Calcufast

Fraction calculator with steps

Add, subtract, multiply or divide fractions. See the reduced fraction, mixed number and decimal with working.

Inputs
Enter values to calculate
First fraction
Second fraction

Enter whole numbers from −1,000,000 to 1,000,000. Denominators must not be zero. Results update as you type.

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Results

Reduced fraction

5/4

Mixed number
1 1/4
Decimal (up to 10 decimal places)
1.25

Show your working

  1. Cross-multiply, then add the numerators.[(1) × (4) + (3) × (2)] / [(2) × (4)] = 10/8
  2. Divide both parts by their GCD (2) and make the denominator positive.5/4

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Check fraction arithmetic and see the working

Enter the top and bottom numbers of two fractions, then choose an operation. The calculator returns a reduced fraction, a mixed number where useful, and a rounded decimal. Use the working to check homework or scale a quantity without rounding intermediate values.

Fraction rules

For a/b and c/d, neither denominator may be zero:

Addition and subtraction
a/b ± c/d = (a × d ± c × b) / (b × d)
Multiplication and division
a/b × c/d = (a × c)/(b × d). Division uses the reciprocal: a/b ÷ c/d = (a × d)/(b × c), where c is not zero.

Reduce the answer by dividing both parts by their greatest common divisor (GCD). Multiplying the two denominators gives a valid common denominator; it does not have to be the least common denominator because the result is reduced afterward.

Step-by-step example

The starting example is 1/2 + 3/4:

  1. Cross-products: 1 × 4 + 3 × 2 = 10.
  2. Common denominator: 2 × 4 = 8, giving 10/8.
  3. The GCD of 10 and 8 is 2. Divide both by 2 to get 5/4.
  4. Mixed number: 1 1/4. Decimal: 1.25.

With the same inputs, subtraction gives −1/4, multiplication gives 3/8, and division gives 2/3. The last answer has a repeating decimal, so use the fraction when exactness matters.

Input limits and negative mixed numbers

Each input must be an integer with absolute value no greater than one million. A zero numerator is valid, but a zero denominator is not. When dividing, the second fraction must also have a nonzero numerator. Negative denominators are moved into the sign of the final numerator. A minus sign on a mixed number applies to the whole value: −1 1/4 means −(1 + 1/4).

Frequently asked questions

Fractions must describe equal-sized parts. Find a common denominator, then add only the equivalent numerators.

Yes. Put the minus sign on either the numerator or denominator. The answer is normalized to a positive denominator.

Not always. The reduced fraction is exact within the input limits; the decimal is rounded to at most 10 decimal places.

Convert it to an improper fraction first: 2 1/3 is 7/3. Enter −7/3 for −2 1/3.

Keep working

The percentage calculator converts a proportion into parts per hundred. Use the scientific calculator for roots and powers, or the weighted average calculator for grades with different weights.

Mathematical reference

OpenStax, Prealgebra 2e, section 4.5 explains unlike denominators. Sections 4.2 and 4.3 cover multiplying and dividing fractions.