Working With Fractions: A Clear Guide

Fractions describe parts of a whole, and once you know the four rules for combining them, they are no harder than working with whole numbers. This guide covers each operation, why it works, and how to tidy up your answer.

Adding and subtracting: find a common denominator

You can only add or subtract fractions that share the same denominator (bottom number). To add 1/2 + 1/3, convert both to sixths: 3/6 + 2/6 = 5/6. The shortcut is to multiply the denominators for the new denominator, and cross-multiply for the numerators.

The calculator writes this out as you would in an exercise book: the common denominator, both fractions expanded onto it, the sum, and then the division by the greatest common divisor that reduces the answer. Your two operands are quoted back exactly as you typed them — 2/4 + 1/2 stays 2/4 + 1/2, because reducing an operand before showing it would be answering a question you didn’t ask.

Multiplying: straight across

Multiplication is the easy one — multiply the numerators together and the denominators together. 2/3 × 3/4 = 6/12, which simplifies to 1/2. No common denominator needed.

Dividing: flip and multiply

To divide by a fraction, flip the second one (its reciprocal) and multiply. 1/2 ÷ 1/4 becomes 1/2 × 4/1 = 4/2 = 2. It feels like a trick, but it follows directly from what division means.

Simplifying and mixed numbers

Always reduce your answer to lowest terms by dividing the top and bottom by their greatest common divisor: 6/12 becomes 1/2. If the numerator is larger than the denominator (an improper fraction), you can write it as a mixed number — 7/2 is 3 1/2.

Converting to a decimal

Divide the numerator by the denominator: 5/8 = 0.625. Decimals are handy for comparisons and for entering values into other calculators.

Six calculators, not six modes

The fraction calculator page carries six separate tools, each with its own fields, its own button and its own answer — none is a tab or a mode of another, so you can leave one filled in while you use the next:

1. Fraction Calculator — the four operations on two fractions.
2. Mixed Numbers Calculator — the same four, on whole-number-and-fraction values.
3. Simplify Fractions Calculator — reduce one fraction to lowest terms.
4. Decimal to Fraction Calculator — turn 0.625 back into 5/8.
5. Fraction to Decimal Calculator — the other direction.
6. Big Number Fraction Calculator — for integers far too large for ordinary arithmetic.

Every answer arrives with the equation, the result in decimals to fourteen significant figures, pie diagrams for the operands and the answer, and the calculation steps in full.

Why the big-number one exists

Ordinary computer arithmetic loses precision above about sixteen digits, and a fraction calculator hits that ceiling fast: adding 1/999999937 and 1/999999893 needs a denominator of 999999830000006741, which does not fit. Every fraction here is held as a pair of exact whole numbers instead, so a thirty-digit denominator is reproduced digit for digit rather than rounded to something plausible.

Where fractions show up

Cooking (half of ¾ cup), construction (⅝-inch bolt), and probability all rely on fractions. The calculator shows the simplified fraction, the mixed number and the decimal at once, so you can check your work in whichever form you need.