Fraction Calculator

Add, subtract, multiply, and divide fractions with step-by-step solution shown.

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Fraction Calculator
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How to use Fraction Calculator

Fractions appear throughout cooking, measurements, construction, academics, and everyday math. This calculator performs all four arithmetic operations on fractions and shows you exactly how each step is done. How to enter fractions: Enter the numerator (top number) and denominator (bottom number) for each fraction. For mixed numbers like 2 and 3/4, enter the whole number separately. Negative fractions are supported. Operations: Addition: To add fractions, find a common denominator, convert both fractions, then add the numerators. Example: 1/3 + 1/4 = 4/12 + 3/12 = 7/12. Subtraction: Same process as addition — find common denominator, then subtract numerators. Example: 3/4 - 1/3 = 9/12 - 4/12 = 5/12. Multiplication: Multiply numerators together and denominators together, then simplify. Example: 2/3 x 3/4 = 6/12 = 1/2. Division: Multiply by the reciprocal of the divisor. Example: 2/3 divided by 3/4 = 2/3 x 4/3 = 8/9. Simplification: All results are automatically simplified to lowest terms using the greatest common divisor. A result of 6/12 is shown as 1/2. Mixed number conversion: Improper fractions (numerator larger than denominator) are shown as both improper and mixed number form. 7/4 is shown as 7/4 = 1 and 3/4. Decimal equivalent: Every result shows the decimal form for context — 1/3 = 0.3333... Step-by-step solution: All intermediate steps are shown so you can follow the calculation and learn the method, not just get the answer.

Frequently Asked Questions

How do you find a common denominator to add fractions?

To add fractions with different denominators, find the Least Common Multiple (LCM) of both denominators. For 1/3 + 1/4: LCM of 3 and 4 is 12. Convert 1/3 to 4/12 (multiply top and bottom by 4) and 1/4 to 3/12 (multiply by 3). Now add: 4/12 + 3/12 = 7/12. The calculator shows each step including the LCM calculation.

How do you multiply fractions?

To multiply fractions: multiply numerators together and multiply denominators together. Example: 2/3 x 3/5 = (2x3)/(3x5) = 6/15. Then simplify by dividing by GCD: 6/15 = 2/5. For mixed numbers, convert to improper fractions first. Multiplication does not require a common denominator — it is the simplest fraction operation.

How do you divide fractions?

To divide fractions: multiply the first fraction by the reciprocal (flipped version) of the second fraction. Example: 2/3 divided by 3/4 becomes 2/3 x 4/3 = 8/9. The phrase "keep, change, flip" helps remember: keep the first fraction, change division to multiplication, flip the second fraction. This works because dividing by a number is the same as multiplying by its inverse.

How do you simplify a fraction?

To simplify a fraction to its lowest terms, divide both numerator and denominator by their Greatest Common Divisor (GCD). For 12/18: GCD of 12 and 18 is 6. 12/6 = 2 and 18/6 = 3, so 12/18 = 2/3. The calculator performs this automatically and shows the GCD used. A fraction is fully simplified when the GCD equals 1.

How do you convert a mixed number to an improper fraction?

For a mixed number like 2 and 3/4: multiply the whole number by the denominator (2 x 4 = 8), then add the numerator (8 + 3 = 11). The result is 11/4. To go back: divide numerator by denominator (11 divided by 4 = 2 remainder 3), giving 2 and 3/4. The calculator accepts mixed numbers and converts automatically for calculation.

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