Enter any two or three fractions into the multiplying fractions calculator. The calculator will evaluate the multiplication of the fractions and display the simplified value of the result.

Multiplying Fractions Formula

The following equation is used to multiply two fractions.

X/Y * A/B = X*A/ GCD /Y*B /GCD

  • Where X/Y is the first fraction
  • A/B is the second fraction
  • X*A/Y*B is the resulting value
  • GCD is the

This formula can be extended to any number of fractions. The process is still the same. Multiply all of the numerators and all of the denominators and then divide by the GCD of the two results.

Multiply Fractions Definition

Multiplying fractions is the process of multiplication on two or more fractions to produce a new fraction. This new fraction typically simplified using the greatest common denominator of the new top and bottom numbers. Multiplying fractions are sometimes referred to as timing fractions, although this is an improper word.

Multiply Fractions Example

How to multiply fractions?

  1. First determine the two fractions

    Determine the values of the two fractions that you want to perform the operation of multiplication on. For this example, the two fractions are 4/5 and 2/3.

  2. Next, multiply the numerators

    4*2 = 8.

  3. Next, multiply the denominators

    5*3 = 15.

  4. Combing the results

    Combine the results from steps 1 and 2 to create your new fraction. 8/15.

  5. Simplify

    Simplify the result using the GCD of the numerator and denominator. In this case there the greatest common denominator is 1 so the result is still 8/15.

How to multiply 3 fractions together?

The following problem is an example of how to multiply 3 fractions together. This example problem specifically goes over the multiplication of fractions with different denominators.

  1. Determine the first fraction X/Y. In this case, the first fraction is found to be 1/3.
  2. Next, determine the second fraction W/Z. This is determined to be 1/5.
  3. Next, determine the third and final fraction. The last value is given as 20/30.
  4. Next, multiply all of the numerators and denominators. This yields a fraction of 20/450.
  5. Finally, divide the result by the greatest common denominator of the numerator and denominator, which is 10. So 20/10 / 450/10 = 2/45.

The method used above can be used for any number of fractions. For example, when considering just two fractions, simply multiply the numerator and denominator values of each and then divide by the GCD. This can be done using the calculator above as well. Just enter only the values of the first two fractions and leave the third as 1 over 1.

Additional Information

How do you multiply fractions with different denominators? Multiplying fractions with different denominators, or different bottom numbers as it’s sometimes referred to, is no different than those with the same denominator. The formula and process are still the same, which is shown above.

What is the easiest way to multiply fractions? The easiest way to multiply fractions is by using a calculator like the one above. The second easiest way is using the formula X/Y * A/B = X*A/ GCD /Y*B /GCD, where X/Y and A/B are different fractions. This is further explored in the formula section above.

multiply fractions calculator
multiply fractions formula