Fraction calculator, with the working shown

The four operations, worked through

The example the calculator opens with, 1 1/2 + 2/3, takes five steps, and the tool shows each one:

1. Turn the mixed number into one fraction: 1 1/2 = (1 × 2 + 1) / 2 = 3/2.
2. Find a common bottom: the smallest number both 2 and 3 go into is 6, so 3/2 = 9/6 and 2/3 = 4/6.
3. Add the tops and keep the bottom: 9 + 4 = 13, so the answer is 13/6.
4. Simplify: nothing but 1 divides both 13 and 6, so 13/6 stays as it is.
5. As a mixed number: 13 ÷ 6 = 2 remainder 1, so 2 1/6, or 2.1666666667 as a decimal.

Subtracting works the same way: 3 1/4 − 1 5/6 is 39/12 − 22/12 = 17/12, which is 1 5/12. Multiplying needs no common bottom: multiply the tops and the bottoms, so 2 1/2 × 3/5 = 5/2 × 3/5 = 15/10 = 3/2. Dividing turns the second fraction upside down and multiplies: 3/4 ÷ 1/8 = 3/4 × 8/1 = 24/4 = 6, which is how many eighths fit in three quarters.

Simplifying, and mixed numbers

A fraction is in its simplest form when no number but 1 divides both its top and its bottom. To get there, divide both by their greatest common divisor. The Simplify a fraction box below the calculator does this and says which number it used: 18/24 shares 6, so it becomes 3/4.

Mixed numbers are easier to picture (2 1/6 cups) while improper fractions are easier to calculate with (13/6). The calculator gives both. Two things trip people up:

• The minus sign belongs to the whole mixed number. −1 1/2 means −(1 + 1/2), which is −3/2, not −1 + 1/2. Type the minus in the whole-number box and the calculator reads it that way.
• Adding tops and bottoms does not add fractions. 1/2 + 1/3 is not 2/5: halves and thirds have to become sixths first, giving 5/6.

The calculator works with whole numbers of any length, so very large tops and bottoms stay exact instead of being rounded. Only the decimal line is rounded, to 10 places.

Decimals to fractions, and the inch ruler

The Decimal to fraction box turns a decimal into its exact fraction: each digit after the point is another factor of ten at the bottom, then the fraction is simplified. 0.375 is 375/1000, which simplifies to 3/8; 2.5 is 5/2, or 2 1/2.

Decimals that came from rounding make awkward exact fractions. 0.333 is exactly 333/1000, so the tool also names the closest simple fraction with a bottom up to 100 (1/3 here) and the nearest sixteenth (5/16), which is how tape measures and drill bits are marked. A measurement of 0.69 inches, for example, is closest to 11/16.

For percentages of a fraction, convert it to a decimal first and use the percentage calculator. For long calculations that mix fractions with other operations, the scientific calculator takes 3/4 + 2/3 typed in one line and answers in decimals.