Adding And Subtracting Equivalent Fractions: Step-by-Step Guide With Examples

Are you struggling with adding and subtracting equivalent fractions?

Don’t worry, you’re not alone. Many people find working with fractions challenging , but with a little practice, you can master this essential skill.

To start, let’s review some basic terminology.

A fraction is a number that represents a part of a whole. It is made up of two parts: the numerator and the denominator.


The numerator represents the number of parts you have, while the denominator represents the total number of parts in the whole.

Equivalent fractions are fractions that have the same value but are written differently.

For example, \frac{1}{2} and \frac{2}{4} are equivalent fractions because they both represent one-half of a whole.

Understanding Equivalent Fractions

Equivalent fractions are fractions that have the same value, but are represented differently. They have different numerators and denominators, but when simplified, they are the same fraction.

For example, \frac{1}{2} and \frac{2}{4} are equivalent fractions because they represent the same amount, half of a whole.

Read more about the basics about equivalent fractions here .

Adding Equivalent Fractions: Example

When adding or subtracting fractions both fractions need to have the same denominator for ease of adding or subtracting the numerator.

Therefore, to convert fractions into the same denominator you need to find their equivalent fraction.

For example, to add \frac{1}{2} + \frac{1}{5} , you need to find a common denominator between the denominators 2 and 5 . Currently, the denominators are different.

To find the common denominator you can use for both fractions you need to find the lowest common denominator between both 2 and 5 .

To do this write a list of all the multiples of both 2 and 5 :

\{2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ... \} \\ \{ 5, 10, 15, 20 ... \}

From both sets of numbers identify the numbers that are the same:

\{2, 4, 6, 8, \fcolorbox{red}{yellow}{10}, 12, 14, 16, 18, \fcolorbox{red}{lightyellow}{20} ... \} \\ \{ 5, \fcolorbox{red}{yellow}{10}, 15, \fcolorbox{red}{lightyellow}{20} ... \}

As you can see from the highlighted numbers above both sets share the numbers 10, 20 , with the smallest of those numbers being the number 10 .

Therefore, to perform the addition of both fractions they both need to be converted into their equivalent form by multiplying the numerator and denominator by the same number that helps to get the denominator to the number 10 .

\frac{1}{2} = \frac{1 \times 5}{2 \times 5} = \frac{5}{10}
\frac{1}{5} = \frac{1 \times 2}{5 \times 2} = \frac{2}{10}

Once the fractions have their equivalent form with the same denominator the operation of addition or subtraction between the numerators can proceed easily:

\frac{5}{10} + \frac{2}{10} = \frac{5 + 2}{10} = \frac{7}{10}

Therefore, \frac{1}{2} + \frac{1}{5} = \frac{7}{10} .

Understanding equivalent fractions is essential when adding and subtracting fractions to change the fractions into their equivalent form by getting the denominators to the same value. Once this is achieved, it is a simple matter of then adding (or subtracting) the numerators together.

You can learn more about adding fractions here .

Subtracting Equivalent Fractions: Example

In the same way you handle the addition of fractions you can similarly do so with subtraction.

Suppose you need to subtract the following: \frac{3}{5} - \frac{1}{3} .

In the same fashion you handled adding fractions, you can similarly apply the same steps with subtracting fractions.

The first thing you need to obtain is the same denominator with both fractions. Therefore, find the multiples of both 5 and 3 .

\{ 5, 10, 15, 20, 25, 30, ... \} \\ \{3, 6, 9, 12, 15, 18, 21, 24, 27, 30,... \}

From the two lists identify a number that is common to both lists and choose the smallest:

\{ 5, 10, \fcolorbox{red}{yellow}{15}, 20, 25, \fcolorbox{red}{lightyellow}{30}, ... \} \\ \{3, 6, 9, 12, \fcolorbox{red}{yellow}{15}, 18, 21, 24, 27, \fcolorbox{red}{lightyellow}{30},... \}

From the multiples above the common numbers shared between both lists were 15 and 30 . The smallest of these is 15 .

Therefore, to operate on the two fractions you need to obtain their equivalent form such that their fractions contain the denominator 15 . Here’s the equivalent fraction for both:

\frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15}
\frac{1}{3} = \frac{1 \times 5}{3 \times 5} = \frac{5}{15}

Once you’ve achieved the same denominator by finding their equivalent form you can perform the necessary subtraction:

\frac{9}{15} - \frac{5}{15} = \frac{9 - 5}{15} = \frac{4}{15}

To find out more about how to subtract fractions click here.

Adding Or Subtracting Equivalent Fractions Summary

By understanding the concept of equivalent fractions, you can easily add and subtract fractions with different denominators.

To add or subtract equivalent fractions, you need to find the lowest common denominator (LCD), which is the smallest multiple of the denominators of the fractions you are adding or subtracting. Once you have found the LCD, you can convert the fractions to equivalent fractions with the same denominator and then add or subtract the numerators.

In summary, adding and subtracting equivalent fractions involves finding the LCD, converting the fractions to equivalent fractions with the same denominator, adding or subtracting the numerators, and simplifying the answer to its lowest terms.

With practice, you will become more comfortable with adding and subtracting equivalent fractions. Keep practicing and soon you will be able to do it quickly and easily!