Equivalent fractions

In order to understand the information on this page, it can be helpful to already know: Fractions Multiply Fractions Factors and Multiples

Outline

Equivalent fractions proportions expressed as one fraction to be expressed with a different fraction of the same value. For example $\frac{1}{3}$ is equal in value to $\frac{2}{6}$ as shown below:

Arithmetically, this is achieved by multiplying the fraction by a fraction that has the same numerator and denominator (so is equal to 1). In this case, we multiply by $\frac{2}{2}$:

${\frac {1}{3}}\times {\frac {2}{2}}={\frac {1\times 2}{3\times 2}}={\frac {2}{6}}$

Graphically, this represents all pieces (the denominator) including the shaded pieces (the numerator) into two pieces each. This gives twice as many pieces in total (six) and twice as many pieces shaded (two).

Worked Examples

Sample question:

Express $\frac{2}{3}$ as twelfths (ie. as a fraction over 12)

Solution:

To convert thirds into twelfths, each piece must be divided into four because $3 \times 4 = 12$. We can achieve this by multiplying the original fraction by $\frac{4}{4}$

${\frac {2}{3}}\times {\frac {4}{4}}={\frac {2\times 4}{3\times 4}}={\frac {8}{12}}$

This shows that $\frac{2}{3}$expressed as twelfths is $\frac{8}{12}$ This can be confirmed visually using the diagram below:

Practice

You can practice skills in percent using the following references:

Khan Academy

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• Equivalent fractions (with diagrams)

Application

Equivalent fractions are used whenever objects or quantities can be broken down into different sized parts. Equivalent fractions can help you to work out how many pieces you would need for each different size to get the same total amount.

For example:

• Cutting food (such as cake) into a different number of equal pieces.

Next Steps

Comfortable with Equivalent Fractions? Check out the follow-on mathematics you can now do:

• Percent
• add fractions
• Lowest Common Denominator (fractions)