Divide Fractions Calculator
To divide fractions, use the Keep-Change-Flip method: keep the first fraction, change the ÷ sign to ×, and flip the second fraction. Then multiply straight across and simplify. Enter your fractions below for an instant answer with step-by-step working, or read on to master the method yourself.
Enter Your Fractions
How Do You Divide Fractions Step by Step?
To divide any two fractions, apply the Keep-Change-Flip method (also called KCF or "invert and multiply"). Every fraction division problem follows the same three steps.
Keep
Keep the first fraction exactly as it is. Don't change the numerator or denominator.
Change
Change the division sign (÷) to a multiplication sign (×).
Flip
Flip the second fraction (swap the numerator and denominator) to get its reciprocal.
Once you've completed those three steps, multiply the two fractions: multiply the numerators together and multiply the denominators together. Then simplify the result to lowest terms if possible. That's it — dividing fractions is really just multiplying by a reciprocal.
Want a deeper walkthrough with visual diagrams? Read our complete guide on how to divide fractions.
What Is ⅔ ÷ ⅘? Worked Examples
Example 1: Simple Fraction ÷ Fraction
- Keep the first fraction: 2/3
- Change ÷ to ×
- Flip the second fraction: 4/5 becomes 5/4
- Multiply: 2 × 5 = 10 and 3 × 4 = 12 → 10/12
- Simplify by dividing both by 2 → 5/6
Example 2: Fraction ÷ Whole Number
- Write 6 as a fraction: 6/1
- Keep 3/4, Change ÷ to ×, Flip 6/1 to 1/6
- Multiply: 3 × 1 = 3 and 4 × 6 = 24 → 3/24
- Simplify by dividing both by 3 → 1/8
Example 3: Mixed Number ÷ Fraction
- Convert 1 1/2 to improper: (1 × 2 + 1) / 2 = 3/2
- Keep 3/2, Change ÷ to ×, Flip 3/4 to 4/3
- Multiply: 3 × 4 = 12 and 2 × 3 = 6 → 12/6
- Simplify → 2
Practice: Divide These Fractions
Test your skills with these problems. Click "Show Answer" to check your work.
Frequently Asked Questions
Keep-Change-Flip (KCF) is a three-step mnemonic for dividing fractions. Keep the first fraction as-is, Change the division sign to multiplication, and Flip (find the reciprocal of) the second fraction. Then multiply across: numerator × numerator and denominator × denominator.
Write the whole number as a fraction with a denominator of 1 (for example, 3 becomes 3/1), then apply Keep-Change-Flip normally. So 2/5 ÷ 3 becomes 2/5 × 1/3 = 2/15.
First convert each mixed number to an improper fraction. For example, 2 1/3 becomes 7/3 (because 2 × 3 + 1 = 7). Then use Keep-Change-Flip on the improper fractions and simplify the result.
Division is the inverse of multiplication. Dividing by a fraction is mathematically the same as multiplying by its reciprocal. This is a fundamental property of arithmetic—flipping the second fraction converts the division into a simpler multiplication problem.
Yes. You can enter negative values for any numerator, denominator, or whole number. The calculator applies standard sign rules automatically: a negative divided by a positive gives a negative result, a positive divided by a negative gives a negative result, and two negatives give a positive result.
The fraction division formula is: a/b ÷ c/d = a/b × d/c = (a × d) / (b × c). In words, multiply the first numerator by the second denominator, and the first denominator by the second numerator. This is the mathematical basis behind the Keep-Change-Flip shortcut.
Using Keep-Change-Flip: keep 3/4, change ÷ to ×, flip 2/3 to 3/2. Multiply: 3 × 3 = 9 and 4 × 2 = 8. The answer is 9/8, which equals the mixed number 1⅛ or approximately 1.125 in decimal form.
Not exactly, but dividing by a fraction is equivalent to multiplying by its reciprocal. When you flip the second fraction and multiply, you get the same result as division. So while the operations are different, every fraction division problem can be converted into a multiplication problem using Keep-Change-Flip.
After multiplying across, find the greatest common factor (GCF) of the numerator and denominator. Divide both by the GCF to reduce the fraction to lowest terms. If the numerator is larger than the denominator, you can also convert the result to a mixed number. Our calculator simplifies automatically.
Yes. Write the whole number over 1 — for example, 6 becomes 6/1. Then apply Keep-Change-Flip: keep 6/1, change ÷ to ×, flip the fraction. Example: 6 ÷ 2/3 = 6/1 × 3/2 = 18/2 = 9. When dividing by a proper fraction (one less than 1), the result is always larger than the original number.