Equivalent Fractions
Equivalent Fractions
Equivalent fractions are different fractions that represent the same value or the same proportion of a whole. Even though their numerators (top numbers) and denominators (bottom numbers) are different, they cover the same amount.
Look at the shaded areas in these two rectangles.
Both the shaded areas are of the same size.
So \(\frac{1}{4} = \frac{2}{8}\). They are called equivalent fractions.
How to find Equivalent Fractions?
You can find equivalent fractions by performing the same operation (multiplication or division) on both the numerator and the denominator.
The following diagram shows how to find equivalent fractions by multiplying or dividing. Scroll down the page for more examples and solutions.
Fraction Worksheets
Practice with the following worksheets.
Printable & Online Fractions Worksheets
1. Multiplication: Multiply both the numerator and the denominator by the same non-zero number.
Example: To find an equivalent fraction to \(\frac{1}{4}\).
Multiply both numerator and denominator by 2.
\(\frac{1}{4}=\frac{1\times 2}{4\times 2}=\frac{2}{8}\)
You can multiply by any number:
\(\frac{1}{4}=\frac{1\times 3}{4\times 3}=\frac{3}{12}\)
So, \(\frac{1}{4}, \frac{2}{8}\), and \(\frac{3}{12}\) are all equivalent.
2. Division (Simplifying Fractions): Divide both the numerator and the denominator by the same common non-zero factor. This is often used to simplify a fraction to its lowest terms.
Example: To simplify \(\frac{10}{20}\).
Divide both numerator and denominator by 10.
\(\frac{10}{20}=\frac{10\div 10}{20\div 10}=\frac{1}{2}\)
The key rule is: Whatever you do to the top, you must do to the bottom. This ensures that you are essentially multiplying or dividing the fraction by 1 (e.g., \(\frac{2}{2}\) or \(\frac{3}{3}\) ), which doesn’t change its overall value.
Check out this lesson on types of fractions:
Types of Fractions
Check out this lesson on equivalent fractions:
Equivalent Fractions
Check out this lesson on how to convert between mixed numbers and improper fractions:
Mixed Numbers & Improper Fractions
Check out this lesson on how to convert between fractions and decimals:
Fractions & Decimals
Check out these lessons on adding, subtracting, multiplying, and dividing fractions:
Adding Fractions
Subtracting Fractions
Multiplying Fractions
Dividing Fractions
Videos
The following video will explain how to get equivalent fractions and how to reduce fractions in great detail.
Finding Equivalent Fractions
Try out our new and fun Fraction Concoction Game.
Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.
We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.