Adding and Subtracting Fractions

Jun 19, 2025

Overview

This lecture explains the correct method for adding and subtracting fractions, focusing on the importance of having common denominators and introducing key terminology.

Why Multiplying Fractions is Easier

  • Multiplying fractions is simple: multiply numerators (top numbers) together and denominators (bottom numbers) together.
  • Adding the numerators and denominators directly does not work for addition.

Rules for Adding Fractions

  • You cannot simply add the numerators and denominators; that breaks the order of operations.
  • To add fractions, denominators (bottom numbers) must be the same.

Adding Like Fractions

  • "Like fractions" have the same denominators.
  • To add like fractions, add the numerators and keep the denominator the same.
  • Example: 1/2 + 1/2 = (1 + 1)/2 = 2/2 = 1 (a whole).
  • Example: 5/16 + 2/16 = 7/16.

Subtracting Like Fractions

  • To subtract like fractions, subtract the numerators and keep the denominator the same.
  • Example: 5/9 - 2/9 = (5 - 2)/9 = 3/9.

Unlike Fractions and Common Denominators

  • "Unlike fractions" have different denominators.
  • To add or subtract unlike fractions, convert them to like fractions by finding a common denominator.
  • The common denominator is a shared bottom number for all fractions involved.

Key Terms & Definitions

  • Numerator — the top number of a fraction showing how many parts are considered.
  • Denominator — the bottom number of a fraction showing total equal parts.
  • Like Fractions — fractions with the same denominator.
  • Unlike Fractions — fractions with different denominators.
  • Common Denominator — a denominator that is the same for multiple fractions, used for addition or subtraction.

Action Items / Next Steps

  • Complete the exercises for this section on adding and subtracting like fractions.
  • Prepare to learn how to find a common denominator for unlike fractions in the next lesson.