Multiplying Fractions Calculator
Including Whole and Mixed Numbers

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The Multiplying Fractions Calculator on this page will multiply any combination of fraction, mixed number, or whole number.

This free online fraction multiplication calculator is handy for multiplying fractions, multiplying fractions and mixed numbers, and multiplying fractions by whole numbers. And in all cases the calculator will restate the product fraction in simplest form.

Plus, unlike other online fraction calculators, this Multiplying Fractions Calculator will show its work and give a detailed step-by-step explanation as to how it arrived at the calculated product.

Also, be sure to check out my other online math calculators for help with fraction division and comparison.

How to Multiply Fractions

Multiplication is the easiest of all operations involving fractions -- because there is no need to worry about the denominators being like or unlike as in the case of adding and subtracting fractions.

Instead, all you need to do is multiply the numerators of each fraction to get a new numerator and then multiply the denominators of each fraction to get a new denominator -- regardless of whether the denominators are different or the same, like this:

Multiply Numerators and Denominators
  1 x 1 = 1  
3 4 12

Multiplying Fractions and Mixed Numbers

If you need to multiply a fraction by a mixed number, you first need to convert the mixed number to an improper fraction. To do that, you simply multiply the denominator by the whole number and add that product to the value of the numerator. That result then becomes the numerator of the improper fraction, while the denominator remains the same.

To illustrate, here is how you would convert the mixed number 2 1/3 (two and one third) into an improper fraction:

Converting a Mixed Number to a Fraction

  2 1 = 3 x 2 + 1 = 7 
3 33

Once you have converted the mixed number to an improper fraction, you simply multiply the numerators and denominators as usual.

Multiplying Fractions By Whole Numbers

Here again, in order to multiply a fraction by a whole number you first need to convert the whole number into an improper fraction. To do that you simply place the whole number over the number 1 (any non-zero number divided by 1 is equal to the number), like this:

Converting a Whole Number to a Fraction

  4 = 4  
1

Once you have converted the whole number into an improper fraction, you simply multiply the numerators and denominators as usual.

With that, let's use the Multiplying Fractions Calculator to multiply any combination of a fraction, a mixed number, or a whole number, and then simplify the result.

Multiplying Fractions Calculator
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Instructions: Enter the whole number, numerator (top) and the denominator (bottom) of the first factor (multiplicand).

Next, enter the whole number, numerator and denominator of the second factor (multiplier), and then click the "Multiply Fractions" button.

Note that for one or both factors you can either enter a whole number only, a mixed number, or a fraction only.

Mouse over the blue question marks for a further explanation of each entry field. More in-depth explanations can be found in the glossary of terms located beneath the Multiplying Fractions Calculator.

  Help Multiplicand   Help Multiplier
  Whole # Fraction   Whole # Fraction
Help Numerators (#): x
Help Denominators (#):
Help Product of fractions, mixed numbers, and/or whole numbers:

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Multiplying Fractions Calculator Glossary of Terms

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Multiplicand: The first factor in a multiplication. In the equation 1/3 x 1/2, 1/3 would be the multiplicand.

Multiplier: The second factor in a multiplication. In the equation 1/3 x 1/2, 1/2 would be the multiplier.

Product: The result of multiplying the multiplicand by the multiplier.

Mixed number: The combination of a whole number and a fraction, such as 3 1/4 (three and one quarter).

Improper fraction: A fraction having a numerator that is larger than the denominator, such as 5/3.

Factor options: If the factor is a whole number only, leave the numerator and denominator blank. If the factor is a mixed number, enter a positive integer for the whole number, the numerator, and the denominator. If the factor is a fraction only, leave the whole number field blank.

Numerators: Enter the top number for each factor (multiplicand and/or multiplier) that contains a fraction. If a factor is a whole number only, leave the numerator and denominator fields blank.

Denominators: Enter the bottom number for each factor that contains a fraction. If a factor is a whole number only, leave the numerator and denominator fields blank.

Product of fractions, whole, or mixed numbers: This is the result of multiplying the entered combination of a fraction, a mixed number, and/or a whole number. After calculating the product of fractions, the multiplying fractions calculator will show its work and give a detailed explanation of each step it took to arrive at this result.

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