Free Fraction Calculator

Worked example

The page opens on "Calculate" with Fraction A at 1/2, the "Operation" menu on + and Fraction B at 1/3. The answer is already there: = 5/6 and "Decimal: 0.833333". Under "Step by step" you read "Find the common denominator: LCM(2, 3) = 6", "Rewrite both fractions: 1/2 = 3/6 and 1/3 = 2/6", "Combine the numerators: 3/6 + 2/6 = 5/6" and "5/6 is already in lowest terms." Now type 2 in the small whole-number box of Fraction A and 1 in the one of Fraction B. The sum becomes 2 1/2 + 1 1/3, the first step reads "Write mixed numbers and decimals as fractions: 2 1/2 = 5/2, 1 1/3 = 4/3", and the answer is 23/6, with "Mixed: 3 5/6" and "Decimal: 3.833333". Press "Decimal → Fraction": "Decimal value" holds 0.75 and the answer is 3/4.

Which settings to use, and the limits

• Type each fraction as a numerator over a denominator. In "Calculate", "Fraction A" and "Fraction B" each have a numerator box above a denominator box, and the "Operation" menu offers +, −, × and ÷. The boxes accept decimals too: 0.5 over 2 is turned into the exact fraction 1/4 before the sum, and a step line shows it. The answer is always reduced. "Mixed" appears only when the answer has both a whole part and a fraction part, such as 3 5/6, and "Decimal" shows up to six decimal places.
• Use the small box on the left for mixed numbers. Each fraction has a dashed box before the numerator for the whole number. Put 2 there, with 1 over 3, to mean 2 1/3. The whole part must be an integer. A negative whole applies to the whole mixed number, so -2 with 1/3 reads as -7/3. An empty box or 0 means a plain fraction, and a negative denominator moves its sign to the numerator. The hint under the boxes reads "For a mixed number like 2 1/3, put the whole number in the small box on the left."
• Read the steps to check homework. For + and −, the steps show the common denominator, the rewritten fractions and the combined numerators. For ×, they multiply the tops and bottoms. For ÷, they invert the divisor first: for 3/4 ÷ 1/2 you see "Invert the divisor and multiply: 3/4 ÷ 1/2 = 3/4 × 2". The last line is either "Reduce by GCD(6, 4) = 2: 6/4 = 3/2" or "… is already in lowest terms." That answer also shows "Mixed: 1 1/2" and "Decimal: 1.5".
• Convert a decimal with Decimal → Fraction. Switch the top toggle to "Decimal → Fraction" and type in "Decimal value". 0.75 gives 3/4, 0.125 gives 1/8, 1.2 gives 6/5, and 2.5 gives 5/2 with "Mixed: 2 1/2". The answer is the exact fraction of the decimal you typed, reduced: 1.01 gives 101/100, 100.5 gives 201/2, and 0.333333 gives 333333/1000000 rather than 1/3. Denominators go up to 1,000,000, so a decimal with more than six places gets the closest fraction within that limit.
• Copy or share the result. "Copy result" copies text such as "5/6 (0.833333)", or only "2" when the answer is a whole number; in "Decimal → Fraction" it copies the fraction only. "Share result" copies a link that rebuilds the same sum, because the fractions are kept in the page address after a #, for example a=1/2, op=add and b=1/3. Browsers do not send that part to a server. The address updates as you type, and the page says "Everything is calculated in your browser — nothing is uploaded."
• Keep the numbers to a sensible size. The calculator uses ordinary JavaScript numbers, which are exact only up to 9,007,199,254,740,991. When you add or subtract, the working multiplies the denominators together, so two denominators near 95 million are enough to pass that, and the answer can then be wrong without any warning. Homework-sized fractions never get near it. Decimals typed into the numerator or denominator boxes are scaled by powers of ten up to 1,000,000,000, which covers nine decimal places.

Common problems and how to fix them

It says "Enter valid fractions (denominators cannot be zero, and you cannot divide by zero)."

This replaces the answer when a numerator or denominator box is empty, a denominator is 0, you divide by a fraction whose numerator is 0 (such as 1/2 ÷ 0/5), or a whole-number box holds a decimal. Fill every box and change any 0 in a denominator or in the divisor.

You typed 2.5 in the small whole-number box and got "Enter valid fractions (denominators cannot be zero, and you cannot divide by zero)."

The message does not say it, but the whole-number box only takes integers, so 2.5 is not read as a mixed number. Put the decimal in the numerator instead, for example 2.5 over 1, or write the amount as 5/2. The numerator and denominator boxes accept decimals; only the whole-number box does not.

It says "Enter a decimal number."

In "Decimal → Fraction" the "Decimal value" box is empty or holds something the number field cannot read. Type a plain number such as 0.75 or 2.5. A fraction like 1/2 does not belong in this box; use the "Calculate" mode with the numerator and denominator boxes for that.

The sum of two very large fractions is wrong, or looks too simple.

The numbers are ordinary JavaScript numbers and lose exactness above 9,007,199,254,740,991. For example, 1/94906267 + 1/94906269 shows 1/47453134, but the correct answer is 189812536/9007199705687823. Use smaller numbers, or reduce each fraction first. Nothing in the page warns you when this happens.

How it compares

This is a worked-example calculator for two fractions at a time: it adds, subtracts, multiplies or divides them, always reduces the answer, shows the mixed-number and decimal forms, and lists the steps. It does not chain three or more fractions, handle percentages, powers or algebraic fractions, or keep an unreduced answer such as 6/8. Decimal → Fraction gives the exact fraction for decimals of up to six places. Numbers are not arbitrary precision. In exchange, nothing needs installing, and the sums are worked out in your browser.