# Equivalent Fractions

Equivalent fractions are fractions that have the same value even though they look different. These fractions may have different numerators and denominators, but utilizing basic multiplication and division reveal that they are actually equal. For example, the following three fractions all have the same value: ## Multiplication

To see if these fractions are equivalent using multiplication, focus on 1/4. If the top and bottom numbers of 1/4 are multiplied by 2 we see that 1/4 and 2/8 have equal values. Now, let’s see if 1/4 is equal to 4/16. Follow the same process, this time multiplying 1/4 by 4 on the top and bottom. Finally, test if 2/8 and 4/16 are equivalent fractions. Multiply the numerator and denominator of 2/8 by 2. In these examples we see how multiplying the numerator and denominator of a fraction can help us determine if two or more fractions are equivalent. Since multiplying causes the numerator and denominator to become the same as those of another fraction, we know these fractions are equivalent.

## Division

Division can also be utilized to determine if two fractions are equal. The following fractions are all equivalent: Similar to using multiplication, divide the top and bottom numbers by the same number to determine if two fractions are equivalent. To see if 18/27 and 6/9 are equal, divide the numerator and denominator of 18/27 by 3. Follow the same process to see if 6/9 and 2/3 are equivalent fractions. Dividing 6/9 by 3 on the top and bottom will give us our answer. Finally, check that 18/27 is equal to 2/3. This time, divide the numerator and denominator of 18/27 by 9. From these exercises, we were able to determine that all three fractions were equal by dividing the numerators and denominators by the same number.

Identifying equivalent fractions may seem difficult at first when working with numerous fractions, each with its own unique numerator and denominator. However, drawing upon basic multiplication and division skills, your child will see how easy it is to test and determine if fractions share a certain value. 