Fraction Calculator
Add, subtract, multiply, or divide two fractions and get the simplified result instantly.
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How to use this calculator
- 1
Enter the numerator and denominator of the first fraction.
- 2
Select the operation: add, subtract, multiply, or divide.
- 3
Enter the numerator and denominator of the second fraction.
- 4
The result is automatically simplified to lowest terms.
Frequently asked questions
What does the calculator show for each answer?
The result reduced to lowest terms, its decimal value (up to 8 places, trailing zeros trimmed) and, when the answer is an improper fraction that is not a whole number, a mixed number. 3/4 + 5/6 gives 19/12, 1.58333333 and 1 7/12. Whole-number results appear as, for example, 2/1 with decimal 2 and no mixed-number line.
Can I enter mixed numbers like 2 1/2?
Not directly. Convert to an improper fraction first: 2 1/2 is (2 × 2 + 1) ÷ 2 = 5/2, so enter 5 and 2. A negative mixed number such as −2 1/2 becomes −5/2. The mixed-number line in the output goes the other way, turning the answer into a whole part and a proper fraction.
What happens with negative numbers and negative denominators?
Signs are handled in the numerator. Entering 1 over −2 plus 1 over 4 returns −1/4 with decimal −0.25, never a negative denominator. Negative results keep the sign on the whole part of the mixed number, so −7/2 displays as −3 1/2.
Why do I get an error when dividing?
Two cases are blocked. A zero in either denominator gives "Denominator cannot be zero". Dividing by a fraction whose numerator is zero, such as 1/2 ÷ 0/3, gives "Cannot divide by zero", because the second fraction equals 0 and has no reciprocal.
Are decimals accepted in the numerator or denominator?
The fields are rounded to the nearest whole number before any arithmetic. Typing 1.6 over 2 is treated as 2 over 2, and the sum with 1/3 comes out as 4/3. If you have decimal values, convert them to fractions first (0.75 is 3/4) or use a different tool.
Does it show common denominators or steps?
No, only the final reduced fraction, decimal and mixed number. The unreduced form is not displayed, though it equals the cross-multiplied numerator over the product of denominators for addition and subtraction. For 3/4 − 5/6 that is 18/24 − 20/24 = −2/24, which the tool reduces to −1/12.
Can it compare two fractions or add more than two?
It works with exactly two fractions. To compare them, subtract: a positive result means the first is larger, as in 5/6 − 3/4 = 1/12. To add three fractions, run two first and feed the reduced answer back in as the first fraction.
Fraction calculator — add, subtract, multiply and divide with automatic reduction
How each operation is carried out
For addition and subtraction the tool cross-multiplies: a/b + c/d becomes (ad + cb)/bd. Multiplication goes straight across, and division flips the second fraction and multiplies. Every result is then divided by the greatest common divisor of its top and bottom, so 6/12 is displayed as 1/2 and 2/24 as 1/12. The decimal and mixed-number lines are derived from the reduced fraction, so they never disagree with it. When the reduced numerator is smaller than the denominator, as in 1/12 or −1/12, the answer is already a proper fraction and no mixed number is shown. A whole-number answer such as 2/1 is displayed over 1 rather than being collapsed to a bare integer.
Worked example: unlike denominators
Adding 3/4 and 5/6 gives 19/12, which is 1.58333333 as a decimal and 1 7/12 as a mixed number. Reversing the order of subtraction flips only the sign: 5/6 − 3/4 is 1/12, while 3/4 − 5/6 is −1/12. Fractions whose denominators share a factor, like 1/3 + 1/6, still reduce correctly and return 1/2.
Worked example: multiplication and division
Multiplying 2/3 by 9/4 gives 3/2, shown as 1.5 and the mixed number 1 1/2. Dividing 7/8 by 7/16 returns 2/1, since the second fraction is exactly half of the first. In both cases the tool cancels the common factors for you, which is the step students most often skip. Dividing by a fraction is the case that surprises people: the answer is bigger than the first fraction whenever the second is below 1, and here halving the divisor exactly doubles the quotient.
Results for the standard operations
The table collects the results above.
| Calculation | Simplified | Decimal | Mixed |
|---|---|---|---|
| 3/4 + 5/6 | 19/12 | 1.58333333 | 1 7/12 |
| 3/4 − 5/6 | −1/12 | −0.08333333 | — |
| 2/3 × 9/4 | 3/2 | 1.5 | 1 1/2 |
| 7/8 ÷ 7/16 | 2/1 | 2 | — |
| 1/3 + 1/6 | 1/2 | 0.5 | — |
Reading the decimal
Decimals stop at eight places, so 1/12 shows as 0.08333333. A repeating decimal is therefore an approximation, while the fraction is exact. Prefer the fraction when you need to carry a value into a further calculation. For example, copy 19/12 into the next sum rather than 1.58333333, and the answer stays exact all the way through a multi-step problem instead of picking up a small rounding error at each stage. The same applies to checking homework: a decimal like 0.08333333 cannot be told apart from 1/12 by eye, but the reduced fraction can be compared with a textbook answer directly.
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