Equivalent fractions
Theory
Equivalent fractions name the same amount written with a different numerator and denominator. Multiply or divide the top and bottom by the same number to build them, and reduce to simplest form when the parts share a common factor.
Equivalent fractions are fractions that name the same amount, such as \(\dfrac{1}{2}\) and \(\dfrac{2}{4}\).
Multiplying the numerator and denominator by the same number makes an equivalent fraction: \(\dfrac{1}{2}=\dfrac{1\times2}{2\times2}=\dfrac{2}{4}\).
Dividing the numerator and denominator by a common factor also keeps the value. A fraction is in simplest form when the top and bottom share no factor other than \(1\).
To simplify, divide the numerator and denominator by a common factor until only \(1\) is left in common.
| Fraction | Divide by | Simplest form |
|---|---|---|
| \(\dfrac{2}{4}\) | \(2\) | \(\dfrac{1}{2}\) |
| \(\dfrac{6}{8}\) | \(2\) | \(\dfrac{3}{4}\) |
| \(\dfrac{4}{6}\) | \(2\) | \(\dfrac{2}{3}\) |
| \(\dfrac{2}{10}\) | \(2\) | \(\dfrac{1}{5}\) |
How to make and simplify equivalent fractions
- To build up, multiply the numerator and denominator by the same number.
- To simplify, divide the numerator and denominator by a common factor.
- Check the fraction is in simplest form when no factor above \(1\) is shared.
The denominator \(3\) is multiplied by \(2\) to make \(6\).
| \(\dfrac{2}{3}\) | \(=\) | \(\dfrac{4}{6}\) |
Divide the top and bottom by the common factor \(2\).
| \(\dfrac{6}{8}\) | \(=\) | \(\dfrac{3}{4}\) |
The numerator \(3\) is multiplied by \(2\) to make \(6\).
| \(\dfrac{3}{4}\) | \(=\) | \(\dfrac{6}{8}\) |
\(\dfrac{2}{4}\) and \(\dfrac{3}{6}\) both equal \(\dfrac{1}{2}\). \(\dfrac{2}{5}\) is not a half, as \(5\) is not double \(2\).
Common pitfalls
Frequently asked questions
What are equivalent fractions?
They are fractions that name the same amount, like \(\dfrac{1}{2}\) and \(\dfrac{2}{4}\). They look different but mark the same point on a number line.
How do you make an equivalent fraction?
Multiply the numerator and denominator by the same number. For example \(\dfrac{1}{3}=\dfrac{2}{6}\) by multiplying top and bottom by \(2\).
How do you write a fraction in simplest form?
Divide the numerator and denominator by a common factor until they share no factor other than \(1\). \(\dfrac{6}{8}\) becomes \(\dfrac{3}{4}\).
Why can you not add to make an equivalent fraction?
Adding the same number to the top and bottom changes the value. Only multiplying or dividing both by the same number keeps a fraction equal.