Fraction Calculator

How to use the fraction calculator

Type two values into the boxes, choose add, subtract, multiply or divide, and the answer appears straight away. You can enter:

• Proper or improper fractions such as 3/4 or 11/8
• Mixed numbers with a space between the whole part and the fraction, such as 1 1/2
• Whole numbers such as 5, and decimals such as 0.25, which are converted to fractions
• Negative values with a leading minus sign, such as -2 1/3

The result is shown as a simplified fraction, a mixed number, a decimal (with repeating digits marked) and a percentage. The steps explain every move — finding a common denominator, flipping the divisor, simplifying with the greatest common factor — so you can check homework or learn the method.

Fraction rules and formulas

For addition and subtraction the calculator uses the least common denominator (the least common multiple of the two denominators) rather than simply multiplying them, which keeps the numbers small. Every answer is then reduced by dividing the numerator and denominator by their greatest common factor.

Worked example: 1 1/2 + 3/4

1. Convert the mixed number to an improper fraction: 1 1/2 = (1 × 2 + 1)/2 = 3/2.
2. The LCD of 2 and 4 is 4.
3. Rewrite: 3/2 = 6/4, and 3/4 stays 3/4.
4. Add the numerators: 6/4 + 3/4 = 9/4.
5. 9 and 4 share no common factor, so 9/4 is in lowest terms.
6. As a mixed number: 9 ÷ 4 = 2 remainder 1, so 2 1/4, or 2.25 as a decimal.

How each operation works

Adding and subtracting

You can only add or subtract fractions that refer to the same-sized pieces, so first rewrite them over a common denominator. Then combine the numerators and keep the denominator. Think of 1/2 + 1/3: halves and thirds are different pieces, but both can be cut into sixths, giving 3/6 + 2/6 = 5/6.

Multiplying

Multiply straight across — numerators together, denominators together — then simplify. There is no need for a common denominator. You can "cross-cancel" common factors before multiplying to keep the numbers small: in 4/9 × 3/8, the 4 and 8 share 4, and the 3 and 9 share 3, leaving 1/3 × 1/2 = 1/6.

Dividing

Keep the first fraction, change ÷ to ×, and flip the second fraction (use its reciprocal). For example 3/2 ÷ 3/4 = 3/2 × 4/3 = 12/6 = 2. This works because dividing by a number is the same as multiplying by its reciprocal.

Fractions, decimals and percentages

Any fraction can be written as a decimal by dividing the numerator by the denominator. If the simplified denominator has only 2 and 5 as prime factors, the decimal terminates (3/8 = 0.375). Otherwise it repeats forever (1/3 = 0.333…, 5/7 = 0.714285714285…), and the calculator marks the repeating block. Multiply the decimal by 100 for the percentage, or use the percentage calculator to work with it further.

Comparing two quantities rather than combining them? A ratio calculator may be the better tool.