➗ Fraction Calculator
By ToolNimba Editorial Team · Updated 2026-06-19
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, 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 fraction 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. Adding and subtracting need a common denominator first. The quickest reliable way is to cross multiply: a/b + c/d = (a x d + c x b) / (b x d), which always lands on a valid common denominator.
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. This calculator does each of these steps for you and also converts the simplified result into a mixed number and a decimal.
When to use it
- Checking a child or student fraction homework answer and seeing the simplified form.
- Scaling a recipe up or down when measurements are given in fractions of a cup or teaspoon.
- Combining measurements in woodworking or sewing, where lengths are often in fractions of an inch.
- Converting an awkward improper fraction into a clean mixed number or a decimal.
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.
- 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)
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% |
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.
- 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.
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.
- 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.
- 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.
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 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.
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 an improper fraction and a mixed number?
An improper fraction such as 7/4 has a numerator larger than its denominator. A mixed number writes the same value as a whole number plus a proper fraction, so 7/4 becomes 1 3/4. The calculator shows both forms.
Why does dividing by 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.