Everyday math
Add, subtract, multiply, or divide two fractions.
Enter your numbers to see the answer.
Fraction calculator guide
A fraction calculator shows the exact value of two fractions combined and its decimal equivalent, so you can check a recipe, a measurement, homework, or a construction dimension without losing precision to early rounding. This page takes a first numerator and denominator and a second numerator and denominator, adds the two fractions, and displays the sum as a decimal rounded to four places alongside the two fractions you entered. The formula section explains how to add, subtract, multiply, and divide fractions by hand so you can carry the exact fraction forward: addition and subtraction need a common denominator, multiplication uses the numerators and denominators directly, and division multiplies by the reciprocal of the second fraction. Keep the numerator and denominator in their labeled fields and check that a denominator is not zero.
Addition or subtraction: a/b ± c/d = (ad ± bc) ÷ bd. Multiplication: a/b × c/d = ac ÷ bd. Division: a/b ÷ c/d = a/b × d/c. Reduce the final numerator and denominator by their greatest common factor. This page displays the decimal value of a/b + c/d.
Worked example with the defaults: the first fraction is 1/2 and the second is 1/4. By hand, the common denominator is 4, so 1/2 + 1/4 = 2/4 + 1/4 = 3/4. The calculator works in decimals: 1 ÷ 2 = 0.5 and 1 ÷ 4 = 0.25, so 0.5 + 0.25 = 0.75, which is the figure it displays as the sum of the two fractions. To check a different operation by hand, 1/2 × 1/4 = 1/8 = 0.125, and 1/2 ÷ 1/4 = 1/2 × 4/1 = 2.
Fractions are dimensionless unless the numbers represent a unit such as inches, cups, or pounds. Keep units consistent, and do not use a zero denominator. A negative sign can apply to the numerator or the whole fraction; enter it in the numerator field. The decimal result is rounded to four places, so 1/3 + 1/3 shows 0.6667 rather than the exact 2/3.
The reduced fraction is the exact result. The decimal display is a convenience and may round repeating values such as 1/3.
Do not add denominators directly: 1/2 + 1/4 is 3/4, not 2/6. Do not invert the wrong fraction during division; only the second fraction is flipped. Avoid rounding before reducing, because 0.3333 + 0.3333 = 0.6666 hides the exact 2/3. Do not mix measurements with different units, such as 1/2 inch with 1/4 foot, without converting one of them first. Finally, a mixed number such as 1 1/2 must be entered as the improper fraction 3/2.
Use the exact fraction for later calculations when possible. Convert to a decimal only when the next step or measurement requires it.
How it works
Add, subtract, multiply, or divide two fractions. This tool explains the calculation so you can adjust the assumptions to match your situation.
Worked example
With First numerator = 1 · First denominator = 2 · Second numerator = 1 · Second denominator = 4 → 0.75 (sum of the two fractions). Change an input above and this example updates with your numbers.
Common questions
Find a common denominator, convert both fractions, add the numerators, and reduce the result. For example, 1/2 + 1/4 = 2/4 + 1/4 = 3/4, which the calculator displays as 0.75.
Multiply the numerators together and the denominators together, then reduce the result. One-half times one-fourth is (1 × 1) ÷ (2 × 4) = 1/8, which is 0.125 as a decimal, so multiplying two proper fractions always gives a smaller value.
Keep the first fraction, multiply by the reciprocal of the second, and reduce the result. For 1/2 ÷ 1/4, flip the second fraction to 4/1 and multiply: 1/2 × 4/1 = 4/2 = 2.
A reduced fraction is easier to read and compare, and it is the same exact value in simplest form. Divide numerator and denominator by their greatest common factor, so 6/8 becomes 3/4.
Convert a mixed number to an improper fraction first, then enter its numerator and denominator. For 2 1/3, multiply 2 × 3 and add 1 to get 7/3, then enter 7 and 3.