Fraction Calculator

What the Fraction Calculator does

This tool takes two fractions, runs an operation on them (add, subtract, multiply, or divide), and shows the answer in three forms at once: a fully reduced fraction, a decimal rounded to six places, and a mixed number. The result updates live as you type, so there is no submit button to chase.

It is built for the situations where a decimal is the wrong answer. A recipe scaled to two-thirds of the original needs 2/3, not 0.666667. A cabinet measurement of 5/8 inch plus 3/16 inch should come out as 13/16, not 0.812500, because your tape measure does not have decimal marks. School algebra answers are almost always graded in fraction form. The calculator keeps the exact value and only converts to decimal as a courtesy.

Who actually uses this

• Students doing pre-algebra, algebra, and basic arithmetic homework.
• Parents helping with that homework who have not added fractions by hand in twenty years.
• Cooks scaling recipes up or down (half a recipe that calls for 3/4 cup, doubling something that calls for 2/3 cup).
• Woodworkers, machinists, and DIYers adding or subtracting imperial measurements where everything is in halves, quarters, eighths, sixteenths, and thirty-seconds.
• Sewists working with seam allowances and yardage.
• Anyone who needs to double-check a hand calculation before writing it down.

How to use it

There are five inputs: two numerator boxes, two denominator boxes, and an operation dropdown between the first fraction and the second. Fill in the numerator and denominator of the first fraction, pick Add, Subtract, Multiply, or Divide from the dropdown, then enter the second fraction. The result panel appears as soon as both fractions and an operation are valid.

One thing to know up front: the operation dropdown looks like it shows Add (+) by default, but the underlying value starts empty. You have to actually click the dropdown and select an operation (even Add) before any result will display. If you have filled both fractions in and still see nothing, that is almost always why.

Three values come back:

• Fraction — the answer in lowest terms, written as numerator/denominator.
• Decimal — the same value as a decimal, always rounded to six places (so 1/3 shows as 0.333333).
• Mixed Number — the whole part separated from the remaining fraction, like 1 1/4. If the answer is a whole number, you just see the whole number. If it is less than one, you see the fraction by itself.

A few rules to know before you start. Both denominators must be non-zero, or no result is shown. For division, the second numerator must also be non-zero, because flipping a zero would mean dividing by zero. Negative answers put the minus sign on the numerator and keep the denominator positive, so subtracting 3/4 from 1/4 displays as -1/2, not 1/-2. Empty or zero denominators produce no result, which is why nothing shows up while you are still typing.

How it actually works

The math is the same arithmetic you would do on paper, just done instantly. For the two fractions a/b and c/d:

• Add: (a·d + c·b) / (b·d)
• Subtract: (a·d − c·b) / (b·d)
• Multiply: (a·c) / (b·d)
• Divide: (a·d) / (b·c), which is the first fraction multiplied by the reciprocal of the second.

Those formulas often produce an answer that is not in lowest terms. 1/2 + 3/4 gives 10/8 before simplification, which is the same number as 5/4 but harder to read. The calculator finds the greatest common divisor (GCD) of the numerator and denominator and divides both by it. The GCD comes from the Euclidean algorithm: replace (a, b) with (b, a mod b) over and over until the second number reaches zero. The first number at that point is the GCD. For 10 and 8, the steps are (10, 8) → (8, 2) → (2, 0), GCD is 2, and 10/8 reduces to 5/4.

After simplification the sign is normalized so the denominator is positive. The decimal output is just the reduced numerator divided by the reduced denominator, written to six decimal places. The mixed number is built by truncating the division toward zero for the whole part and taking the absolute value of the remainder over the denominator for the fractional part.

A worked example, start to finish

Say you want to compute 1/2 + 3/4.

1. Enter 1 as Numerator 1 and 2 as Denominator 1.
2. Pick Add (+) from the operation dropdown. You have to actively select it, even though it visually appears first.
3. Enter 3 as Numerator 2 and 4 as Denominator 2.

The tool computes (1·4 + 3·2) / (2·4) = (4 + 6) / 8 = 10/8. The GCD of 10 and 8 is 2, so it reduces to 5/4. The result panel shows:

• Fraction: 5/4
• Decimal: 1.250000
• Mixed Number: 1 1/4

One more, this time a subtraction that goes negative. 1/4 − 3/4 gives (1·4 − 3·4) / (4·4) = -8/16. GCD is 8, the result reduces to -1/2, and you see Fraction -1/2, Decimal -0.500000, Mixed Number -1/2 (since the whole part is zero, it just shows the fraction).

Mixed numbers: convert them first

The calculator has only numerator and denominator boxes. There is no separate field for the whole part of a mixed number. If your problem starts with something like 2 1/3, convert it to an improper fraction before typing:

whole × denominator + numerator, all over the denominator.

So 2 1/3 becomes (2·3 + 1) / 3 = 7/3. Enter 7 and 3. The result still comes back in mixed-number form when it makes sense to.

Common pitfalls

• Forgetting to select the operation. The dropdown displays Add (+) visually but starts with an empty underlying value. Until you click the dropdown and pick something, no result will show, even with both fractions filled in.
• Leaving a denominator blank. Empty is treated the same as zero for the purposes of validation, and a zero denominator is undefined, so no result will show. Fill both denominators.
• Trying to divide by zero. If the second numerator is empty or zero with Divide selected, the tool returns nothing. That is on purpose, because there is no answer to give.
• Reading 5/4 as a smaller number than expected. The fraction is always reduced. 10/8 and 5/4 are the same value; the second is just the form anyone would write down.
• Thinking the decimal is the precise answer. The decimal is rounded to six places. For repeating values like 1/3, the fraction form is the precise one; the decimal is a convenience.
• Typing a decimal into the numerator or denominator. The fields accept decimals because of how the input parses, but the GCD step assumes whole numbers and the results will not simplify correctly if you mix them in. Stick to whole numbers; if you have a decimal, convert it to a fraction first (for example, 0.5 becomes 1/2).

When this is not the right tool

• Three or more fractions at once. The calculator works on exactly two fractions. To add 1/2 + 1/3 + 1/4, do the first two, then take that result and add 1/4 to it.
• Algebra with variables. If your fraction has an x in it, this is the wrong tool. You need to do the symbolic work by hand or in a computer algebra system.
• Repeating-decimal precision past six places. If you genuinely need 1/7 to twenty decimal places, the decimal output will not give that. Use the fraction form, which is exact.
• Imperial measurements that need a specific denominator at the end. If you add 1/4 + 1/8 and want the answer as eighths instead of the reduced form, 3/8 is already eighths. But adding 1/2 + 1/4 reduces to 3/4, not 6/8. The reduced form is the standard; you can always re-expand if your context demands a specific denominator.

If the result looks wrong

Most "wrong" answers turn out to be input mistakes. Check, in order:

• Did you actually select an operation from the dropdown? The default state is empty even though Add (+) appears at the top. No selection means no result.
• Are the two fractions in the right boxes? Numerator 1 and Denominator 1 go together; Numerator 2 and Denominator 2 go together. Crossing them gives a different problem.
• For subtraction, is the order correct? Subtraction is not commutative, so 1/4 − 3/4 is not the same as 3/4 − 1/4.
• If you converted a mixed number to an improper fraction, did you do whole × denominator + numerator, not whole × numerator + denominator?
• If the answer is in lowest terms and still surprises you, do the math by hand on paper using the formulas above. The calculator will not disagree with a correct hand calculation.

Adjacent concepts and tools

The two pieces of math underneath this calculator are the greatest common divisor and the least common multiple. The GCD is what reduces a fraction to lowest terms. The LCM is the smallest number that two denominators both divide into evenly, and it is the smallest common denominator you can use when adding or subtracting by hand. Both have dedicated tools on the site if you want to find them on their own (linked below the calculator). The cross-multiply trick this tool uses for adding, (a·d + c·b) / (b·d), always produces a valid common denominator, but not necessarily the smallest one; that is why the reduction step at the end matters.

If you are converting between decimals and fractions outside the context of an operation, a dedicated decimal-to-fraction converter handles repeating decimals more transparently than reading a rounded six-decimal output. For percentages, remember that a percent is just a fraction over 100, so 25% is 25/100, which reduces to 1/4.