Overview
This lecture explains how to add and subtract fractions, focusing on finding common denominators and converting mixed numbers to improper fractions.
Adding and Subtracting Fractions
- Fractions must have a common denominator (same bottom number) to be added or subtracted.
- Only numerators (top numbers) are added or subtracted once denominators match.
Steps to Add or Subtract Fractions
- Find the lowest common multiple (LCM) of denominators for a shared denominator.
- Adjust each fraction so denominators are the LCM by multiplying both numerator and denominator.
- Add or subtract the numerators; keep the denominator the same.
- Simplify the final fraction if possible.
Example Problems
- To add 3/4 and 1/3, LCM of 4 and 3 is 12; convert to 9/12 + 4/12 = 13/12.
- To subtract 2/5 from 5/3, LCM of 3 and 5 is 15; convert to 25/15 - 6/15 = 19/15.
- Improper fractions (numerator larger than denominator) can be used directly.
- Mixed numbers (e.g., 2 3/4) must be converted to improper fractions before operations:
- 2 3/4 becomes 11/4; add to 5/12 by converting to 33/12 + 5/12 = 38/12 = 19/6.
- For 5/6 - 4/15, LCM of 6 and 15 is 30; convert to 25/30 - 8/30 = 17/30.
Key Terms & Definitions
- Numerator — The top number in a fraction, showing how many parts are taken.
- Denominator — The bottom number in a fraction, showing the total number of parts.
- Common Denominator — A shared denominator between two or more fractions.
- Lowest Common Multiple (LCM) — The smallest number that is a multiple of two denominators.
- Improper Fraction — A fraction where the numerator is equal to or larger than the denominator.
- Mixed Number — A number made up of a whole number and a fraction.
Action Items / Next Steps
- Practice converting mixed numbers to improper fractions.
- Complete exercises adding and subtracting fractions with different denominators.
- Review simplification of the resulting fractions after addition or subtraction.