Fraction Calculator — Add, Subtract, Multiply, Divide Fractions
Calculate fractions with step-by-step simplification. Add, subtract, multiply, or divide any two fractions and get the result as a simplified fraction and decimal. See also Fraction to Decimal and Decimal to Fraction.
How to Calculate Fractions
To calculate with fractions, you need to understand the four basic operations. For addition and subtraction, find a common denominator first, then add or subtract the numerators. For multiplication, multiply the numerators together and the denominators together. For division, flip the second fraction (reciprocal) and multiply. After computing, always simplify the result by dividing both numerator and denominator by their greatest common divisor (GCD).
Fraction Formulas
Addition: a/b + c/d = (a×d + c×b) / (b×d)
Subtraction: a/b − c/d = (a×d − c×b) / (b×d)
Multiplication: a/b × c/d = (a×c) / (b×d)
Division: a/b ÷ c/d = (a×d) / (b×c)
Simplify: divide numerator and denominator by GCD
Worked Example
1/2 + 1/3 = ?
Step 1: Find common denominator: 2 × 3 = 6
Step 2: Convert: 1/2 = 3/6, 1/3 = 2/6
Step 3: Add numerators: 3 + 2 = 5
Result: 5/6 ≈ 0.8333
Frequently Asked Questions
How do you add fractions with different denominators?
Find the least common denominator (LCD), convert each fraction to an equivalent fraction with that denominator, then add the numerators. For example, 1/4 + 1/6: LCD = 12, so 3/12 + 2/12 = 5/12.
What does it mean to simplify a fraction?
Simplifying (or reducing) a fraction means dividing both the numerator and denominator by their greatest common divisor (GCD) until no common factor remains. For example, 6/8 simplifies to 3/4 because GCD(6,8) = 2.
How do you divide fractions?
To divide fractions, multiply the first fraction by the reciprocal (flipped version) of the second. For example, 2/3 ÷ 4/5 = 2/3 × 5/4 = 10/12 = 5/6.
Can fractions have negative numbers?
Yes. A fraction is negative if either the numerator or denominator (but not both) is negative. This calculator handles negative values and always places the sign on the numerator in the simplified result.
Solved Examples — Fractions
Example: Add 3/8 + 5/12
Solution:
Step 1: Find LCD of 8 and 12. LCD = 24
Step 2: Convert: 3/8 = 9/24, 5/12 = 10/24
Step 3: Add numerators: 9 + 10 = 19
Step 4: Result = 19/24 (already simplified, GCD(19,24) = 1)
Answer: 19/24 ≈ 0.7917
Example: Subtract 7/9 − 2/5
Solution:
Step 1: Find LCD of 9 and 5. LCD = 45
Step 2: Convert: 7/9 = 35/45, 2/5 = 18/45
Step 3: Subtract numerators: 35 − 18 = 17
Step 4: Result = 17/45 (GCD(17,45) = 1, already simplified)
Answer: 17/45 ≈ 0.3778
Example: Multiply 5/6 × 9/10
Solution:
Step 1: Multiply numerators: 5 × 9 = 45
Step 2: Multiply denominators: 6 × 10 = 60
Step 3: Simplify 45/60: GCD(45,60) = 15
Step 4: 45 ÷ 15 = 3, 60 ÷ 15 = 4
Answer: 3/4 = 0.75
Example: A recipe calls for 2/3 cup of flour. If you're making 1.5 batches, how much flour?
Solution:
Step 1: 1.5 = 3/2
Step 2: Multiply: 2/3 × 3/2 = (2×3)/(3×2) = 6/6
Step 3: Simplify: 6/6 = 1
Answer: 1 cup of flour
Practice Questions
Try these on your own:
- Add 4/7 + 3/14 (Answer: 11/14)
- Subtract 5/6 − 1/4 (Answer: 7/12)
- Multiply 7/8 × 4/5 (Answer: 7/10)
- Divide 3/4 ÷ 9/16 (Answer: 4/3)
- Simplify 48/72 to lowest terms (Answer: 2/3)
- A pizza has 8 slices. You eat 3 slices, your friend eats 2 slices. What fraction is left? (Answer: 3/8)
Common Mistakes to Avoid
The most common mistake when adding fractions is adding both numerators and denominators directly — for example, writing 1/2 + 1/3 = 2/5 (wrong!). You must find a common denominator first. When multiplying, students sometimes find a common denominator unnecessarily — just multiply straight across. When dividing, remember to flip only the second fraction (the divisor), not the first. Another pitfall is forgetting to simplify the final answer: always check if the numerator and denominator share a common factor. Also, be careful with mixed numbers — convert them to improper fractions before calculating. For example, 2 1/3 = 7/3, not 2/3. Finally, watch signs carefully: −3/4 is the same as 3/−4, but not the same as −3/−4 (which equals positive 3/4).
Key Takeaways
- For addition/subtraction: find the LCD, convert fractions, then add/subtract numerators only.
- For multiplication: multiply numerators together, multiply denominators together, then simplify.
- For division: flip the second fraction (take its reciprocal) and multiply.
- Always simplify your answer by dividing numerator and denominator by their GCD.
- Convert mixed numbers to improper fractions before performing operations.
- A fraction equals zero only when its numerator is zero (denominator can never be zero).