How do you divide fractions?

To divide fractions, use the keep, change, flip method. Keep the first fraction as it is, change the division sign to a multiplication sign, and flip (find the reciprocal of) the second fraction by swapping its numerator and denominator. Then multiply the numerators together and multiply the denominators together. Finally, simplify the result by dividing numerator and denominator by their greatest common divisor (GCD). For example, 1/2 divided by 1/3 becomes 1/2 x 3/1 = 3/2.

Why do you flip the second fraction when dividing?

Dividing by a fraction is the same as multiplying by its reciprocal because division is the inverse of multiplication. Any number divided by a fraction a/b gives the same answer as that number multiplied by b/a. This works because a fraction and its reciprocal multiply to give 1 (for example, 2/3 x 3/2 = 1), so flipping and multiplying cancels out the division cleanly and gives an equivalent calculation that is easier to carry out.

How do you divide mixed numbers?

To divide mixed numbers, first convert each mixed number to an improper fraction. Multiply the whole number by the denominator, add the numerator, and place the result over the original denominator. For example, 1 3/4 becomes (1 x 4 + 3)/4 = 7/4. Then apply the keep, change, flip method to the two improper fractions. Convert the result back to a mixed number if needed by dividing the numerator by the denominator: the quotient is the whole part and the remainder is the numerator of the fractional part.

Dividing Fractions Calculator

This calculator divides one fraction by another and shows you the full working, not just the final answer. Enter the numerator and denominator of your first fraction (the dividend) and the numerator and denominator of your second fraction (the divisor), and it applies the keep, change, flip method: the first fraction stays as it is, the division sign becomes a multiplication sign, and the second fraction is flipped to its reciprocal. The two numerators are then multiplied together, as are the two denominators, and the result is reduced to its lowest terms using the greatest common divisor. You get the simplified answer as a fraction, with a mixed number version shown underneath whenever the result is an improper fraction, plus the reciprocal used and the unsimplified product before reduction. A step-by-step breakdown walks through every stage of the working, and separate panels show the fraction details, including the multiplication and simplification steps, and the decimal equivalents of both fractions and the final quotient. Use whole numbers only; for mixed numbers, convert each one to an improper fraction first (for example, 1 3/4 becomes 7/4) before entering it. The divisor's numerator cannot be zero, since dividing by zero is undefined. It is a handy way to check homework or any calculation where you need to divide fractions accurately and see exactly how the answer was reached.

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Standard method Uses the keep, change, flip rule (multiply by the reciprocal) and GCD reduction. Works for proper fractions and improper fractions.

1. First Fraction (Dividend)

Numerator (top number)

Denominator (bottom number)

2. Second Fraction (Divisor)

Numerator (top number)

Denominator (bottom number)

Please enter whole numbers only. Denominators cannot be zero.

Result

Answer (simplified)
3/2
As mixed number: 1 and 1/2

Reciprocal of Divisor

Second fraction flipped

Before Simplifying

3/2

Product before reduction

Step-by-Step Working

Fraction Details

First fraction (dividend)1/2

Second fraction (divisor)1/3

Reciprocal of divisor3

Multiply numerators1 x 3 = 3

Multiply denominators2 x 1 = 2

Quotient (simplified)3/2

As Decimal

First fraction0.5000

Second fraction0.3333

Quotient (decimal)1.5000

How to Divide Fractions

Dividing fractions uses a different method to adding or subtracting them: there is no need to find a common denominator. Instead, you use the keep, change, flip rule, which turns the division into an equivalent multiplication problem.

The Standard Method: Keep, Change, Flip

Keep the first fraction as it is. This is the dividend, the number being divided.
Change the division sign to a multiplication sign.
Flip the second fraction. Swap its numerator and denominator to get its reciprocal. This is the divisor turned upside down.
Multiply the fractions. Multiply the two numerators together and the two denominators together.
Simplify the result. Divide both numerator and denominator by their greatest common divisor (GCD). If the GCD is 1, the fraction is already in its simplest form.

Worked Example

Step	Working	Result
Fractions to divide	1/2 ÷ 1/3
Keep the first fraction	1/2	1/2
Flip the second fraction	1/3 becomes 3/1	3/1
Multiply numerators	1 x 3	3
Multiply denominators	2 x 1	2
Simplify	GCD(3, 2) = 1, already simplified	3/2

Why Flipping and Multiplying Works

Dividing by a number is the same as multiplying by its reciprocal. A fraction multiplied by its own reciprocal always equals 1 (for example, 2/3 x 3/2 = 1), so flipping the divisor and multiplying gives a mathematically equivalent result to dividing directly. This makes fraction division far simpler than trying to divide numerators and denominators directly, which does not follow a straightforward rule.

Simplifying the Result

A fraction is in its lowest terms (simplest form) when the numerator and denominator share no common factor other than 1. To simplify, find the GCD of the numerator and denominator using the Euclidean algorithm, then divide both by it. For example, 6/8 has GCD(6, 8) = 2, so 6/8 = 3/4.

Improper Fractions and Mixed Numbers

If the result of dividing is an improper fraction (numerator greater than or equal to denominator, such as 3/2), it can also be expressed as a mixed number. Divide the numerator by the denominator: the quotient becomes the whole number, and the remainder becomes the new numerator over the same denominator. So 3/2 = 1 remainder 1 = 1 and 1/2, written as 1 1/2. For mixed number division, first convert each mixed number to an improper fraction, then apply the keep, change, flip method.

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Fraction to Decimal Calculator: convert any fraction to its decimal equivalent.

Method: Keep, change, flip: multiply the first fraction by the reciprocal of the second. Result reduced by dividing by GCD(numerator, denominator) via the Euclidean algorithm.

This calculator works with whole-number numerators and denominators. For mixed number division, convert each mixed number to an improper fraction first (for example, 1 3/4 becomes 7/4) then enter the numerator and denominator. The divisor's numerator cannot be zero, since dividing by zero is undefined.