Fraction visualizer

Why find a common denominator?

Adding 3/4 and 1/6 means combining different-sized pieces. Rewrite them as 9/12 and 2/12 so the pieces match. Then 9/12 + 2/12 = 11/12. On the operation line, move from zero to 3/4, then move another 1/6 to the right.

Subtraction and negative values

For A − B, the second jump is −B. Subtracting a positive value moves left; subtracting a negative value moves right. For example, 1/6 − 3/4 = −7/12. The line expands to include negative values and fractions greater than one.

Method and diagram limits

The common denominator is the least common multiple of the two positive denominators. Scale each numerator to that denominator, combine the numerators and simplify using their greatest common divisor. Comparison uses the scaled numerators directly.

This tool accepts integer numerators from −100 to 100 and denominators from 1 to 24. Enter a mixed number as an improper fraction: 1 1/2 becomes 3/2. It supports addition, subtraction and comparison. Decimal values are rounded; fraction results are exact within these bounds.

The IES fractions workbook uses number lines to connect fractions and their size. Our SVG is an original diagram, sized for a screen or lesson document. It is not an actual-size measuring template. Close points can overlap; read the exact working alongside the diagram.

Explore chance with the birthday-paradox simulator or Monty Hall simulator.