Multiplying Fractions Calculator
Multiply fractions and simplify results
How to Multiply Fractions
Multiply Numerators
Multiply the top numbers (numerators) together.
Multiply Denominators
Multiply the bottom numbers (denominators) together.
Simplify
Reduce the fraction to its lowest terms by dividing by the GCD.
Formula & Examples
a/b × c/d = (a × c) / (b × d)
Then simplify by dividing by GCD
Example 1: Multiply 2/3 × 3/4
Numerators: 2 × 3 = 6
Denominators: 3 × 4 = 12
Result: 6/12 = 1/2 (simplified)
Answer: 1/2
Example 2: Multiply 5/8 × 2/5
Numerators: 5 × 2 = 10
Denominators: 8 × 5 = 40
Result: 10/40 = 1/4 (simplified)
Answer: 1/4
Example 3: Multiply 3/5 × 5/9
Numerators: 3 × 5 = 15
Denominators: 5 × 9 = 45
Result: 15/45 = 1/3 (simplified)
Answer: 1/3
About Multiplying Fractions
Multiplying fractions is actually easier than adding or subtracting them because you do not need to find a common denominator. Simply multiply straight across - numerator times numerator and denominator times denominator.
Why Multiplying is Easier
Unlike addition and subtraction, you do NOT need to find a common denominator when multiplying fractions. Just multiply across and simplify at the end.
Cross-Canceling Tip
Before multiplying, you can cross-cancel (simplify diagonally) to make calculations easier. For example, in 4/9 × 3/8, you can cancel the 4 and 8 (both divisible by 4), and the 3 and 9 (both divisible by 3) to get 1/3 × 1/2 = 1/6.
Real-World Applications
- Cooking: Half of a 2/3 cup recipe = 1/2 × 2/3 = 1/3 cup
- Shopping: 1/4 off of a $3/4 price = 1/4 × 3/4
- Construction: 2/3 of a 3/4 inch board thickness
- Probability: Chance of two independent events occurring
Special Cases
- Multiplying by 1: Any fraction × 1 = the same fraction
- Multiplying by 0: Any fraction × 0 = 0
- Multiplying reciprocals: a/b × b/a = 1
- Multiplying by whole number: Convert whole number to fraction (n/1)
About Multiplying Fractions Calculator
The Multiplying Fractions Calculator multiplies two fractions and simplifies the result. Unlike adding or subtracting fractions, multiplying fractions does not require finding a common denominator—just multiply straight across!
When to Use This Calculator
- Math Homework: Quickly multiply and simplify fractions
- Cooking: Scale recipes (e.g., half of 2/3 cup = 1/2 × 2/3)
- Construction: Calculate fractional measurements
- Shopping: Calculate discounts and fractional prices
- Probability: Calculate probabilities of multiple events
- Exam Preparation: Practice fraction multiplication
Why Use Our Calculator?
- ✅ Automatic Simplification: Reduces fractions to lowest terms
- ✅ Shows Steps: Displays the 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 Multiplication
Multiplying fractions is simpler than adding or subtracting because you don't need a common denominator. Just multiply numerators together and denominators together, then simplify.
- No common denominator needed—just multiply across
- Always simplify the result to lowest terms
- Use cross-canceling to simplify before multiplying
- Multiplying by 1 leaves the fraction unchanged
- Multiplying reciprocals gives 1 (e.g., 2/3 × 3/2 = 1)
Real-World Applications
Cooking: If a recipe calls for 2/3 cup and you want half, multiply: 1/2 × 2/3 = 2/6 = 1/3 cup.
Shopping: If something costs 3/4 of the original price and you have a 1/4 coupon, calculate: 3/4 × 1/4 = 3/16.
Construction: If you need 2/3 of a 3/4 inch board, multiply: 2/3 × 3/4 = 6/12 = 1/2 inch.
Tips for Using This Calculator
- Enter whole numbers as numerators (denominator = 1)
- The calculator automatically simplifies results
- Use cross-canceling mentally to verify results
- Remember: multiplying by a fraction < 1 makes the result smaller
- Denominators cannot be zero (division by zero is undefined)
- Check the decimal result to verify your answer
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.
Frequently Asked Questions
Do I need a common denominator to multiply fractions?
No! Unlike addition and subtraction, you do NOT need a common denominator. Just multiply straight across—numerator times numerator, denominator times denominator.
What is cross-canceling?
Cross-canceling is simplifying before multiplying by canceling common factors between a numerator and a denominator (diagonally across the multiplication sign). For example, in 2/3 × 3/4, you can cancel the 3s to get 2/4 = 1/2.
Why does multiplying fractions make them smaller?
When both fractions are less than 1, multiplying them gives a smaller result. Think of it as taking a fraction of a fraction—like 1/2 of 1/2 = 1/4. You're taking part of a part, which is smaller than either part alone.
How do I multiply a fraction by a whole number?
Convert the whole number to a fraction by putting it over 1. For example, 5 becomes 5/1. Then multiply normally: 5/1 × 3/4 = 15/4 = 3 3/4.
Can I multiply more than two fractions?
Yes! Multiply all numerators together and all denominators together, then simplify the result. For example, 1/2 × 2/3 × 3/4 = 6/24 = 1/4.
What happens if I multiply by 0?
Any fraction multiplied by 0 equals 0. For example, 3/4 × 0 = 0, or 0 × 3/4 = 0.
What happens if I multiply by 1?
Any fraction multiplied by 1 equals itself. For example, 3/4 × 1 = 3/4, or 3/4 × 1/1 = 3/4. One is the multiplicative identity.