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EXACT FRACTIONS · CLEAR WORKING

Fraction calculator
with step-by-step answers.

Add, subtract, multiply or divide fractions and mixed numbers. Get a simplified fraction, a mixed number and a decimal, with the working shown.

Keep the whole part at 0 for an ordinary fraction. For −1 ½, choose − and enter 1, 1 and 2. Every visible field must be filled.

First fraction
Second fraction

How to use the fraction calculator

Ordinary fractions and mixed numbers

The numerator is the number above the line; the denominator is below it. Enter 0 as the whole part for ¾, or 2 as the whole part for 2 ¾. The sign applies to the entire number: −2 ¾ means −(2 + ¾) = −11/4.

Choose a calculation

Select one of the four operations for two fractions. Choose Simplify for just one fraction, or Decimal to fraction for a terminating decimal. Calculate displays exact working. Editing any input hides the old result so it cannot be mistaken for an answer to the new values.

Fraction formulas and worked examples

Add or subtract with a common denominator

For a/b + c/d, a general formula is (ad + bc)/(bd); subtraction replaces + with −. This calculator uses the least common denominator to keep intermediate numbers smaller. For ⅓ + ⅙, use denominator 6: ²⁄₆ + ⅙ = ³⁄₆ = ½. For ¾ − ⅔, use denominator 12: 9/12 − 8/12 = 1/12.

Multiply fractions

Multiply the numerators and multiply the denominators: (a/b) × (c/d) = ac/bd. For ⅔ × ¾, the product is 6/12. Dividing both parts by their greatest common divisor, 6, gives ½.

Divide using the reciprocal

For a nonzero second fraction, (a/b) ÷ (c/d) = (a/b) × (d/c). Convert mixed numbers first: 1 ½ = 3/2. Then 3/2 ÷ 3/4 = 3/2 × 4/3 = 12/6 = 2. Division by a fraction equal to zero is undefined.

Simplify with the greatest common divisor

Divide both parts by their greatest common divisor. For 84/126, the greatest common divisor is 42, so 84 ÷ 42 over 126 ÷ 42 gives 2/3. An improper result can also be written as a mixed number: 11/4 = 2 ¾.

Convert a finite decimal exactly

Write the digits over a power of ten, then reduce. Since 0.125 has three decimal places, 0.125 = 125/1000 = 1/8. The same process gives −0.125 = −1/8. Entering 0.333 gives 333/1000, not 1/3: those are different numbers.

Precision and input limits

Calculations use JavaScript BigInt integer arithmetic, so the fraction result is exact for the entered values. Each integer field accepts up to 60 digits; the decimal converter accepts up to 60 digits in total. Decimal output is rounded to 12 places, with ties rounded away from zero. An approximation symbol identifies a rounded result, including tiny nonzero fractions that display as approximately zero.

Fraction calculator questions

Can a denominator be zero?

No. A denominator of zero does not define a fraction. A zero numerator with a nonzero denominator is valid and simplifies to 0.

Can I use negative and improper fractions?

Yes. Use the sign selector for a negative value, and keep the individual parts nonnegative. The numerator may be larger than the denominator. For example, sign − with whole part 0, numerator 7 and denominator 3 represents −7/3, also written −2 ⅓.

Are my inputs saved?

The arithmetic runs in your browser. This calculator does not send inputs to a server or store a calculation history. Reloading restores the initial example. Ordinary page requests may be logged by the web server.

Methods and corrections

The calculator uses the standard rules for rational arithmetic and Euclid’s algorithm for the greatest common divisor. See OpenStax: multiplying and dividing fractions for a mathematical reference. Report a reproducible calculation error to infos@web-calculator.net, including your inputs and expected answer.

Need roots, powers or trigonometry? Use the scientific calculator.

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