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ToolMoose

Fraction Calculator

Add, subtract, multiply, and divide fractions with reduced results.

Reduced fraction
3/4
Decimal value0.75

Worked examples

1/2 + 1/4
Common denominator 4 gives 2/4 + 1/4 = 3/4, which is already reduced (0.75).
1/2 ÷ 3/4
Keep, change, flip: 1/2 × 4/3 = 4/6, reduced to 2/3 (about 0.666667).

How it works

A fraction is just a numerator over a denominator, and every operation comes down to integer arithmetic followed by reducing the answer. Enter two fractions, pick an operation, and the calculator returns the reduced fraction, the mixed number (when the result is improper), and the decimal value.

Adding and subtracting

Addition and subtraction need a common denominator. The direct formulas are:

  • Addition: a/b + c/d = (ad + cb) / (bd)
  • Subtraction: a/b − c/d = (ad − cb) / (bd)

For 1/2 + 1/4, that is (1×4 + 1×2) / (2×4) = 6/8, which reduces to 3/4. Using the product of the two denominators (bd) always gives a valid common denominator, and reducing at the end cleans up any extra factors.

Multiplying

Multiplication is the simplest case: multiply the tops together and the bottoms together.

  • Multiplication: a/b × c/d = ac / bd

So 2/3 × 3/4 = 6/12, which reduces to 1/2.

Dividing

To divide, multiply by the reciprocal of the second fraction (keep, change, flip):

  • Division: a/b ÷ c/d = ad / bc

For 1/2 ÷ 3/4 you get (1×4) / (2×3) = 4/6, which reduces to 2/3. If the second numerator is zero, the division is undefined, and the calculator shows a friendly message instead of an error value.

Reducing the result

Once the raw numerator and denominator are known, the calculator reduces the fraction using the greatest common divisor (GCD). It finds the largest number that divides both, then divides each by it. It also keeps the denominator positive, moving any negative sign to the numerator, so 1/-2 displays as -1/2.

Reading the output

  • Reduced fraction: the answer in lowest terms, such as 3/4.
  • Mixed number: shown when the result is improper, such as 1 1/4 for 5/4.
  • Decimal value: the same result as a decimal, rounded to about six significant digits with trailing zeros trimmed, so 1/3 shows as 0.333333.

A denominator of zero is never allowed, so entering 0 on the bottom prompts you to fix it rather than returning a broken result.

Frequently asked questions

How do I add fractions with different denominators?
Give both fractions a common denominator, then add the numerators. The quick formula is a/b + c/d = (ad + cb) / (bd). For example, 1/2 + 1/4 becomes (1×4 + 1×2) / (2×4) = 6/8, which reduces to 3/4. This calculator does the common-denominator step for you and reduces the answer automatically.
How do I simplify or reduce a fraction?
Find the greatest common divisor (GCD) of the numerator and denominator, then divide both by it. For 6/8, the GCD is 2, so 6/8 reduces to 3/4. A fraction is fully reduced when the numerator and denominator share no common factor other than 1.
How do I convert an improper fraction to a mixed number?
Divide the numerator by the denominator. The whole-number part is the quotient, and the remainder becomes the new numerator over the same denominator. For 5/4, 5 ÷ 4 is 1 with a remainder of 1, so the mixed number is 1 1/4.
How do you divide fractions (keep, change, flip)?
To divide, keep the first fraction, change the divide sign to multiply, and flip the second fraction (use its reciprocal). So a/b ÷ c/d = a/b × d/c = ad / bc. For example, 1/2 ÷ 3/4 = 1/2 × 4/3 = 4/6, which reduces to 2/3.

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Last updated: 2026-07-01