Divide Fractions Calculator

Divide fractions using the Keep-Change-Flip method with automatic GCD simplification.

Enter Fractions

First Fraction (a/b)
3/4 ÷ 2/5
Second Fraction (c/d)

Result

Quotient
--
--
Unsimplified result --
GCD --
Simplified result --
Mixed number --
Decimal --

Step-by-Step Solution

(a/b) / (c/d) = (a/b) x (d/c) = ad/bc

How to Divide Fractions

Dividing fractions is straightforward once you learn the "Keep-Change-Flip" (KCF) method, also known as "Multiply by the reciprocal." To divide one fraction by another, you keep the first fraction, change the division sign to multiplication, and flip (take the reciprocal of) the second fraction.

The Keep-Change-Flip Method

Step 1: Keep

Keep the first fraction exactly as it is. Do not change it.

a/b stays as a/b

Step 2: Change

Change the division sign to a multiplication sign.

/ becomes x

Step 3: Flip

Flip the second fraction (take its reciprocal).

c/d becomes d/c

Step 4: Multiply

Multiply numerators together and denominators together.

(a x d) / (b x c)

Step 5: Simplify

Find the GCD and reduce to lowest terms.

Divide by GCD(ad, bc)

Complete Formula

The complete division formula in one expression.

(a/b) / (c/d) = ad / bc

Why Does Keep-Change-Flip Work?

Division is defined as multiplication by the reciprocal. When you divide by a fraction c/d, you are asking "how many groups of c/d fit into a/b?" This is mathematically equivalent to multiplying a/b by d/c. The reciprocal of c/d is d/c because (c/d) x (d/c) = 1.

Worked Examples

  1. 1/2 / 3/4: Keep 1/2, change to multiply, flip 3/4 to 4/3. Result: 1/2 x 4/3 = 4/6 = 2/3.
  2. 5/6 / 2/3: 5/6 x 3/2 = 15/12 = 5/4 = 1 1/4.
  3. 7/8 / 7/8: 7/8 x 8/7 = 56/56 = 1 (any number divided by itself is 1).

Dividing with Whole Numbers

A whole number can be written as a fraction with denominator 1. For example, to divide 3/4 by 2: 3/4 / 2/1 = 3/4 x 1/2 = 3/8. To divide a whole number by a fraction: 5 / (1/3) = 5/1 x 3/1 = 15.

Common Mistakes to Avoid

  • Flipping the wrong fraction (always flip the second fraction, the divisor).
  • Forgetting to simplify the final answer.
  • Dividing numerator by numerator and denominator by denominator (this does not work for division).
  • Not handling negative signs correctly.

Real-World Applications

  • Cooking: Dividing a recipe that calls for 3/4 cup into 1/2 portions.
  • Sewing: Determining how many pieces of 2/3 yard can be cut from 4 yards of fabric.
  • Construction: Splitting materials into fractional portions.
  • Finance: Dividing fractional shares or percentages.