Home >> Science & Nature >> Science

How to Decide if Fractions Are Equivalent

Fractions show up in a great many math problems, so it's helpful to be able to recognize equivalent fractions, since this can sometimes help you simplify equations. Equivalent fractions are just fractions which are equal to one another. This is a basic concept, but spotting equivalent fractions is not always an easy task, because fractions which are equal are not always obvious. There are several ways to find equivalent fractions, but one quick method is to bring both of them to a common denominator.

Things You'll Need

Calculator

Instructions

- 1
  Write out both of the fractions you wish to test for equivalency. For example, you might want to determine whether 2/3 and 12/15 are equivalent.
- 2
  Multiply the numerator (the top number) and the denominator (the bottom number) of the first fraction by the denominator of the second fraction. In the example, you would calculate (2 x 15)/(3 x 15) to obtain 30/45.
- 3
  Multiply the numerator and denominator of the second fraction by the denominator of the first fraction. You have now brought both fractions to the same denominator. The example calculation would be (12 x 3)/(15 x 3) or 36/45.
- 4
  Compare the two new fractions you have generated. If they are equal, then the original two fractions were equivalent. If not, the original fractions were not equivalent. The two fractions generated in the example are 30/45 and 36/45, which are not equal, thus the two original fractions 2/3 and 12/15 were not equivalent.

Science