How to use the fraction calculator
- Type the First number. For a mixed number such as 1 3/4, put 1 in Whole, 3 in the numerator box and 4 in the denominator box. For a plain fraction leave Whole empty.
- Choose plus, minus, times or divided by, then type the Second number the same way.
- Read the answer as a fraction, a mixed number and a decimal. The steps underneath show each move and update as you type.
- Leave the second number empty to simplify or convert the first number on its own. Put a minus sign on Whole (-1 1/2) or on the numerator (-1/2) for negatives.
How the calculation works
A mixed number becomes an improper fraction first: (whole ร denominator + numerator) รท denominator. To add or subtract, the calculator finds the least common denominator, LCD = (dโ ร dโ) รท GCD(dโ, dโ), converts both fractions and combines the numerators, as in OpenStax Prealgebra, section 4.5. To multiply it multiplies straight across, and to divide it flips the second fraction and multiplies. The result is then divided by the greatest common divisor, found with Euclid's algorithm. All arithmetic uses exact whole-number math, so there are no rounding errors even with very large numerators.
Worked example with the starting numbers
The page opens with 1 3/4 + 2 5/6. As improper fractions that is 7/4 + 17/6. The LCD of 4 and 6 is 12, so 7/4 = 21/12 and 17/6 = 34/12, and 21/12 + 34/12 = 55/12. The GCD of 55 and 12 is 1, so it cannot be reduced. The tool shows 1 3/4 + 2 5/6 = 4 7/12, with 55/12 as the fraction and โ 4.58333333 as the decimal.
Limits and edge cases
Every box takes whole numbers of up to 18 digits. Decimals such as 1.5 are refused with a message, because a fraction needs whole parts; convert them first with the decimal to fraction converter. A denominator of zero and dividing by zero are refused. The denominator must be positive, so write -1/2 rather than 1/-2, and a mixed number takes its minus sign on the whole part. The decimal is rounded to 8 places and marked with โ when it does not end. For other sums use the scientific calculator, and for parts of a whole as a percent the percentage calculator.
Source: OpenStax, Prealgebra 2e, 4.5 Add and Subtract Fractions with Different Denominators.
Fraction calculator FAQ
How do I add fractions with different denominators?
Find a common denominator, usually the least common denominator, rewrite both fractions with it, then add the numerators. For 1/4 + 1/6 the LCD is 12, so 3/12 + 2/12 = 5/12.
How do I add mixed numbers?
Turn each mixed number into an improper fraction, add as usual, then convert back. For 1 3/4 + 2 5/6, that is 7/4 + 17/6 = 55/12 = 4 7/12.
How do I simplify a fraction?
Divide the numerator and the denominator by their greatest common divisor. For 18/24 the GCD is 6, so 18/24 = 3/4. To do it here, enter the fraction as the first number and leave the second number empty.
How do you divide fractions?
Flip the second fraction and multiply. For 2/3 รท 4/5 you calculate 2/3 ร 5/4 = 10/12, which simplifies to 5/6.
How do I turn an improper fraction into a mixed number?
Divide the numerator by the denominator. The whole-number part of the quotient is the whole number, and the remainder goes over the denominator. For 7/3, 7 รท 3 is 2 remainder 1, so 7/3 = 2 1/3.