Fraction Calculator

Calculate fractions, simplify fractions, add, subtract, multiply, divide, and convert fractions with step-by-step accuracy.

Fraction Calculator

Add, subtract, multiply, divide, and simplify fractions, with results shown in lowest terms and as mixed numbers where appropriate. The calculator works with proper fractions, improper fractions, and mixed numbers.

Fraction arithmetic rules

  • Addition and subtraction require a common denominator: a/b + c/d = (a x d + c x b) / (b x d), then reduce. Using the least common denominator keeps the numbers smaller but any common denominator works.
  • Multiplication is direct: a/b x c/d = (a x c) / (b x d).
  • Division multiplies by the reciprocal: a/b / (c/d) = a/b x d/c = (a x d) / (b x c).
  • Simplifying divides numerator and denominator by their greatest common factor: 18/24 has GCF 6, so it reduces to 3/4.

A mixed number converts to an improper fraction before calculating: 2 1/3 = 7/3, because 2 x 3 + 1 = 7. An improper result converts back by dividing: 17/12 = 1 5/12, since 12 goes into 17 once with remainder 5.

Worked example

Add 2/3 + 3/4. The least common denominator of 3 and 4 is 12. Convert each fraction: 2/3 = 8/12 and 3/4 = 9/12. Adding the numerators gives 8/12 + 9/12 = 17/12, which is the mixed number 1 5/12.

Now multiply the same pair: 2/3 x 3/4 = 6/12, which simplifies to 1/2 after dividing the numerator and denominator by their GCF of 6. Finally, divide them: 2/3 / (3/4) = 2/3 x 4/3 = 8/9. Notice that multiplication and division never need a common denominator — only addition and subtraction do.

When to use this calculator

  • Checking homework in pre-algebra or algebra, where an unreduced answer like 6/12 often loses credit even when it is numerically correct.
  • Working through recipe or measurement problems in family and consumer science classes, such as scaling 3/4 cup by 2/3.
  • Verifying steps in longer problems — a slope of 2/3 divided by a factor of 3/4 — without introducing decimal rounding.
  • Converting between improper fractions and mixed numbers when a teacher requires answers in a specific form.

Tips for accurate results

  • Always reduce your final answer to lowest terms; most instructors require it.
  • Convert mixed numbers to improper fractions before any operation, not after.
  • Keep answers as fractions instead of decimals when the decimal repeats — 1/3 is exact, 0.33 is not.
  • When subtracting, keep track of which fraction comes first; 3/4 - 2/3 = 1/12, but reversing the order gives -1/12.
  • A denominator of zero is undefined, so double-check division problems where the second fraction's numerator could be zero.

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Frequently asked questions

How do I add fractions with different denominators?
Rewrite both fractions over a common denominator, then add the numerators. For 2/3 + 3/4, the least common denominator is 12, giving 8/12 + 9/12 = 17/12, or 1 5/12 as a mixed number. Multiplication and division do not need a common denominator; only addition and subtraction do.
How do I divide one fraction by another?
Multiply the first fraction by the reciprocal of the second: flip the second fraction, then multiply numerators and denominators straight across. So 2/3 divided by 3/4 becomes 2/3 x 4/3 = 8/9. Always simplify the result to lowest terms afterward.
How does the calculator simplify fractions?
It divides the numerator and denominator by their greatest common factor. For 18/24, the GCF is 6, so the fraction reduces to 3/4. A fraction is in lowest terms when the numerator and denominator share no common factor other than 1.
What is the difference between a mixed number and an improper fraction?
An improper fraction has a numerator at least as large as its denominator, such as 7/3, while the equivalent mixed number writes the whole part separately, as 2 1/3. Convert to improper form before calculating by multiplying the whole part by the denominator and adding the numerator. The calculator can express results either way.
When should I use fractions instead of decimals?
Use fractions when the decimal form repeats or the assignment requires exact answers: 1/3 is exact, while 0.33 introduces rounding error that can compound across steps. Fractions are also standard in algebra for slopes, ratios, and probabilities. Convert to decimals only when a measurement or final answer calls for it.
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