Fraction Calculator: Add, Subtract, Multiply, Divide

How to use the calculator

Enter the numerator (top number) and denominator (bottom number) of the first fraction.
Choose the operation: add, subtract, multiply or divide.
Enter the numerator and denominator of the second fraction.

Use whole numbers only. Negative fractions are fine: type the minus sign in the numerator, as in −7/3. To enter a whole number, use a denominator of 1 (5 = 5/1). To enter a mixed number, convert it to an improper fraction first: 2 3/4 = (2 × 4 + 3)/4 = 11/4.

The result shows the simplified fraction, the mixed number when the answer is greater than 1 (or less than −1), and the decimal.

How fractions are calculated

For fractions a/b and c/d, the calculator uses the standard rules:

Add: a/b + c/d = (a·d + c·b) / (b·d)
Subtract: a/b − c/d = (a·d − c·b) / (b·d)
Multiply: a/b × c/d = (a·c) / (b·d)
Divide: a/b ÷ c/d = (a·d) / (b·c), that is, multiply by the reciprocal.

For addition and subtraction it multiplies the denominators instead of searching for the least common denominator. The final answer is the same, because the result is then reduced to lowest terms: numerator and denominator are divided by their greatest common divisor (GCD), found with Euclid’s algorithm. A negative sign always ends up in the numerator.

If the simplified numerator is larger than the denominator, the calculator also writes it as a mixed number: the whole part is the integer quotient and the remainder becomes the new numerator. The decimal is numerator ÷ denominator, rounded for display, so repeating decimals such as 0.8333… are shortened.

Worked examples

1. Adding fractions with different denominators

1/2 + 1/3 = (1·3 + 1·2)/(2·3) = 5/6, or about 0.8333. And 3/4 + 5/6 = 38/24, which reduces to 19/12: the mixed number 1 7/12, or 1.5833.

2. Subtracting mixed numbers on a tape measure

You cut 3/8 inch off a board that is 2 3/4 inches wide. Enter 11/4 − 3/8. The answer is 19/8, which is 2 3/8 inches, or 2.375.

3. Multiplying and dividing

Problem	Result	Mixed number	Decimal
2/3 × 9/4	3/2	1 1/2	1.5
3/4 ÷ 2/5	15/8	1 7/8	1.875
5/2 ÷ 1/4	10	—	10
−7/3 + 1/6	−13/6	−2 1/6	−2.1667

Notice that when a fraction simplifies to a whole number, like 10, no mixed number is shown.

Frequently asked questions

How do you add fractions with different denominators?

Rewrite both fractions with a common denominator, add the numerators and simplify. For 1/4 + 1/6, the least common denominator is 12: 3/12 + 2/12 = 5/12. Multiplying the denominators also works; you just simplify more at the end.

How do you divide fractions?

Keep the first fraction, change division to multiplication and flip the second fraction (use its reciprocal). So 3/4 ÷ 2/5 becomes 3/4 × 5/2 = 15/8.

What does simplest form or lowest terms mean?

A fraction is in lowest terms when the numerator and denominator have no common factor other than 1. To get there, divide both by their greatest common divisor: 38/24 divided by 2 gives 19/12.

How do I convert a mixed number to an improper fraction?

Multiply the whole number by the denominator and add the numerator; keep the same denominator. For 3 2/5: 3 × 5 + 2 = 17, so it equals 17/5. For a negative mixed number such as −1 1/2, enter −3/2.

Why can’t the denominator be zero?

A fraction is a division, and division by zero is undefined. For the same reason you cannot divide by a fraction whose numerator is 0, because that fraction equals zero.

Can I enter decimals like 0.5?

Not directly; fields accept whole numbers only. Write the decimal as a fraction first: 0.5 = 1/2, 0.75 = 3/4, 1.25 = 5/4.

Sources

This calculator is a learning and checking aid. Results are exact fractions; decimal values are rounded for display.