# Dividing Fractions CalculatorIncluding Whole and Mixed Numbers

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

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

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

Also, if you're ever unsure if the fraction you're dividing by is greater or less than the fraction you are dividing into, be sure to check out my fraction comparison calculator.

### How to Divide Fractions

While fraction division has one more step than fraction multiplication, it is still much easier than adding and subtracting fractions -- because there is no need to worry about the denominators being like or unlike.

Instead, all you need to do is invert (flip upside down) the divisor (second term in the division equation) and change the sign from division (÷) to multiplication (x), then multiply the dividend (first term in the division equation) by the inverted divisor.

To complete the fraction division you simply 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.

The following illustrates how you would divide a dividend of 1/2 by a divisor of 1/3:

Step #1: Invert the Divisor

 1 ÷ 1 = 1 x 3 2 3 2 1

Step #2: Multiply Dividend by Inverted Divisor

 1 x 3 = 3 = 1 1 2 1 2 2

### Dividing Fractions and Mixed Numbers

If you need to divide 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 3 3

Once you have converted the mixed number to an improper fraction, you simply divide the fractions as normal. Of course, the dividing fractions calculator will do all of this for you with the click of the "Calculate Fraction Division" button.

### Dividing Fractions By Whole Numbers

Here again, in order to divide 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 divide the fractions as explained earlier.

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

Dividing Fractions Calculator

Instructions: Enter the whole number, numerator (top) and the denominator (bottom) of the dividend.

Next, enter the whole number, numerator and denominator of the divisor, and then click the "Calculate Fraction Division" button.

Note that for the dividend or the divisor you can either enter a whole number only, a mixed number, or a fraction only. The dividing fractions calculator will automically detect which type you entered.

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 Dividing Fractions Calculator.

Important: This first version of the calculator is not designed to work with negative signs, so please limit your entries to positive numbers. You can then use the rule of dividing negative numbers to apply a sign to the result.

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Dividend   Divisor
Whole # Fraction   Whole # Fraction
Numerators (#): ÷
Denominators (#):
Quotient of fractions, whole, or mixed numbers:
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### Dividing Fractions Calculator Glossary of Terms

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Dividend: The first term in the division equation. If the dividend is a whole number only, leave the numerator and denominator blank. If the dividend is a mixed number, enter a positive integer for the whole number, the numerator, and denominator. If the dividend is a fraction only, leave the whole number field blank.

Divisor: The second term in the division equation. If the divisor is a whole number only, leave the numerator and denominator blank. If the divisor is a mixed number, enter a positive integer for the whole number, the numerator, and denominator. If the divisor is a fraction only, leave the whole number field blank.

Numerators: Enter the top number for the dividend if it contains a fraction and enter the top number for the divisor if it contains a fraction. Leave the numerator and denominator fields blank for any dividend or divisor that is a whole number only.

Denominators: Enter the bottom number for the dividend if it contains a fraction and enter the bottom number for the divisor if it contains a fraction. Leave the numerator and denominator fields blank for any dividend or divisor that is a whole number only.

Quotient of fractions, whole, or mixed numbers: This is the result of dividing the entered fractions, mixed numbers, and/or whole numbers. After inverting the divisor and calculating the quotient of fractions, the dividing fractions calculator will show its work and give a detailed explanation of each step it took to arrive at the quotient.

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.

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.

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