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## Equivalent Fractions

#### Introduction

Equivalent fractions are fractions that are equal. In order to determine if one fraction is equal or equivalent to another, both fractions must first be simplified if needed.

#### Terms

- Fractions are used when using numbers to express parts of whole.
- a fraction expressed in its lowest terms.

## Lesson

To determine if a fraction is equivalent to another, we need to compare the two fractions in their simplest form. So if we are given and , we can see that is in its simplest form, but can be further reduced to by dividing the top and bottom by 2.

Therefore and are equivalent fractions.

Similarly, if we are given and , we first simplify both fractions.

We can now see that is NOT equivalent to , because is not equivalent to

To find the equivalent of a fraction when we are given either the numerator or denominator is similar to expressing a fraction in higher terms. If we are told to solve the following problem:

>we can determine that in order for the new numerator to equal 15, the original numerator must be multiplied by 5. So we multiply the denominator by 5 as well, and get the answer

## Examples

#### Equivalent Fractions (Example #1)

Are these fractions equivalent?
and
First, write each fraction in lowest terms
The greatest common divisor of and is 1, so is already in lowest terms
can be reduced, since is a factor of both and :
The fraction is now in lowest terms
is equal to

#### Make Equivalent Fraction (Example #1)

Find the value of the denominator that makes the following fractions equivalent
We have to multiply the first numerator (6) by 0 to get the second numerator (3)
To make an equivalent fraction, we need to multiply the denominator by 0 as well

#### Equivalent Fractions (Example #2)

Are these fractions equivalent?
and
First, write each fraction in lowest terms
The greatest common divisor of and is 1, so is already in lowest terms
The greatest common divisor of and is 1, so is already in lowest terms
is not equal to

#### Make Equivalent Fraction (Example #2)

Find the value of the denominator that makes the following fractions equivalent
We have to multiply the first numerator (3) by 1 to get the second numerator (3)
To make an equivalent fraction, we need to multiply the denominator by 1 as well