Fraction Calculator

Add, subtract, multiply, divide, and simplify fractions with mixed number and decimal results.

Fraction Calculator tool

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Example

Input: 1/2 + 1/3

Result: 5/6 (decimal 0.83333333)

Using the common denominator 6: 1/2 + 1/3 = 3/6 + 2/6 = 5/6, which is already in lowest terms.

  1. Enter the numerator and denominator of each fraction in the input fields.
  2. Select the operation: addition, subtraction, multiplication, or division.
  3. View the simplified result displayed as both an improper fraction and a mixed number.
  4. Review the unsimplified fraction, decimal equivalent, and full expression to see how the answer was reached.
  5. Click the copy button to copy the simplified result.

Adding, Subtracting, Multiplying and Dividing Fractions

This fraction calculator adds, subtracts, multiplies and divides two fractions and gives the answer in lowest terms. For example, 1/2 + 1/3 = 5/6. Along with the simplified fraction, you get the mixed number, the decimal value, the unsimplified result and the whole sum written out.

Here is what happens behind each operation. To add or subtract, the calculator cross-multiplies to put both fractions over the same bottom number, then combines the tops. To multiply, it multiplies straight across, top by top and bottom by bottom. To divide, it flips the second fraction and multiplies. Last, it divides the top and bottom by their greatest common divisor, so 12/16 comes out as 3/4. The unsimplified result helps when you are checking homework. For 2/4 + 1/4 it shows 12/16 before reducing, which matches the cross-multiply method step by step. When the answer is more than 1, the mixed number shows it the way a recipe or tape measure would, such as 1 and 3/4.

A few input rules are worth knowing. Numerators and denominators must be whole numbers. To enter a mixed number such as 2 1/2, turn it into an improper fraction first: 2 x 2 + 1 = 5, so type 5/2. For a negative fraction, put the minus sign on the top number. A denominator of 0 is not allowed. To reduce a fraction by hand, the GCD and LCM Calculator finds the number to divide by. To scale a whole recipe, the Recipe Scaler does the fraction math for every ingredient.

Formula / How It Works

a/b + c/d = (ad + bc) / bd | a/b - c/d = (ad - bc) / bd | a/b x c/d = ac / bd | a/b / c/d = ad / bc

Frequently Asked Questions

Give them a common denominator, then add the tops. For 1/3 + 1/4, the lowest common denominator is 12, so the sum becomes 4/12 + 3/12 = 7/12. The calculator cross-multiplies instead, which gives 7/12 straight away here. When the bottoms share a factor, it gets a larger fraction first and then simplifies it.
Multiply the tops together and the bottoms together, then simplify. For 2/3 x 4/5, that is 8/15, which is already in lowest terms. You can cancel common factors before you multiply to keep the numbers small, and you will reach the same answer.
Flip the second fraction and multiply. So 2/3 divided by 4/5 becomes 2/3 x 5/4 = 10/12, which simplifies to 5/6. A handy phrase to remember it is "keep, change, flip". Dividing by a fraction with 0 on top is not possible, so the calculator shows an error.
Turn it into an improper fraction first. Multiply the whole number by the denominator and add the numerator: 2 x 2 + 1 = 5. Keep the same denominator, so 2 1/2 becomes 5/2. The answer comes back as both an improper fraction and a mixed number, so you do not need to convert it back.
Simplifying means dividing the top and bottom by the largest number that divides both. That number is the greatest common divisor. For 8/12 it is 4, so 8/12 simplifies to 2/3. The value does not change, only how it is written. The calculator always shows the simplified form as its main answer.

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