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Fractions & Decimals

Fractions & Decimals

At a Glance - Equivalent Fractions

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.

1234568 number line

Since 1/4 and 2/8 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 2/3:

2/3 x 2/2 = 4/6 

2/3 x 3/3 = 6/9

2/3 x 4/4 = 8/12

2/3 x 5/5 = 10/15

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 1/1. If we multiply both the numerator and denominator by a common number, we can find boatloads of equivalent fractions.

1 = 1/1 ...

Equivalent Fractions Example 1

Write 2/5 as a fraction with a denominator of 30.

Equivalent Fractions Example 2

Write as a fraction with denominator of .

Equivalent Fractions Example 3

Equivalent Fractions Exercise 1

Write 5/6 as a fraction with a denominator of 18.

Equivalent Fractions Exercise 2

Write 3/8 as a fraction with a denominator of 32.

Equivalent Fractions Exercise 3

Equivalent Fractions Exercise 4

1234568 number line

Use the number line to find fractions equivalent to 1/2

Equivalent Fractions Exercise 5

Use the number line to find fractions equivalent to 3/4

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