Divide two fractions and get the simplified answer instantly. Enter any numerators and denominators below. The calculator keeps the first fraction, flips the second fraction (its reciprocal), multiplies, and reduces the result to its lowest terms.
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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)
2. Second Fraction (Divisor)
Please enter whole numbers only. Denominators cannot be zero.
Result
Answer (simplified)
3/2
Reciprocal of Divisor
3/1
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 divisor3/1
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.
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.
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