Adding fractions with unlike denominators requires recognizing that the fractions must be expressed in equivalent forms with a common denominator, often the least common multiple, before combining their numerators; the result is then simplified and interpreted as a fraction or mixed number. The reasoning applies to numerical positive and negative fractions and reinforces equivalence, magnitude, and the meaning of a common unit, but does not extend to algebraic rational expressions, symbolic denominators, or more advanced generalizations.
To add fractions with unlike denominators, first rewrite them with a common denominator. Then add the numerators and simplify the result.
Example:
The denominators are and . Their least common multiple is , so use as the common denominator.
Rewrite each fraction:
Now the fractions have the same-sized parts, so add the numerators:
The answer is an improper fraction. Convert it to a mixed number:
Therefore,
Remember: find a common denominator, make equivalent fractions, add the numerators, and simplify or convert to a mixed number if needed.
Click a topic below to practice the foundational skills you'll need, learn the steps, or master this skill
Earned ?