As you can see from the number line, many fractions can have the same value. Different fractions with the same value are called equivalent fractions.

Since and share a spot on the number line, they are equivalent, or equal to the same value.

Find equivalent fractions by multiplying the numerator and denominator by the same number

The following fractions are all equivalent to :

You could continue this pattern and find an infinite number of equivalent fractions. (However, that doesn't sound like much fun, so let’s stop here.)

It's often helpful to convert fractions to a particular denominator

1. Find the number you need to multiply with the original denominator to get the new denominator
2. Then multiply the numerator by that same number

For example, let's think about the number 1. Any whole number can be written as a fraction with a denominator of 1, so the number 1 can also be written as . If we multiply both the numerator and denominator by a common number, we can find boatloads of equivalent fractions.

Equivalent Fractions Practice:

Equivalent Fractions Example 1

Write  as a fraction with a denominator of .
To make the denominator 30, we have to multiply  That means we must also multiply the numerator by

Equivalent Fractions Example 2

Write as a fraction with denominator of .
To make the denominator 24, we must multiply  So, that means we must also multiply the numerator by

Equivalent Fractions Example 3

Since  we must also multiply the numerator by .

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Equivalent Fractions Exercise 1

Write  as a fraction with a denominator of .

Hint

Answer

Equivalent Fractions Exercise 2

Write as a fraction with a denominator of .

Hint

Answer

Equivalent Fractions Exercise 3

Hint

Answer

Equivalent Fractions Exercise 4

Use the number line to find fractions equivalent to

Answer

Equivalent Fractions Exercise 5

Use the number line to find fractions equivalent to

Answer

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