Free Fraction Calculator
Add, subtract, multiply, or divide two fractions or mixed numbers, with the result automatically simplified to lowest terms. Every calculation shows its working, step by step, so you can check your homework or learn the method.
How Fraction Operations Work
- Adding/subtracting: find a common denominator, then add or subtract the numerators
- Multiplying: multiply the numerators together and the denominators together
- Dividing: multiply by the reciprocal (flip the second fraction, then multiply)
Simplifying Fractions
Every result is automatically reduced to lowest terms by dividing both the numerator and denominator by their greatest common divisor (GCD). For example, 6/8 simplifies to 3/4 because both numbers share a common factor of 2.
Mixed Numbers
A mixed number like 2½ combines a whole number and a fraction. Enter the whole number in the small box before the fraction — leave it at 0 for a plain fraction. Results over 1 are automatically converted back to a mixed number for readability.
Worked Examples
The "Show the working" panel prints these steps for any inputs you enter. Here are three you can check by hand.
Adding: 2/3 + 3/4. The denominators 3 and 4 share no factor, so the lowest common denominator is 3 × 4 = 12. Rewrite each fraction: 2/3 = 8/12 and 3/4 = 9/12. Add the numerators: 8 + 9 = 17, giving 17/12. That is an improper fraction, so convert it: 12 goes into 17 once with 5 left over, and the answer is 1 5/12.
Subtracting mixed numbers: 3 1/4 − 1 2/3. Convert both to improper fractions first: 3 1/4 = 13/4 and 1 2/3 = 5/3. The LCD of 4 and 3 is 12, so 13/4 = 39/12 and 5/3 = 20/12. Subtract: 39 − 20 = 19, giving 19/12 = 1 7/12. Subtracting the whole parts and fraction parts separately also works, but you have to borrow whenever the second fraction is larger than the first, which is where most hand errors creep in.
Dividing: 5/6 ÷ 2/9. Flip the second fraction and multiply: 5/6 × 9/2 = 45/12. The GCD of 45 and 12 is 3, so 45/12 simplifies to 15/4, which is 3 3/4 as a mixed number.
Finding the Lowest Common Denominator
Any common denominator works for adding and subtracting, and multiplying the two denominators together always produces one. The lowest common denominator (LCD) simply keeps the numbers small. It is the least common multiple of the two denominators, which you can find in two ways:
- List multiples until one appears in both lists. For 8 and 12: 8, 16, 24 and 12, 24, so the LCD is 24.
- Use the GCD. LCM(a, b) = a × b ÷ GCD(a, b). For 8 and 12 the GCD is 4, so the LCM is 96 ÷ 4 = 24.
Using 8 × 12 = 96 as the denominator instead gives the same final answer after simplifying, just with more arithmetic on the way.
Common Mistakes
- Adding the denominators. 1/2 + 1/3 is not 2/5. Half of something plus a third of it must be more than half, and 2/5 is less than half. The correct answer is 3/6 + 2/6 = 5/6.
- Multiplying mixed numbers part by part. 2 1/2 × 1 1/2 is not 2 × 1 plus 1/2 × 1/2. Convert first: 5/2 × 3/2 = 15/4 = 3 3/4.
- Flipping the wrong fraction when dividing. Only the divisor (the second fraction) is inverted. 3/4 ÷ 1/2 = 3/4 × 2/1 = 3/2, not 4/3 × 1/2.
- Cancelling across a plus sign. You can cancel a common factor between a numerator and a denominator when multiplying, but never between terms that are being added.
- Stopping before lowest terms. 6/8 is a correct value, but most teachers and exam boards expect 3/4.
Fractions, Decimals and Percentages
The decimal shown under each result is simply the numerator divided by the denominator: 3/8 = 3 ÷ 8 = 0.375, which is 37.5%. Some fractions produce recurring decimals, so 1/3 becomes 0.333… and 2/7 becomes 0.285714 repeating. That is why fractions are preferred when an exact value matters, such as in algebra, ratios, or measurements in eighths and sixteenths of an inch, while decimals are easier to compare at a glance and to type into a calculator. For percentage work, the percentage calculator handles the conversion directly.
Frequently Asked Questions
Why do I need a common denominator to add fractions? Fractions represent parts of a whole, and you can only add "like parts" — quarters with quarters, thirds with thirds. Converting to a common denominator makes the pieces the same size before combining them.
What if my denominator is 0? Division by zero is undefined in mathematics — the calculator will flag this as an invalid input rather than showing a result.
Does this handle negative fractions? Yes — enter a negative number in the numerator or whole-number field and the calculator handles the sign correctly through every operation.
How is dividing by a fraction the same as multiplying? Dividing by a number is the same as multiplying by its reciprocal (1 divided by that number). So a/b ÷ c/d = a/b × d/c — flip the second fraction and multiply.
What is the difference between a proper and an improper fraction? A proper fraction has a numerator smaller than its denominator, so its value is less than 1 (3/4). An improper fraction has a numerator equal to or larger than its denominator (7/4) and can always be rewritten as a mixed number (1 3/4). Both forms are correct: improper fractions are easier to calculate with, mixed numbers are easier to read.
How do I simplify a fraction by hand? Find the largest number that divides both the numerator and the denominator, then divide both by it. If that is hard to spot, divide repeatedly by small primes (2, 3, 5, 7) until nothing divides both: 18/24 becomes 9/12, then 3/4.
How do I convert a fraction to a decimal? Divide the top number by the bottom number: 5/8 = 5 ÷ 8 = 0.625. To go the other way, write the decimal over a power of ten and simplify: 0.625 = 625/1000 = 5/8.