Overview
This lecture explains how to add and subtract mixed numbers by finding common denominators and simplifying answers, using one example each for addition and subtraction.
Adding Mixed Numbers
- Line up mixed numbers vertically for clarity.
- Check if the fractional parts have a common denominator; if not, find the least common denominator (LCD).
- Rename fractions so both have the same denominator.
- Convert each fraction: multiply top and bottom by necessary factors to reach LCD.
- Add the numerators of the fractions and keep the common denominator.
- Add the whole numbers.
- Check if the resulting fraction can be simplified; simplify if possible.
- Example: (5\frac{2}{7} + 3\frac{1}{2} = 8\frac{11}{14})
Subtracting Mixed Numbers
- Write mixed numbers vertically to keep work organized.
- Determine if the denominators are the same; if not, find the LCD.
- Convert fractions to have the LCD, if needed.
- Subtract the numerators and keep the common denominator.
- Subtract the whole numbers.
- Simplify the fractional part if possible.
- Example: (7\frac{11}{12} - 2\frac{3}{4} = 5\frac{1}{6}) (after simplifying (2/12) to (1/6))
Key Terms & Definitions
- Mixed number — a number made up of a whole number and a fraction, e.g., (3\frac{1}{2}).
- Common denominator — a shared denominator between two or more fractions.
- Least common denominator (LCD) — the smallest number that both denominators divide into evenly.
- Simplest form — a fraction where numerator and denominator have no common factors other than one.
Action Items / Next Steps
- Practice adding and subtracting mixed numbers using different denominators.
- Check and simplify answers in each problem.