Fraction Calculator

Fractions show up in almost every real task that involves splitting something: a recipe that calls for half a cup of flour, a discount that knocks one-third off a price, a time log where you bill a quarter hour at a time, or a woodworking cut that leaves you with five-eighths of an inch of clearance. Doing arithmetic on fractions by hand means hunting for common denominators, cross-multiplying, and then reducing the result — three places where even careful students slip. This fraction calculator does all of that in one step and shows the result as a reduced fraction, a mixed number, and a decimal, so you can compare formats at a glance.

Type any two fractions, pick the operation, and the answer appears instantly. Negative numerators and zero are handled correctly, and very large numerators (think recipe scaling in bulk kitchens or material estimates in construction) reduce without rounding errors.

How to Use

1. Enter the First Numerator — the top number of the first fraction. For negative fractions, type the minus sign here, e.g. -3.
2. Enter the First Denominator — the bottom number. It cannot be zero.
3. Choose the Operation: add, subtract, multiply, or divide.
4. Enter the Second Numerator and Second Denominator the same way.
5. Read the result card: the reduced fraction at the top, the mixed number, and the decimal equivalent below.

The engine reduces every answer automatically using the greatest common divisor (GCD), so 4/8 always comes back as 1/2. The result card shows the reduced numerator and denominator, the decimal equivalent (rounded to 4 decimal places), and a true mixed-number decomposition: a whole-part value plus a proper-fraction numerator over the result denominator. For example, 3/2 comes back as whole part 1 with fraction numerator 1 over denominator 2, i.e. 1 1/2. The fraction itself stays exact integer arithmetic; only the decimal display is rounded to four places, so repeating values like 1/3 show as 0.3333 rather than an endless tail. If you choose divide and the second fraction's numerator is zero, the calculator flags a division-by-zero error instead of returning a nonsense number.

The Four Fraction Operations

• Addition — you need a common denominator. a/b + c/d = (ad + bc) / bd. Example: 1/2 + 1/3 = (3 + 2) / 6 = 5/6.
• Subtraction — same common-denominator rule. a/b − c/d = (ad − bc) / bd. Example: 3/4 − 1/6 = (9 − 2) / 12 = 7/12.
• Multiplication — no common denominator needed. Multiply straight across: a/b × c/d = ac / bd. Example: 2/3 × 4/5 = 8/15.
• Division — flip the second fraction and multiply: a/b ÷ c/d = a/b × d/c = ad / bc. Example: 3/4 ÷ 1/2 = 3/4 × 2/1 = 6/4 = 3/2.

After any operation the result is divided by the GCD of the numerator and the denominator so it lands in lowest terms. That is the same procedure Python's built-in fractions.Fraction uses under the hood, and it is why this calculator never shows an unreduced answer.

Examples

Example 1 — Baking conversion. A bread recipe calls for 1/2 cup of olive oil and you want to add 1/3 cup more to test a richer loaf. Choose Add, enter 1/2 + 1/3, and the result is 5/6 cup (about 0.833 cup). The mixed number output also tells you this is just under one full cup, so you do not overshoot.

Example 2 — Splitting a dinner bill. Four friends share a $96 dinner. Each person owes 96 / 4 = 24, but one person only ate 1/3 of their share and wants to top up. Enter 24 as a whole number by writing 24/1, then subtract 1/3 of 24: 24/1 − 1/3 = 72/3 − 1/3 = 71/3, which is 23 2/3 or about $23.67. Using the fraction form avoids the rounding drift you would get if you converted to decimals first.

Example 3 — Scaling a construction cut. You have a board that is 3/4 inch thick and you need to divide it into 1/2-inch laminations. Choose Divide: 3/4 ÷ 1/2 = 3/2, which tells you the board yields one full lamination with a half-lamination left over — useful when you plan the cut list for a batch of 200 pieces.

Example 4 — Large numbers. If a bulk recipe needs 1,000,000/2 grams of flour (that is, 500,000 g) plus 1/2 gram of salt, the calculator still returns the exact fraction 1000001/2 (500000.5) rather than a floating-point approximation.

Common Mistakes to Avoid

• Adding straight across. The single most common error is adding numerator to numerator and denominator to denominator (1/2 + 1/2 = 2/4), which is wrong. Addition and subtraction require a common denominator first.
• Forgetting to reduce. 6/8 is mathematically equal to 3/4, but leaving it unreduced makes later steps error-prone. This calculator always divides by the GCD for you.
• Dropping the sign on subtraction. 1/4 - 1/2 is negative (-1/4), not positive. Put the minus on the numerator and the reduced result keeps the sign correctly.
• Converting to decimals too early. 1/3 as 0.3333 drifts after a few operations. Keep the fraction form until the final step, then read the decimal only for display.

FAQ

How do I add fractions with different denominators?

Find a common denominator (usually the least common multiple of the two), convert both fractions, then add the numerators. With this calculator, just type the two fractions and pick Add — the common-denominator step is done for you.

Why is my answer shown as a mixed number?

When the numerator is larger than the denominator, the result is an improper fraction. The calculator also renders it as a mixed number (a whole number plus a proper fraction) because that is how people usually read measurements like wood lengths, cooking times, and amounts of money.

Can I use negative fractions?

Yes. Put the minus sign on the numerator, for example -1/2. The calculator treats -1/2 and 1/-2 as the same value and keeps the sign on the numerator in the reduced result.

What happens if I divide by zero?

Division by zero is not defined. If the second fraction's numerator is zero (so the second fraction equals 0/1, or anything over a denominator), the calculator shows an error rather than returning a number.

How do I simplify a fraction like 24/36?

Type 24/36 as the first fraction and 0/1 as the second, then choose Add — the engine reduces the result automatically using the GCD. 24/36 reduces to 2/3. You can also use the same reduction step on any answer this calculator produces; every output is already in lowest terms.

What is the difference between a fraction and a decimal?

A fraction keeps the exact ratio between two integers; a decimal is an approximate place-value expansion. For repeating values like 1/3 = 0.3333…, the fraction is exact and the decimal is not. Use the fraction output when precision matters (mixing chemicals, scaling recipes, doing homework), and the decimal output when you need to compare with a ruler or a price tag.

Disclaimer

This fraction calculator is provided for informational purposes only and does not constitute mathematical, engineering, cooking, or financial advice. Results are computed with exact rational arithmetic and reduced automatically, but you are responsible for verifying inputs and applying the output correctly in your own context. Always double-check measurements, dosages, and money calculations before acting on them. For more about this tool, see our About page and Privacy Policy; no inputs you enter are stored or transmitted.