Overview
This lecture introduces the basics of adding and subtracting fractions, focusing on when the denominators (bottom numbers) are the same and hinting at the next step: finding common denominators.
Adding Fractions with the Same Denominator ("Like" Fractions)
- To add fractions with the same denominator, add the numerators (top numbers) and keep the denominator unchanged.
- Example: ( \frac{1}{2} + \frac{1}{2} = \frac{2}{2} = 1 ).
- Example: ( \frac{5}{16} + \frac{2}{16} = \frac{7}{16} ).
Subtracting Fractions with the Same Denominator
- To subtract fractions with the same denominator, subtract the numerators and keep the denominator unchanged.
- Example: ( \frac{5}{9} - \frac{2}{9} = \frac{3}{9} ).
Why You Can't Just Add Numerators and Denominators
- Adding numerators and denominators directly (e.g., ( \frac{1}{2} + \frac{1}{2} = \frac{2}{4} )) is incorrect.
- This breaks the "Order of Operations," which requires division before addition.
Like vs. Unlike Fractions
- "Like" fractions have the same denominator; adding or subtracting them is straightforward.
- "Unlike" fractions have different denominators and must be converted to like fractions before addition or subtraction.
Finding Common Denominators (Preview)
- To add or subtract unlike fractions, first convert them to like fractions by finding a common denominator.
- The process of making denominators the same is called "finding a common denominator."
Key Terms & Definitions
- Numerator — the top number of a fraction, representing the number of parts considered.
- Denominator — the bottom number of a fraction, representing the total number of parts.
- Like Fractions — fractions that have the same denominator.
- Unlike Fractions — fractions that have different denominators.
- Common Denominator — a shared denominator between two or more fractions.
Action Items / Next Steps
- Complete the exercises for adding and subtracting like fractions.
- Prepare to learn about finding common denominators in the next lesson.