Fraction calculator
Enter two fractions or mixed numbers and choose add, subtract, multiply or divide. The answer is in lowest terms, as a mixed number when it has a whole part, and as a decimal, with the steps of the working under it.
This answer is for the example values in the boxes above. 1 1/2 + 1/3. Change the boxes to see your own answer.
How it works
The calculator turns each mixed number into one fraction: 1 1/2 becomes 3/2, because 1 times 2 plus 1 is 3. Adding and subtracting give both fractions the smallest common denominator and then work on the tops. Multiplying multiplies the tops and the bottoms, and dividing turns the second fraction over and multiplies.
Then it brings the answer to lowest terms by dividing the top and the bottom by their greatest common factor. Each step of the working has its own line under the answer.
A worked example
1 1/2 plus 1/3 starts as 3/2 and 1/3. The smallest common denominator is 6, which makes 9/6 and 2/6. Their sum is 11/6, which is 1 5/6 and 1.833333 as a decimal.
3/4 minus 1/6 is 9/12 minus 2/12, or 7/12. 2/3 times 3/4 is 6/12, which comes down to 1/2 in lowest terms. 3 divided by 3/4 is 3 times 4/3, or 12/3, which is 4.
How exact the answer is
The arithmetic is done on whole numbers, so even a product of two large numbers keeps every digit. Each box takes a whole number up to a billion. A decimal is exact when it ends within six places, like 3/8 at 0.375, and rounded to six places otherwise, like 1/3 at 0.333333.
What it leaves out
The boxes take whole numbers, so a decimal such as 1.5 has to be written as 3/2. A denominator of 0 is refused, and so is a division by 0, because neither has an answer.
Questions
How do I add fractions with different denominators?
Give both fractions the same denominator, add the tops and keep the bottom. For 1/4 and 1/6 the smallest common denominator is 12, so 3/12 plus 2/12 is 5/12.
How do I enter a mixed number?
Type the whole number in the first box and the fraction in the other two. For 1 1/2, enter 1, 1 and 2. For a whole number alone, fill in the first box and leave the other two empty.
How do I divide by a fraction?
Turn the second fraction over and multiply. 3 divided by 3/4 is 3 times 4/3, which is 12/3, or 4.
How do I simplify a fraction?
Divide the top and the bottom by their greatest common factor. 6/12 divided by 6 over 6 is 1/2. The calculator does this on every answer and shows a step when it changes the fraction.
Can I use negative numbers?
Yes. Check the Negative box of a number to make the whole number and the fraction together negative. Minus 2 1/2 plus 1 1/4 is minus 1 1/4.
What does rounded to 6 places mean?
Some fractions have decimals that never end, like 1/3. The calculator then shows six places, rounded: 0.333333. A fraction whose decimal ends within six places, like 3/8, is shown exactly: 0.375.
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