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Free Fraction Calculator

Enter two fractions, pick an operation (+, −, ×, ÷), and this calculator returns the exact answer in lowest terms. It also shows the decimal value and, when the result is larger than 1, the equivalent mixed number — so you can read it however you need.

Result (simplified)
5/6
Decimal
0.833333

Quick answer

To calculate with two fractions, put them over a common denominator for addition or subtraction, multiply straight across for multiplication, or flip the second fraction and multiply for division — then reduce by dividing the numerator and denominator by their greatest common divisor (GCD). For example, 1/2 + 1/3 rewrites as 3/6 + 2/6 = 5/6, which is already in lowest terms and equals about 0.8333. This calculator performs each of those steps automatically and shows the simplified fraction, its decimal, and a mixed number when the value exceeds 1.

Formula & method

Addition / Subtraction of fractions

a/b ± c/d = (a·d ± c·b) / (b·d)
  • a — numerator of the first fraction
  • b — denominator of the first fraction
  • c — numerator of the second fraction
  • d — denominator of the second fraction

Multiplication / Division of fractions

a/b × c/d = (a·c)/(b·d)   and   a/b ÷ c/d = (a·d)/(b·c)
  • a — numerator of the first fraction
  • b — denominator of the first fraction
  • c — numerator of the second fraction
  • d — denominator of the second fraction

The calculator reads four whole numbers — numerator1, denominator1, numerator2, denominator2 — plus the chosen operation. For addition and subtraction it cross-multiplies to a common denominator using (a·d ± c·b)/(b·d); for multiplication it multiplies numerators and denominators straight across; for division it inverts the second fraction and multiplies (multiply by the reciprocal). It then computes the greatest common divisor (GCD) of the resulting numerator and denominator with the Euclidean algorithm and divides both by it, producing a fraction in lowest terms. Finally it derives the decimal by dividing numerator by denominator, and — if the absolute value is 1 or more — converts to a mixed number using integer division and remainder. A zero second fraction is rejected for division because dividing by zero is undefined.

Common fractions and their decimal equivalents (rounded to 4 places)

FractionDecimal
1/20.5
1/30.3333
1/40.25
2/30.6667
3/40.75
1/80.125
5/80.625
1/160.0625

Examples

Example 1: Adding fractions with different denominators
Input
2/3 + 1/4
Result
11/12 ≈ 0.9167
Why
Common denominator is 3·4 = 12. Rewrite: 2/3 = 8/12 and 1/4 = 3/12. Add the numerators: 8 + 3 = 11, so the sum is 11/12. The GCD of 11 and 12 is 1, so it is already in lowest terms. As a decimal, 11 ÷ 12 ≈ 0.9167.
Example 2: Subtracting fractions
Input
7/8 − 1/3
Result
13/24 ≈ 0.5417
Why
Common denominator is 8·3 = 24. Rewrite: 7/8 = 21/24 and 1/3 = 8/24. Subtract: 21 − 8 = 13, giving 13/24. The GCD of 13 and 24 is 1, so no reduction is needed. As a decimal, 13 ÷ 24 ≈ 0.5417.
Example 3: Dividing fractions (multiply by the reciprocal)
Input
5/6 ÷ 2/3
Result
5/4 = 1 1/4 = 1.25
Why
Flip the second fraction and multiply: 5/6 × 3/2 = (5·3)/(6·2) = 15/12. The GCD of 15 and 12 is 3, so reduce: 15÷3 = 5 and 12÷3 = 4, giving 5/4. Since 5/4 is greater than 1, the mixed number is 1 1/4 (4 goes into 5 once with remainder 1), and the decimal is 1.25.

When to use this tool

  • Homework and exam prep when you need the exact reduced fraction plus the decimal and mixed-number forms to check your own work.
  • Cooking, baking, and woodworking where measurements come in fractions (e.g., scaling 3/4 cup by 2/3, or adding 7/8 in. and 1/3 in.).
  • Any quick conversion between a fraction, its decimal, and a mixed number — for instance turning 11/4 into 2 3/4 or 2.75.

Common mistakes

  • Adding the denominators together. To add or subtract you need a common denominator, not the sum of the denominators: 1/2 + 1/3 is 5/6, not 2/5. Only the numerators are added once the denominators match.
  • Forgetting to flip when dividing. Division means multiply by the reciprocal of the second fraction, so 5/6 ÷ 2/3 = 5/6 × 3/2. Dividing numerator-by-numerator and denominator-by-denominator is incorrect.
  • Leaving the answer unreduced. An answer like 15/12 is correct in value but not in lowest terms; divide both parts by their GCD (3) to get 5/4. Always reduce before reporting the final fraction.

Frequently asked questions

Does the calculator always simplify the answer?

Yes. After performing the operation it computes the greatest common divisor (GCD) of the numerator and denominator and divides both by it, so the result is always shown in lowest terms — for example 15/12 is reported as 5/4.

How does it handle negative fractions?

Enter a minus sign on the numerator (e.g., −3 over 4 for −3/4). The sign is carried through the arithmetic, and the simplified result keeps a single sign on the numerator, such as −1/2 rather than 1/−2.

What is a mixed number and when is it shown?

A mixed number combines a whole number and a proper fraction, like 1 1/4. The calculator shows it whenever the result's absolute value is 1 or greater; for example 5/4 becomes 1 1/4. Proper fractions below 1 stay as a single fraction.

Can it divide by zero?

No. A fraction with a denominator of zero, or dividing by a fraction whose numerator is zero, is undefined in mathematics, so the calculator flags it as an error instead of returning a number.

Why is the decimal sometimes rounded?

Some fractions are repeating decimals — 5/6 = 0.8333… and 2/3 = 0.6667… — so the decimal display is rounded for readability. The fraction form remains exact, so use it when you need a precise value.

How do I turn a decimal back into a fraction?

Write the decimal over a power of ten matching its places, then reduce. For example, 0.75 = 75/100, and dividing both by their GCD of 25 gives 3/4. Terminating decimals always convert to exact fractions this way.

Sources & references

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