Fraction Calculator

A calculator for solving problems with simple and mixed fractions.

How to use this calculator

Enter a whole number, numerator, and denominator for each value. Leave the whole-number field blank for a simple fraction, choose Add, Subtract, Multiply, or Divide, then select Calculate. To enter 2 1/4, use 2 as the whole number, 1 as the numerator, and 4 as the denominator. Use integer entries and a denominator greater than zero.

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ADDITION AND SUBTRACTION

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Fractions need a common denominator before their numerators can be added or subtracted. For 1/2 + 1/3, rewrite the values as 3/6 + 2/6 to obtain 5/6. For 1/2 − 2/3, use 3/6 − 4/6 = −1/6. A negative answer means the second value is larger than the first.

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MULTIPLICATION AND DIVISION

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Multiply numerators together and denominators together: 2/3 × 3/4 = 6/12 = 1/2. To divide, multiply by the reciprocal of the second fraction: 2/3 ÷ 1/4 = 2/3 × 4/1 = 8/3, or 2 2/3. Division by a zero-valued fraction is undefined.

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UNDERSTANDING SIMPLIFIED RESULTS

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Equivalent fractions express the same value in different forms. Dividing the numerator and denominator of 6/12 by their greatest common divisor, 6, gives 1/2. Simplification changes the notation, not the quantity. A mixed number such as 2 2/3 combines a whole-number part and a proper fraction.

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When scaling a recipe, make sure the measurements refer to the same unit before combining them. One-half cup plus one-third cup is five-sixths of a cup; adding cups to tablespoons requires a unit conversion first. Use the unsimplified calculation as a check if the final form looks unfamiliar.