
15 5 • 3/ 5
Reduce to different numbers:
10 2 • 5/
2/ • 1 1
=
=
=
Not Equivalent!
50 10 • 5/ 2/ • 5 5
Way #2: Cross multiply:
6 10
?
15 50
50 • 6 10 • 15
300
150
Different product:
Not Equivalent!
Way #3: Get a common denominator between both fractions:
Numerators are different:
Not Equivalent!
6 10 60
• =
15 10 150
10 3 30
• =
50 3 150