Use this free fraction calculator to add, subtract, multiply and divide fractions, mixed numbers and whole numbers, to find a fraction of a number, or to simplify a fraction. You can use up to three numbers at once, and negative numbers too. You get the answer in lowest terms, as a mixed number, a decimal and a percent, with a picture of the answer, the calculation steps (with the LCD and GCF) and the formula. Common fraction problems are listed underneath, and you can click one to try it. It is free and instant, and your numbers stay in your browser.
What is a fraction?
A fraction is a part of a whole. The top number (the numerator) says how many parts you have, and the bottom number (the denominator) says how many equal parts make a whole. In 3/8, a pizza cut into 8 slices has 3 slices taken. The bottom number can never be 0.
How to add and subtract fractions
Fractions can only be added or subtracted when they have the same bottom number. If they do not, find the lowest common denominator (LCD): the smallest number that both bottom numbers divide into. Change each fraction to use it, add or subtract the top numbers, then simplify.
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/b × d/c1/2 + 1/3: the LCD of 2 and 3 is 6. 1/2 becomes 3/6 and 1/3 becomes 2/6, and 3 + 2 = 5, so the answer is 5/6.
1/4 + 2/3: the LCD of 4 and 3 is 12, so 3/12 + 8/12 = 11/12.
2/3 − 1/2: the LCD is 6, so 4/6 − 3/6 = 1/6.
How to multiply fractions
Multiply the tops together and the bottoms together, then simplify. You do not need a common denominator. 2/3 × 3/4 = 6/12, which simplifies to 1/2. With three fractions, multiply all three tops and all three bottoms: 2/3 × 2/3 × 2/3 = 8/27.
How to divide fractions
Keep the first fraction, change the division sign to multiplication, and flip the second fraction (swap its top and bottom). 2/3 ÷ 3/2 = 2/3 × 2/3 = 4/9. You cannot divide by zero, so the fraction you divide by cannot be 0.
What “of” means
In a fraction problem, “of” means multiply. 1/3 of 3/8 is 1/3 × 3/8 = 3/24 = 1/8. Use the Of tab for problems worded this way, such as “what is half of 1/3?”.
Working with mixed numbers
A mixed number such as 2 3/4 has a whole part and a fraction part. To calculate with it, turn it into an improper fraction: multiply the whole by the bottom, add the top, and keep the bottom. 2 × 4 + 3 = 11, so 2 3/4 = 11/4. The calculator does this for you and shows the answer both ways.
2 3/4 ÷ 2/3: 11/4 × 3/2 = 33/8, which is 4 1/8. 3 2/3 × 2: 11/3 × 2/1 = 22/3, which is 7 1/3. 2 1/3 − 2/3: 7/3 − 2/3 = 5/3, which is 1 2/3.
To go back from an improper fraction to a mixed number, divide the top by the bottom. 11/4: 11 ÷ 4 = 2 remainder 3, so 11/4 = 2 3/4.
Simplifying fractions
To simplify a fraction, divide the top and the bottom by the biggest number that goes into both: the greatest common factor (GCF). For 12/18 the GCF is 6, so 12/18 = 2/3. Every answer is shown in its simplest form. To find the greatest common factor of your own numbers, use the Factor Calculator.
Negative fractions
Put the minus sign in front of the top number, or in front of the whole number of a mixed number. A negative sign on the top and one on the bottom cancel out. −3/4 + (−5/8) = −6/8 − 5/8 = −11/8, which is −1 3/8.
Fractions as decimals and percents
Divide the top by the bottom to get the decimal, and multiply by 100 for the percent. 5/4 = 1.25 = 125%. The calculator shows both with every answer. To turn any fraction into a decimal and see how it repeats, use the Fraction to Decimal Calculator. For more on percents, see the Percentage Calculator.
Why the answer is exact
The calculator uses whole-number sums rather than decimals, so there is no rounding until the decimal and percent at the end. You can use very large numerators and denominators without losing accuracy.
