Chapter IX – Of the Addition and Subtraction of Fractions
Summary: Explains how to add and subtract fractions by reducing them to a common denominator, derives the general two-fraction formula, and covers mixed-number arithmetic.
Sources: chapter-1.1.9
Last updated: 2026-04-24
§94: Same Denominator
When denominators are equal, simply add or subtract numerators:
Also: and (source: chapter-1.1.9).
§95–97: Different Denominators
Convert each fraction to an equivalent form with a common denominator, then add/subtract numerators. The general formula for two fractions is:
Example: : convert to and ; sum , difference (source: chapter-1.1.9).
For several fractions, find the least common denominator (LCD) — a number divisible by all denominators. Example with : LCD ; sum (source: chapter-1.1.9).
§98: Comparing Fractions
To compare and , reduce to a common denominator and compare numerators. Example: vs becomes vs , so by (source: chapter-1.1.9).
§99: Subtracting a Fraction from an Integer
Convert one unit of the integer to a fraction with the same denominator:
§100: Mixed Number Addition
Add the integer parts and the fractional parts separately; carry any integer arising from the fraction sum:
(source: chapter-1.1.9)