➗ Fraction Calculator: Add, Subtract, Multiply, Divide
By ToolNimba Editorial Team · Updated 2026-06-20
Enter whole-number numerators and denominators. Denominators cannot be zero.
This fraction calculator adds, subtracts, multiplies, and divides two fractions and shows the answer in three forms: a fully simplified fraction, a mixed number, and a decimal. Type a numerator and denominator for each fraction, pick the operation, and the result updates instantly. It handles negative values and improper fractions, so you can use it for homework checks, recipe scaling, woodworking measurements, or any quick everyday calculation.
What is the Fraction Calculator?
A fraction represents a part of a whole and is written as a numerator over a denominator, for example 3/4. The denominator (the bottom number) tells you how many equal parts the whole is divided into, and the numerator (the top number) tells you how many of those parts you have. A proper fraction such as 3/4 is less than one whole. A fraction equal to or larger than one whole, such as 7/4, is called an improper fraction, and the same value can be written as the mixed number 1 3/4.
The method depends on the operation. To multiply, you multiply the numerators together and the denominators together: 2/3 x 6/5 = 12/15. To divide, you flip the second fraction and then multiply (this is the reciprocal rule): 7/8 divided by 1/2 becomes 7/8 x 2/1 = 14/8. Multiplication and division never need a common denominator, which surprises a lot of people who assume every fraction operation works the same way.
Adding and subtracting are different because you can only combine parts that are the same size, so the fractions must share a denominator first. There are two reliable routes. The least common denominator (LCD) method finds the smallest number both denominators divide into and rewrites each fraction over it, which keeps the numbers small: 1/4 + 1/3 becomes 3/12 + 4/12 = 7/12. The cross multiplication method, sometimes called the butterfly method, skips the search for the LCD and uses the formula a/b + c/d = (a x d + c x b) / (b x d). It always lands on a valid common denominator, though the result may need more simplifying afterward. This calculator uses cross multiplication internally and then reduces, so you always get the lowest-terms answer.
Mixed numbers follow the same rules once you convert them. To turn a mixed number into an improper fraction, multiply the whole number by the denominator and add the numerator: 1 3/4 becomes (1 x 4 + 3) / 4 = 7/4. After any operation you can convert back the other way by dividing the top by the bottom: the whole-number part is the quotient and the remainder sits over the original denominator. Converting first means you never have to juggle whole numbers and fraction parts separately.
Whatever the operation, the final step is to simplify. Every result is reduced by dividing the top and bottom by their greatest common divisor (GCD), so 12/15 becomes 4/5 and 14/8 becomes 7/4. Simplifying does not change the value, it just expresses it in the lowest terms, which is the form teachers, recipes, and tape measures expect. This calculator does each of these steps for you and also converts the simplified result into a mixed number and a decimal so you can read the answer in whichever form you need.
When to use it
- Checking a child or student fraction homework answer and seeing the fully simplified form.
- Scaling a recipe up or down when measurements are given in fractions of a cup or teaspoon.
- Combining measurements in woodworking, construction, or sewing, where lengths are often in fractions of an inch.
- Converting an awkward improper fraction into a clean mixed number or a decimal.
- Adding or subtracting mixed numbers without converting everything by hand first.
- Working out probabilities, ratios, or test scores that are easier to read as a single reduced fraction.
How to use the Fraction Calculator
- Type the numerator (top) and denominator (bottom) of the first fraction.
- Choose the operation: plus, minus, times, or divide.
- Type the numerator and denominator of the second fraction.
- For a mixed number, convert it to an improper fraction first (whole x denominator + numerator over the same denominator).
- Read off the simplified fraction, the mixed number, and the decimal in the result boxes.
- Use a minus sign in front of a numerator to enter a negative fraction.
Formula & method
Worked examples
Add 1/2 and 1/3.
- Cross multiply for a common denominator: (1×3 + 1×2) ÷ (2×3)
- = (3 + 2) ÷ 6 = 5/6
- GCD of 5 and 6 is 1, so it is already simplified
- As a decimal: 5 ÷ 6 = 0.8333…
Result: 5/6 (about 0.8333)
Subtract 5/6 from 3/4.
- Cross multiply: (3×6 - 5×4) ÷ (4×6)
- = (18 - 20) ÷ 24 = -2/24
- GCD of 2 and 24 is 2, so divide both: -1/12
- As a decimal: -1 ÷ 12 = -0.0833…
Result: -1/12 (about -0.0833)
Multiply 2/3 by 6/5.
- Multiply tops and bottoms: (2×6) ÷ (3×5) = 12/15
- GCD of 12 and 15 is 3, so divide both: 4/5
- As a decimal: 4 ÷ 5 = 0.8
Result: 4/5 (0.8)
Divide 7/8 by 1/2.
- Flip the second fraction and multiply: 7/8 × 2/1
- = (7×2) ÷ (8×1) = 14/8
- GCD of 14 and 8 is 2, so divide both: 7/4
- As a mixed number: 1 3/4, or 1.75 as a decimal
Result: 7/4 = 1 3/4 (1.75)
Add the mixed numbers 2 1/2 and 1 3/4.
- Convert each to an improper fraction: 2 1/2 = 5/2 and 1 3/4 = 7/4
- Cross multiply: (5×4 + 7×2) ÷ (2×4) = (20 + 14) ÷ 8 = 34/8
- GCD of 34 and 8 is 2, so divide both: 17/4
- Convert back to a mixed number: 17 ÷ 4 = 4 remainder 1, so 4 1/4
Result: 17/4 = 4 1/4 (4.25)
Common fractions as decimals and percentages
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.3333… | 33.33% |
| 2/3 | 0.6667… | 66.67% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/10 | 0.1 | 10% |
Inch fractions as decimals (tape measure reference)
| Fraction of an inch | Decimal inches | Millimeters (approx) |
|---|---|---|
| 1/16 | 0.0625 | 1.59 mm |
| 1/8 | 0.125 | 3.18 mm |
| 3/16 | 0.1875 | 4.76 mm |
| 1/4 | 0.25 | 6.35 mm |
| 3/8 | 0.375 | 9.53 mm |
| 1/2 | 0.5 | 12.70 mm |
| 5/8 | 0.625 | 15.88 mm |
| 3/4 | 0.75 | 19.05 mm |
Which step applies to each operation
| Operation | What to do | Example |
|---|---|---|
| Add (+) | Common denominator, then add tops | 1/2 + 1/3 = 5/6 |
| Subtract (-) | Common denominator, then subtract tops | 3/4 - 5/6 = -1/12 |
| Multiply (x) | Multiply tops, multiply bottoms | 2/3 x 6/5 = 4/5 |
| Divide (/) | Flip the second fraction, then multiply | 7/8 / 1/2 = 7/4 |
Common mistakes to avoid
- Adding the denominators. A common slip is to write 1/2 + 1/3 = 2/5 by adding tops and bottoms separately. That is wrong. You must find a common denominator first, giving 5/6.
- Finding a common denominator before multiplying. Multiplication and division do not need a common denominator. For 2/3 x 6/5 you just multiply straight across. Forcing a common denominator first wastes time and invites errors.
- Forgetting to flip when dividing. Dividing by a fraction means multiplying by its reciprocal. 7/8 divided by 1/2 is not 7/16. Flip the 1/2 to 2/1 first, giving 7/8 x 2/1 = 7/4.
- Leaving the answer unsimplified. An answer like 12/15 is correct but not in lowest terms. Always divide the top and bottom by their greatest common divisor, here 3, to get 4/5.
- Mishandling negative signs. When a fraction is negative, the minus applies to the whole fraction. -3/4 is the same as 3/-4, so keep the sign consistent and put it on the numerator to avoid confusion.
- Operating on mixed numbers without converting. Adding 2 1/2 and 1 3/4 by combining the whole parts and fraction parts separately is error prone. Convert each to an improper fraction first, then operate, then convert back.
Glossary
- Numerator
- The top number of a fraction. It counts how many equal parts you have.
- Denominator
- The bottom number of a fraction. It tells you how many equal parts make up one whole.
- Proper fraction
- A fraction whose numerator is smaller than its denominator, such as 3/4. Its value is less than one whole.
- Improper fraction
- A fraction where the numerator is larger than or equal to the denominator, such as 7/4. It is greater than or equal to one whole.
- Mixed number
- A whole number combined with a proper fraction, such as 1 3/4, which equals the improper fraction 7/4.
- Reciprocal
- A fraction flipped upside down. The reciprocal of 2/3 is 3/2. Dividing by a fraction is the same as multiplying by its reciprocal.
- Least common denominator (LCD)
- The smallest number that both denominators divide into evenly. Using it to add or subtract keeps the numbers as small as possible.
- Greatest common divisor (GCD)
- The largest whole number that divides both the numerator and denominator exactly. Dividing by it reduces a fraction to its lowest terms.
Frequently asked questions
How do you add fractions with different denominators?
Find a common denominator, rewrite both fractions over it, then add the numerators. The quickest method is cross multiplication: a/b + c/d = (a×d + c×b) ÷ (b×d). For example, 1/2 + 1/3 = (3 + 2) ÷ 6 = 5/6. This calculator does it automatically and reduces the answer.
What is 1/3 plus 1/4?
The answer is 7/12. The least common denominator of 3 and 4 is 12, so 1/3 becomes 4/12 and 1/4 becomes 3/12. Adding the numerators gives 4 + 3 = 7, leaving 7/12. Because 7 and 12 share no common factor, 7/12 is already fully simplified.
How do you divide fractions?
Flip the second fraction (take its reciprocal) and then multiply. For example, 7/8 divided by 1/2 becomes 7/8 x 2/1 = 14/8, which simplifies to 7/4. Never divide the numerators and denominators directly.
How do you multiply fractions?
Multiply the two numerators together to get the new top, and multiply the two denominators together to get the new bottom, then simplify. For example, 2/3 x 6/5 = 12/15, which reduces to 4/5. No common denominator is needed for multiplication.
How does the calculator simplify the answer?
It finds the greatest common divisor (GCD) of the numerator and denominator and divides both by it. For example 12/15 has a GCD of 3, so it reduces to 4/5. The value stays the same, just in lowest terms.
How do you add or subtract mixed numbers?
Convert each mixed number to an improper fraction first: multiply the whole number by the denominator and add the numerator. Then add or subtract as usual and convert the result back to a mixed number. For example, 2 1/2 + 1 3/4 = 5/2 + 7/4 = 17/4 = 4 1/4.
How do you convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The whole-number part is the quotient and the remainder goes over the original denominator. For example, 7/4 gives 7 ÷ 4 = 1 remainder 3, so the mixed number is 1 3/4.
Can I use negative fractions?
Yes. Put a minus sign in front of the numerator, for example -3 over 4 for negative three quarters. The calculator keeps the sign on the numerator and reports the correctly signed result.
What is the difference between the LCD method and cross multiplication?
Both give the right answer for adding and subtracting. The least common denominator (LCD) method uses the smallest shared denominator, which keeps numbers small. Cross multiplication multiplies the two denominators together, which is faster to apply but may need more simplifying afterward.
Why does a denominator of zero not work?
A denominator of zero means dividing a whole into zero parts, which is undefined in mathematics. The calculator will ask you to change any zero denominator before it shows a result.