Fraction Calculator – Add, Subtract, Multiply and Divide Fractions

How to use the fraction calculator

1. Type the first fraction — for example 3/4, 1 1/2, 5 or 0.25.
2. Choose +, −, × or ÷.
3. Type the second fraction.

The answer appears straight away in simplest form, with the mixed number (if it is bigger than 1), the decimal, the percentage and a line explaining the method.

The rules for fractions

Adding and subtracting

Multiplying

Dividing — multiply by the reciprocal

After each step, the result is simplified by dividing the top and bottom by their greatest common factor.

Worked examples

• 1/2 + 1/3 = 3/6 + 2/6 = 5/6 (≈ 0.8333)
• 3/4 − 1/6 = 9/12 − 2/12 = 7/12
• 2/3 × 9/10 = 18/30 = 3/5
• 3/4 ÷ 2/3 = 3/4 × 3/2 = 9/8 = 1 1/8
• 1 1/2 + 2/3 = 3/2 + 2/3 = 9/6 + 4/6 = 13/6 = 2 1/6

Converting between forms

• Mixed number to improper fraction: multiply the whole number by the denominator and add the numerator. 2 3/4 = (2 × 4 + 3)/4 = 11/4.
• Improper fraction to mixed number: divide; the quotient is the whole number and the remainder is the new numerator. 11/4 = 2 remainder 3 = 2 3/4.
• Fraction to decimal: divide the top by the bottom. 3/8 = 0.375.
• Decimal to fraction: write it over a power of ten and simplify. 0.375 = 375/1000 = 3/8.

Where fractions come up

Cooking and baking (half a cup, three quarters of a teaspoon), woodwork and DIY in inches (5/8 inch), music time signatures, probability, and school maths homework all use fractions. For recipes, try the cooking converter; for ratios such as 3 : 4, see the ratio calculator.

Why simplest form matters

Teachers and textbooks usually expect answers in simplest form, and it makes fractions easier to compare: it is much clearer that 3/4 is bigger than 2/3 than that 18/24 is bigger than 16/24. To simplify by hand, find the greatest common factor of the numerator and denominator and divide both by it. The calculator always does this for you and shows the decimal too, so you can check the size of the answer at a glance.

Negative fractions

A minus sign can go in front of the whole fraction or the numerator: −3/4 and −3 over 4 mean the same thing. The calculator always puts the sign on the numerator in its answers, and it handles negative mixed numbers such as −2 1/2, which means −(2 + 1/2).

Common mistakes

• Adding the denominators — 1/2 + 1/3 is not 2/5. You need a common denominator first.
• Forgetting to flip when dividing.
• Not simplifying the final answer.
• Mixing up a mixed number and multiplication — 1 1/2 means one and a half, not 1 × 1/2.

To find a common denominator by hand, use the least common multiple — the LCM and GCF calculator works it out. For anything else, there is the scientific calculator.