Dividing Fractions Calculator
Divide fractions using the reciprocal method
How to Divide Fractions
Keep the First Fraction
Leave the first fraction (dividend) as it is.
Flip the Second Fraction
Find the reciprocal of the second fraction by flipping it (swap numerator and denominator).
Multiply
Multiply the first fraction by the flipped second fraction.
Simplify
Reduce the result to its lowest terms.
Remember: "Keep, Change, Flip"
Keep the first fraction, Change ÷ to ×, Flip the second fraction
Formula & Examples
a/b ÷ c/d = a/b × d/c = (a × d) / (b × c)
Divide = Multiply by reciprocal
Example 1: Divide 3/4 ÷ 2/5
Reciprocal of 2/5 = 5/2
3/4 × 5/2 = (3 × 5) / (4 × 2) = 15/8
15/8 = 1 7/8 (mixed number)
Answer: 15/8 or 1 7/8
Example 2: Divide 1/2 ÷ 1/4
Reciprocal of 1/4 = 4/1
1/2 × 4/1 = (1 × 4) / (2 × 1) = 4/2 = 2
Answer: 2
There are 2 quarters in a half
Example 3: Divide 5/6 ÷ 2/3
Reciprocal of 2/3 = 3/2
5/6 × 3/2 = (5 × 3) / (6 × 2) = 15/12 = 5/4
5/4 = 1 1/4 (mixed number)
Answer: 5/4 or 1 1/4
About Dividing Fractions
Dividing fractions is one of the easiest fraction operations once you know the secret: flip and multiply! Instead of dividing, you multiply by the reciprocal (flipped version) of the second fraction.
Why Does Flip and Multiply Work?
Division is the inverse operation of multiplication. When you divide by a fraction, it is the same as multiplying by its reciprocal. For example, dividing by 1/2 is the same as multiplying by 2 (which is 2/1, the reciprocal of 1/2).
Understanding Division
When you divide 1/2 ÷ 1/4, you are asking "how many quarters fit into a half?" The answer is 2, because two 1/4 pieces equal 1/2.
Real-World Applications
- Cooking: Recipe calls for 2/3 cup but your measuring cup is 1/6 cup. How many scoops? 2/3 ÷ 1/6 = 4 scoops
- Sewing: You have 3/4 yard of fabric. Each project needs 1/8 yard. How many projects? 3/4 ÷ 1/8 = 6 projects
- Construction: A 5/8 inch board needs to be cut into 1/16 inch strips. 5/8 ÷ 1/16 = 10 strips
- Time: A task takes 1/4 hour. How many can you complete in 2/3 hour? 2/3 ÷ 1/4 = 2 2/3 tasks
Special Cases
- Dividing by 1: Any fraction ÷ 1 = the same fraction
- Dividing by itself: Any fraction ÷ itself = 1
- Dividing into 0: 0 ÷ any fraction = 0
- Cannot divide by 0: Any fraction ÷ 0 = undefined
- Dividing by whole number: Convert it to fraction (n/1), then flip to get 1/n
About Dividing Fractions Calculator
The Dividing Fractions Calculator divides two fractions using the reciprocal method (flip and multiply). Dividing fractions is simpler than it seems—just multiply by the reciprocal of the second fraction!
When to Use This Calculator
- Math Homework: Quickly divide and simplify fractions
- Cooking: Scale recipes and calculate portions (e.g., 2/3 cup ÷ 1/6 cup = 4 portions)
- Construction: Calculate how many pieces fit into a given length
- Sewing: Determine how many smaller pieces can be cut from fabric
- Time Management: Calculate how many tasks fit in available time
- Exam Preparation: Practice fraction division
Why Use Our Calculator?
- ✅ Automatic Simplification: Reduces fractions to lowest terms
- ✅ Shows Steps: Displays the reciprocal and multiplication process
- ✅ Mixed Numbers: Converts to mixed number when applicable
- ✅ Decimal Result: Shows the decimal equivalent
- ✅ 100% Accurate: Precise mathematical calculations
- ✅ Completely Free: No registration required
Understanding Fraction Division
Dividing fractions uses the "Keep, Change, Flip" method: Keep the first fraction, Change ÷ to ×, Flip the second fraction. This works because division is the inverse of multiplication.
- Always flip the second fraction (divisor), not the first
- The reciprocal of a/b is b/a (swap numerator and denominator)
- Multiplying by a reciprocal converts division to multiplication
- Always simplify the final result to lowest terms
- Cannot divide by zero—the divisor cannot be zero
Real-World Applications
Cooking: A recipe calls for 2/3 cup but your measuring cup is 1/6 cup. Calculate: 2/3 ÷ 1/6 = 2/3 × 6/1 = 12/3 = 4 scoops.
Sewing: You have 3/4 yard of fabric. Each project needs 1/8 yard. Calculate: 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6 projects.
Construction: A 5/8 inch board needs to be cut into 1/16 inch strips. Calculate: 5/8 ÷ 1/16 = 5/8 × 16/1 = 80/8 = 10 strips.
Tips for Using This Calculator
- Remember: "Keep, Change, Flip"—Keep first, Change ÷ to ×, Flip second
- Always flip the second fraction (divisor), never the first
- The calculator automatically simplifies results
- Use cross-canceling mentally to verify results
- Dividing by a fraction < 1 gives a larger result
- Cannot divide by zero—check that the divisor is not zero
How to Use This Calculator
Enter Your Values
Input the required values in the calculator fields above. Make sure all inputs are valid numbers.
Click Calculate
Press the "Calculate" button to perform the calculation and see your results.
Review Results
Review the calculated results displayed below. Use these values for your needs.
Formula
a/b ÷ c/d = a/b × d/c = (a × d) / (b × c)
Divide by multiplying by reciprocal (flip second fraction)
Example: Divide 3/4 ÷ 2/5
Step 1: Flip second fraction: 2/5 → 5/2
Step 2: Multiply: 3/4 × 5/2 = (3×5)/(4×2) = 15/8
Step 3: Simplify if needed (15/8 is already simplified)
Answer: 15/8 or 1 7/8
Frequently Asked Questions
Why do we flip the second fraction?
Dividing by a number is the same as multiplying by its reciprocal. Flipping the fraction gives you its reciprocal, turning division into multiplication. This is why "flip and multiply" works.
What is a reciprocal?
A reciprocal is what you get when you flip a fraction. The reciprocal of a/b is b/a. When you multiply a fraction by its reciprocal, you always get 1. For example, 3/4 × 4/3 = 1.
Do I flip the first or second fraction?
Always flip the SECOND fraction (the divisor, the one you are dividing BY). Keep the first fraction as is. Remember: "Keep, Change, Flip"—keep the first, flip the second.
Why does dividing by a fraction make the answer bigger?
When you divide by a fraction less than 1, you are asking "how many of these small pieces fit into the original?" The answer is more than the original number. For example, 2 ÷ 1/2 = 4 (there are 4 halves in 2).
How do I divide a fraction by a whole number?
Convert the whole number to a fraction by putting it over 1 (e.g., 5 = 5/1), then flip it to get 1/5 and multiply normally. For example, 3/4 ÷ 5 = 3/4 × 1/5 = 3/20.
Can I divide more than two fractions?
Yes! Divide them in order or convert all to multiplication by flipping all divisors. For example, 1/2 ÷ 2/3 ÷ 3/4 = 1/2 × 3/2 × 4/3 = 12/12 = 1.
What happens if I divide by 1?
Any fraction divided by 1 equals itself. For example, 3/4 ÷ 1 = 3/4, or 3/4 ÷ 1/1 = 3/4 × 1/1 = 3/4. One is the multiplicative identity.