How to figure out if fractions are equivalent

Why are they the same? Because when you multiply or divide both the top and bottom by the same number, the fraction keeps it's value.

The rule to remember is:

"Change the bottom using multiply or divide,
And the same to the top must be applied"

Here is why those fractions are really the same:

See Fractions on the Number Line ...

Also see the Chart of Fractions with many examples of equivalent fractions.

Dividing

Here are some more equivalent fractions, this time by dividing:

 ÷ 3 ÷ 6 

Choose the number you divide by carefully, so that the results (both top and bottom) stay whole numbers.

If we keep dividing until we can't go any further, then we have simplified the fraction (made it as simple as possible).

Summary:

• You can make equivalent fractions by multiplying or dividing both top and bottom by the same amount.
• You only multiply or divide, never add or subtract, to get an equivalent fraction.
• Only divide when the top and bottom stay as whole numbers.

Introduction to Fractions Fraction Number Line Fraction/Decimal Chart Simplifying Fractions Adding Fractions Subtracting Fractions Fractions Index

Equivalent fractions are fractions that represent the same value, even though they look different. For example, if you have a cake, cut it into two equal pieces, and eat one of them, you will have eaten half the cake. If you cut a cake into eight equal pieces and eat four of them, you will still have eaten half the cake. These are equivalent fractions. This section explains equivalent fractions in more detail.

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Find equivalent fractions. Enter a fraction, mixed number or integer to get fractions that are equivalent to your input. Example entries:

• Fraction - like 2/3 or 15/16
• Mixed number - like 1 1/2 or 4 5/6
• Integer - like 5 or 28

What are Equivalent Fractions?

Equivalent fractions are fractions with different numbers representing the same part of a whole. They have different numerators and denominators, but their fractional values are the same.

For example, think about the fraction 1/2. It means half of something. You can also say that 6/12 is half, and that 50/100 is half. They represent the same part of the whole. These equivalent fractions contain different numbers but they mean the same thing: 1/2 = 6/12 = 50/100

How to Find Equivalent Fractions

Multiply both the numerator and denominator of a fraction by the same whole number. As long as you multiply both top and bottom of the fraction by the same number, you won't change the value of the fraction, and you'll create an equivalent fraction.

Example Equivalent Fractions

Find fractions equivalent to 3/4 by multiplying the numerator and denominator by the same whole number:

\( \dfrac{3}{4} \times \dfrac{2}{2} = \dfrac{6}{8} \)

\( \dfrac{3}{4} \times \dfrac{3}{3} = \dfrac{9}{12} \)

\( \dfrac{3}{4} \times \dfrac{4}{4} = \dfrac{12}{16} \)

\( \dfrac{3}{4} \times \dfrac{5}{5} = \dfrac{15}{20} \)

\( \dfrac{3}{4} \times \dfrac{6}{6} = \dfrac{18}{24} \)

Therefore these are all equivalent fractions:

\( \dfrac{3}{4} = \dfrac{6}{8} = \dfrac{9}{12} = \dfrac{15}{20} = \dfrac{18}{24} \)

Note that if you reduce all of these fractions to lowest terms, they equal 3/4.

For additional fraction help see our Fractions Calculator, Simplify Fractions Calculator and Mixed Numbers Calculator.