Overview
The lecture introduces the basics of adding and subtracting fractions, explains why you can't simply add numerators and denominators, and covers the concept of like and unlike fractions.
Multiplying vs. Adding Fractions
- Multiplying fractions: multiply the numerators (top numbers) and denominators (bottom numbers) directly.
- Adding fractions: cannot add numerators and denominators directly.
Why Addition Doesn't Work Like Multiplication
- Adding numerators and denominators breaks the Order of Operations.
- Fractions represent division, and addition must follow division rules.
Adding and Subtracting Like Fractions
- Like fractions have the same denominators (bottom numbers).
- To add like fractions: add 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.
- To subtract like fractions: subtract numerators and keep the denominator the same.
- Example: 5/9 - 2/9 = (5-2)/9 = 3/9.
Like vs. Unlike Fractions
- Like fractions: same denominators, easy to add or subtract.
- Unlike fractions: different denominators, cannot use the simple addition/subtraction rule.
Introduction to Common Denominator
- To add or subtract unlike fractions, make denominators the same (find a common denominator).
- Common denominator: a shared bottom number for the fractions.
Key Terms & Definitions
- Fraction — a number showing part of a whole, written as numerator over denominator.
- Numerator — the top number in a fraction.
- Denominator — the bottom number in a fraction.
- Like Fractions — fractions with the same denominator.
- Unlike Fractions — fractions with different denominators.
- Common Denominator — a denominator that is the same for two or more fractions.
Action Items / Next Steps
- Complete the exercises for this section before moving on.
- Prepare to learn how to find a common denominator in the next lesson.