Multiplying Fractions Calculator – Guide & Formulas
Multiply fractions instantly. Shows numerators and denominators multiplied, then simplified to lowest terms with step-by-step solutions.
Multiply fractions with ease. Enter two fractions to see the product with step-by-step multiplication of numerators and denominators, plus simplification to lowest terms.
Key Takeaway
Use the free Multiplying Fractions Calculator to multiply fractions instantly. shows numerators and denominators multiplied, then simplified to lowest terms with step-by-step solutions. Get instant results with step-by-step explanations.
How to Use the Multiplying Fractions Calculator
- Enter the numerator and denominator for the first fraction.
- Enter the numerator and denominator for the second fraction.
- Click "Multiply" to see the product and step-by-step breakdown.
- Review the multiplication and simplification steps.
- Copy the result if needed.
The Formula
Variable Definitions
- a/b: First fraction
- c/d: Second fraction
- GCD: Greatest Common Divisor used to simplify the result
Multiplying 2/3 × 3/4
Multiply the fractions 2/3 and 3/4.
- Step 1: Multiply numerators: 2 × 3 = 6.
- Step 2: Multiply denominators: 3 × 4 = 12.
- Step 3: Result before simplifying: 6/12.
- Step 4: Find GCD of 6 and 12: GCD = 6.
- Step 5: Simplify: 6 ÷ 6 = 1, 12 ÷ 6 = 2. Final answer: 1/2.
Frequently Asked Questions
How do you multiply fractions?
Multiply the numerators together to get the new numerator, multiply the denominators together to get the new denominator, then simplify the result by dividing both by their GCD.
What is 1/2 × 1/3?
1/2 × 1/3 = (1 × 1)/(2 × 3) = 1/6. The result is already in lowest terms.
What is 3/4 × 2/5?
3/4 × 2/5 = (3 × 2)/(4 × 5) = 6/20 = 3/10. Simplify by dividing both by GCD = 2.
How do I multiply a fraction by a whole number?
Write the whole number as a fraction with denominator 1, then multiply normally. For example, 3 × 2/5 = 3/1 × 2/5 = 6/5 = 1 1/5.
What is 2/3 × 4/5?
2/3 × 4/5 = (2 × 4)/(3 × 5) = 8/15. The result is already in lowest terms since GCD(8,15) = 1.
What is 5/6 × 3/10?
5/6 × 3/10 = (5 × 3)/(6 × 10) = 15/60 = 1/4. Simplify by dividing both by GCD = 15.
What is 4/7 × 7/8?
4/7 × 7/8 = (4 × 7)/(7 × 8) = 28/56 = 1/2. Simplify by dividing both by GCD = 28.
What is 3/8 × 2/9?
3/8 × 2/9 = (3 × 2)/(8 × 9) = 6/72 = 1/12. Simplify by dividing both by GCD = 6.
Can I simplify before multiplying?
Yes! You can cross-cancel common factors before multiplying. For 3/4 × 2/3, cancel the 3s: 1/4 × 2/1 = 2/4 = 1/2. This keeps numbers smaller.
What is 1 1/2 × 2 1/3?
Convert: 3/2 × 7/3 = (3 × 7)/(2 × 3) = 21/6 = 7/2 = 3 1/2. Cancel the 3s first: 1/2 × 7/1 = 7/2.
What is 5/8 × 4/15?
5/8 × 4/15 = (5 × 4)/(8 × 15) = 20/120 = 1/6. Simplify by dividing both by GCD = 20.
What is 2/9 × 3/4?
2/9 × 3/4 = (2 × 3)/(9 × 4) = 6/36 = 1/6. Simplify by dividing both by GCD = 6.
What is 7/10 × 5/14?
7/10 × 5/14 = (7 × 5)/(10 × 14) = 35/140 = 1/4. Simplify by dividing both by GCD = 35.
What is 3/5 × 10/9?
3/5 × 10/9 = (3 × 10)/(5 × 9) = 30/45 = 2/3. Simplify by dividing both by GCD = 15.
What is 4/15 × 9/8?
4/15 × 9/8 = (4 × 9)/(15 × 8) = 36/120 = 3/10. Simplify by dividing both by GCD = 12.
What is 1/6 × 3/5?
1/6 × 3/5 = (1 × 3)/(6 × 5) = 3/30 = 1/10. Simplify by dividing both by GCD = 3.
What is 2/7 × 14/5?
2/7 × 14/5 = (2 × 14)/(7 × 5) = 28/35 = 4/5. Simplify by dividing both by GCD = 7.
What is 6/11 × 22/9?
6/11 × 22/9 = (6 × 22)/(11 × 9) = 132/99 = 4/3 = 1 1/3. Simplify by dividing both by GCD = 33.
How do I multiply three fractions?
Multiply all numerators together and all denominators together: (a/b) × (c/d) × (e/f) = (a×c×e)/(b×d×f), then simplify.
What is 1/2 × 1/4 × 1/3?
1/2 × 1/4 × 1/3 = (1×1×1)/(2×4×3) = 1/24. Already in lowest terms.