Davided.

Fraction Calculator

Add, subtract, multiply or divide two fractions (or mixed numbers) — simplified, as a mixed number, and as a decimal.

✓ Last reviewed: Sources: OpenStax Prealgebra 2e — 4.2 Multiply and Divide Fractions

Report a correction

Spotted a wrong result, label or typo? Tell us — we review every report.

The top number of the first fraction.

The bottom number of the first fraction — can't be 0.

The top number of the second fraction.

The bottom number of the second fraction — can't be 0.

Advanced options

Mixed numbers (whole parts)

Optional — makes the 1st fraction a mixed number (e.g. 1 1/2). The sign applies to the whole value, e.g. -2 1/3 = -7/3.

Optional — makes the 2nd fraction a mixed number (e.g. 2 1/3). The sign applies to the whole value, e.g. -2 1/3 = -7/3.

Your result

Fill in the fields above to see your result.

Related calculators

Fraction calculator: add, subtract, multiply and divide fractions

The Davided fraction calculator takes two fractions and one operation — add, subtract, multiply or divide — and returns the answer in three forms at once: the simplified fraction, the mixed number (if the result is top-heavy), and the decimal equivalent. Type a numerator and denominator for each fraction, pick the operation, and the result updates instantly.

You can also enter mixed numbers directly (a whole number plus a fraction, like 1 1/2) using the optional advanced fields, so you don’t have to convert to an improper fraction by hand first. Negative numerators and denominators are handled automatically, including the classic sign trap in negative mixed numbers (more on that below).

This fraction calculator is built for homework help, recipe scaling, woodworking and sewing measurements, or any situation where you need an exact fractional answer rather than a rounded decimal.

How to use the fraction calculator

  1. Enter the first fraction. Type its numerator and denominator into the two fields.
  2. Choose the operation. Pick add, subtract, multiply or divide.
  3. Enter the second fraction. Same two fields, for the second numerator and denominator.
  4. Read the result. You get the answer as a simplified fraction (or a whole number, when it works out evenly), plus its decimal value.

If either fraction is a mixed number — say you’re working with 2 1/3 rather than 7/3 — open Advanced options and fill in the whole-number part for that fraction. Leave it blank (or 0) if the fraction has no whole-number part.

A denominator of zero isn’t a valid fraction, so the calculator blocks the calculation and asks you to fix it. Dividing by a fraction that equals zero (like 0/5) isn’t valid either, for a different reason — see “What if a denominator is zero?” below.

How the calculator works

Adding and subtracting fractions

To add or subtract fractions, you first need a common denominator. The calculator does this by cross-multiplying: for a/b and c/d,

a/b + c/d = (a×d + c×b) / (b×d) a/b − c/d = (a×d − c×b) / (b×d)

Multiplying the two denominators together always gives a common denominator, even if it isn’t the smallest one (the “lowest common denominator”). That’s fine — the fraction gets simplified afterwards anyway, so the final answer is identical either way; the only difference is the size of the numbers in the middle of the calculation.

Example: 1/4 + 1/6 = (1×6 + 1×4) / (4×6) = 10/24.

Multiplying fractions

Multiplying is more direct — multiply the numerators together and the denominators together:

a/b × c/d = (a×c) / (b×d)

Example: 4/6 × 3/8 = (4×3) / (6×8) = 12/48.

Dividing fractions

Dividing by a fraction means multiplying by its reciprocal (flip the numerator and denominator of the second fraction):

a/b ÷ c/d = a/b × d/c = (a×d) / (b×c)

Example: 3/4 ÷ 2/5 = 3/4 × 5/2 = 15/8.

This only works if the second fraction isn’t zero — zero has no reciprocal, since no number multiplied by zero gives 1.

Simplifying the result

Every result gets reduced to its lowest terms by dividing the numerator and denominator by their greatest common divisor (GCD) — the largest number that divides both exactly. Take 12/48 from the multiplication example above: the GCD of 12 and 48 is 12, so 12/48 simplifies to 1/4. If the numerator and denominator only share the factor 1, the fraction is already in its simplest form.

Mixed numbers and decimals

If the simplified result is top-heavy (numerator bigger than denominator), the calculator also shows it as a mixed number: divide the numerator by the denominator to get the whole-number part, and whatever is left over becomes the new numerator over the same denominator. For 15/8: 15 ÷ 8 = 1 remainder 7, so 15/8 = 1 7/8.

Every result also gets a decimal value. Some fractions convert exactly (1/4 = 0.25) because their simplified denominator only has 2 and 5 as prime factors. Others never terminate — 5/12 = 0.41666…, repeating the 6 forever. The calculator rounds these to six decimal places (0.416667) rather than showing an endless string of digits.

Negative fractions and mixed numbers

A minus sign on the numerator, the denominator, or both is normalized before the calculation runs: −3/−4 is the same value as 3/4 (the two negatives cancel), and −3/4 is the same as 3/−4. The result is always shown with the sign attached to the numerator and a positive denominator.

Negative mixed numbers deserve a specific warning: the sign belongs to the whole value, not just the whole-number part. −2 1/3 means −(2 + 1/3) = −7/3, not −2 + 1/3. It’s a common calculation mistake, and it’s exactly why the calculator asks for numerator, denominator and whole number as separate fields rather than trying to parse a typed-in mixed number.

What if a denominator is zero?

A fraction with a zero denominator, like 5/0, isn’t a number — division by zero is undefined, so the calculator stops and flags the input rather than guessing. That’s different from dividing by a fraction that happens to equal zero, such as 3/4 ÷ 0/5: here both fractions are valid, but the division itself has no answer, because 0 has no reciprocal. The calculator reports this as a separate error so you can tell which side of the calculation needs fixing.

Step-by-step examples

Example 1: adding fractions with different denominators — 1/4 + 1/6

  1. Cross-multiply: (1×6 + 1×4) / (4×6) = 10/24.
  2. Simplify: GCD(10, 24) = 2, so 10/24 = 5/12.
  3. Decimal: 5/12 = 0.41666…, rounded to 0.416667.

Example 2: dividing fractions into a mixed number — 3/4 ÷ 2/5

  1. Multiply by the reciprocal: 3/4 × 5/2 = 15/8.
  2. Simplify: GCD(15, 8) = 1, so it’s already in lowest terms — 15/8.
  3. Convert to a mixed number: 15 ÷ 8 = 1 remainder 7, so 1 7/8.
  4. Decimal: 15 ÷ 8 = 1.875 (exact — the denominator 8 is a power of 2).

Example 3: adding mixed numbers directly — 1 1/2 + 2 1/3

  1. Convert each to an improper fraction: 1 1/2 = (1×2+1)/2 = 3/2; 2 1/3 = (2×3+1)/3 = 7/3.
  2. Cross-multiply: (3×3 + 7×2) / (2×3) = (9+14)/6 = 23/6.
  3. Simplify: GCD(23, 6) = 1 — already lowest terms.
  4. Mixed number: 23 ÷ 6 = 3 remainder 5, so 3 5/6.
  5. Decimal: 23/6 = 3.8333…, rounded to 3.833333.

Example 4: the negative mixed-number sign trap — −2 1/3 + 1/3

  1. Convert −2 1/3 correctly: the sign covers the whole value, so −2 1/3 = −(2×3+1)/3 = −7/3 (not −5/3).
  2. Cross-multiply: (−7×3 + 1×3) / (3×3) = (−21+3)/9 = −18/9.
  3. Simplify: GCD(18, 9) = 9, so −18/9 = −2/1.
  4. Because the denominator is 1, the result is a whole number: −2.

Frequently asked questions

How do you add fractions with different denominators?

Cross-multiply: for a/b + c/d, the sum is (a×d + c×b) / (b×d). For 1/4 + 1/6 that’s (1×6 + 1×4) / (4×6) = 10/24, which simplifies to 5/12. You don’t need to find the lowest common denominator first — multiplying the two denominators together always works, and the result gets reduced afterwards anyway.

How do you simplify (reduce) a fraction?

Divide the numerator and denominator by their greatest common divisor (GCD) — the largest whole number that divides both exactly. For 12/48, the GCD is 12, so dividing both by 12 gives 1/4. If the only common divisor is 1, the fraction is already in its simplest, or “irreducible,” form.

How do you convert a fraction to a decimal?

Divide the numerator by the denominator. Some fractions terminate exactly, like 1/4 = 0.25, because their simplified denominator only contains the prime factors 2 and 5. Others repeat forever, like 5/12 = 0.41666…; the calculator shows these rounded to six decimal places.

How do you convert an improper fraction to a mixed number?

Divide the numerator by the denominator to get the whole-number part, then put the remainder over the original denominator. For 15/8: 15 ÷ 8 = 1 remainder 7, so 15/8 = 1 7/8. This only applies when the numerator is bigger than the denominator (an “improper” fraction); a fraction smaller than 1 has no whole-number part to show.

How do you divide fractions?

Multiply the first fraction by the reciprocal of the second — flip the second fraction’s numerator and denominator, then multiply straight across. 3/4 ÷ 2/5 becomes 3/4 × 5/2 = 15/8. This only works when the second fraction isn’t zero, since zero has no reciprocal.

What’s the difference between a proper and an improper fraction?

A proper fraction has a numerator smaller than its denominator, so its value is less than 1 (like 3/4). An improper fraction has a numerator equal to or larger than its denominator, so its value is 1 or more (like 15/8 or 6/3). Improper fractions are usually shown as a mixed number for readability, but they’re mathematically identical either way.

How do I enter a negative mixed number correctly?

The minus sign applies to the whole value, not just the whole-number part: −2 1/3 means −(2 + 1/3) = −7/3, not −2 + 1/3 (= −5/3). That’s why the calculator’s advanced fields treat the whole number, numerator and denominator as separate values rather than parsing typed text — it removes the chance of making that sign mistake.

What happens if I try to divide by zero?

Two different things, depending on where the zero is. If a denominator you type in is 0 (like 5/0), that’s not a valid fraction at all, and the calculator blocks the calculation. If both fractions are valid but you’re dividing by a fraction equal to zero (like 3/4 ÷ 0/5), the division itself is undefined — zero has no reciprocal — and the calculator reports that as a separate error.

Sources