CalcRover

Fraction Calculator

Do arithmetic on two fractions and see every step: finding the common denominator, flipping the reciprocal for division, reducing by the GCF, and converting to a mixed number. Negative numerators are fine.

Fraction arithmetic rules

Adding and subtracting need a common denominator — the least common denominator (LCD) is the LCM of the two denominators. Multiplying is straight across (tops together, bottoms together). Dividing flips the second fraction and multiplies:

Every answer should be reduced to lowest terms: divide the top and bottom by their greatest common factor. If the numerator ends up larger than the denominator, the result can also be written as a mixed number — 3/2 = 1 1/2.

a/b + c/d = (ad + cb) / bd (then reduce)
a/b × c/d = ac / bd
a/b ÷ c/d = a/b × d/c

Worked examples

Example 1: adding unlike fractions

1/2 + 1/3

  1. The LCD of 2 and 3 is 6.
    LCD(2, 3) = 6
  2. Rewrite both fractions over 6.
    1/2 = 3/6; 1/3 = 2/6
  3. Add the numerators.
    3 + 2 = 5 → 5/6

1/2 + 1/3 = 5/6.

Example 2: dividing fractions

1/2 ÷ 3/4

  1. Flip the second fraction and multiply.
    1/2 × 4/3 = 4/6
  2. Reduce by the GCF of 4 and 6, which is 2.
    4/6 = 2/3

1/2 ÷ 3/4 = 2/3 — a half is two-thirds of three-quarters.

Example 3: recipe scaling with mixed numbers

A recipe needs 3/4 cup of flour; you're making 2 1/2 times the batch. How much flour?

  1. Convert the mixed number to an improper fraction.
    2 1/2 = 5/2
  2. Multiply.
    3/4 × 5/2 = 15/8
  3. Convert back to a mixed number.
    15/8 = 1 7/8 cups

1 7/8 cups of flour.

FAQ

Why do fractions need a common denominator to add?+

Because you can only count pieces of the same size. Halves and thirds are different sizes; rewriting both as sixths makes the pieces equal, and then the counts (numerators) can be added.

What's an improper fraction and a mixed number?+

An improper fraction has a numerator at least as large as its denominator (15/8); a mixed number writes the same value as a whole part plus a proper fraction (1 7/8). Both are correct — math classes often want improper, cooking wants mixed.

How do I reduce a fraction to lowest terms?+

Divide numerator and denominator by their greatest common factor. For 36/48 the GCF is 12, so it reduces to 3/4. Our GCF calculator shows that step in detail.

Why does dividing by a fraction make numbers bigger?+

Dividing by a half asks "how many halves fit?" — twice as many as wholes. Dividing by any fraction under 1 gives a result larger than the starting number; the reciprocal trick (× d/c) makes that visible.

How do I turn a fraction into a decimal?+

Divide the top by the bottom: 5/6 = 0.8333…. This calculator shows the decimal to 4 places. Some fractions terminate (1/4 = 0.25); fractions whose reduced denominator has prime factors other than 2 and 5 repeat forever.

Related calculators