Calculate with fractions
For a simple fraction, enter a numerator and denominator. For a mixed number, also enter the whole-number part. For a whole number or a decimal such as 0.75, fill in only the first box. To make a mixed number negative, put the minus sign on the whole number.
Result
See it as a picture
Each bar is drawn to the same scale. Thick lines mark whole units and thin lines mark the pieces, so you can count the parts. Negative values are shaded in orange to the left of zero.
Step-by-step working
How to use the fraction calculator
Fill in the whole number, numerator and denominator for each value. The first box is optional, so for 3/4 just enter 3 and 4. For a decimal, type it into the first box on its own, and the calculator turns it into a fraction: 0.75 becomes 75/100, which simplifies to 3/4. Pick the operation, then press Calculate or Enter.
Need more than two values? Select Add another fraction for up to six. The page address updates with your problem, so you can bookmark it or send the link to someone else.
Adding and subtracting fractions
To add or subtract fractions, first rewrite them so they count pieces of the same size. The calculator finds the least common denominator, creates equivalent fractions, combines their numerators and reduces the result. For example, 5/12 + 7/18 becomes 15/36 + 14/36 = 29/36.
With three or more fractions, the calculator uses one common denominator for all of them. For 1/2 + 1/3 + 1/6, that’s 6: 3/6 + 2/6 + 1/6 = 6/6 = 1.
The bar model makes the denominator change visible. For 5/12 + 7/18, the input bars count twelfths and eighteenths, which are different-sized pieces. Rewriting both values in thirty-sixths produces matching pieces, so 15 of them and 14 of them can be combined to make 29/36.
Multiplying and dividing fractions
For multiplication, form a new numerator from the two numerators and a new denominator from the two denominators. Division is rewritten as multiplication by the reciprocal of the divisor, so that fraction’s numerator and denominator exchange places. Before multiplying, the calculator cancels factors shared by a numerator and the opposite denominator to keep the intermediate numbers smaller.
When a problem mixes operations, such as 1/2 + 1/3 × 3/4, the calculator follows the order of operations: × and ÷ first, then + and −. Here 1/3 × 3/4 = 1/4 is worked out first, then 1/2 + 1/4 = 3/4.
Proper, improper and mixed fractions
A proper fraction has a numerator smaller than its denominator, such as 3/4. An improper fraction has a numerator at least as big as its denominator, such as 7/4. A mixed number writes the same value as a whole number plus a fraction: 7/4 = 1 3/4.
Negative fractions
A fraction is negative when either its numerator or its denominator is negative, but not both. For a negative mixed number, put the minus sign on the whole number only: enter −1, 1 and 2 for −1 1/2. The calculator won’t accept a minus sign in the fraction part of a mixed number, because −1 −1/2 could mean two different things.
Everyday fraction examples
Scaling a recipe
A recipe uses 3/4 cup of stock, but you’re making one and a half batches. Multiplying 3/4 by 1 1/2 gives 9/8, or 1 1/8 cups. Enter 3/4 as the first value, 1 1/2 as the second and choose multiplication.
Measuring a cut
A board is 5 7/8 inches long and you cut off 2 5/16 inches. What’s left is 3 9/16 inches. Working in sixteenths keeps the measurement exact instead of rounding it to a decimal too early.
Sharing a distance
Split a 7 1/2-mile route into four equal stages and each one is 7 1/2 ÷ 4 = 1 7/8 miles. For a whole number like 4, fill in just the whole box.
Large fraction puzzles
Do consecutive large fractions almost make 2?
Try 999,999/1,000,000 + 1,000,001/1,000,000. The numerators add up to 2,000,000, so the answer is exactly 2. Big-looking inputs can still collapse to a simple answer.
Can two improper fractions multiply to 1?
Yes, if they’re reciprocals: 12,345/6,789 × 6,789/12,345 = 1. The calculator’s cancelling step shows every factor dropping out before anything gets multiplied.
A fraction between two close fractions
For two distinct positive fractions a/b and c/d, the mediant (a + c)/(b + d) lies between them. Between 5/12 and 6/13, the mediant is 11/25. It is not their arithmetic mean, but it gives a convenient fraction between the two values.
Check the operation before simplifying
Addition and multiplication answer different questions. For 3/5 + 1/4, twentieths give 12/20 + 5/20 = 17/20, while multiplying the same inputs gives 3/20. Estimate before accepting an answer: a sum of two positive fractions must exceed either input, while their product can be smaller.
Frequently asked questions
Why do addition and subtraction need a common denominator?
The denominator tells you the size of the pieces. You can only add or subtract numerators once both fractions are counting pieces of the same size.
Do I need a common denominator for multiplication?
No. Multiply the numerators, multiply the denominators and then reduce. For example, 4/7 × 21/32 simplifies to 3/8.
How do I divide by a fraction?
Replace division with multiplication by the divisor’s reciprocal, provided the divisor is not zero. For example, 5/6 ÷ 10/9 becomes 5/6 × 9/10 = 3/4.
Can a denominator be zero?
No. A fraction with a denominator of zero is undefined, so the calculator asks you to change it.
Are an improper fraction and a mixed number different values?
No. 7/4 and 1 3/4 are the same value written in two forms. The calculator shows both.
How do I enter negative one and a half?
Enter −1 in the whole-number box, 1 in the numerator and 2 in the denominator. The minus sign applies to the whole mixed number.
What is the least common denominator?
It’s the least common multiple of the denominators. Using it gives the smallest shared denominator, which keeps the numbers as small as possible.
How is a fraction reduced to lowest terms?
Divide the numerator and denominator by their greatest common divisor. The value doesn’t change, because both parts are divided by the same number.
Can I enter a decimal like 0.75?
Yes. Type it in the first box and leave the numerator and denominator empty. The calculator writes it as a fraction over 10, 100, 1,000 and so on, so 0.75 = 75/100, and then simplifies, giving 3/4.
Can I add three or more fractions at once?
Yes, up to six. Select “Add another fraction” and choose an operation for each gap. If you mix operations, × and ÷ are done before + and −.
What do the brackets in the decimal answer mean?
They mark digits that repeat forever. 5/12 = 0.41(6) means 0.41666…, and 1/7 = 0.(142857) means 0.142857142857…. If the repeating block is very long, the decimal is shown rounded, but the fraction answer is always exact.
Can the calculator handle large numerators and denominators?
Yes. Each box takes whole numbers up to 300 digits, and every step is worked out exactly, with no rounding. Very large results are shown with commas to make them easier to read.