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.