Overview
This lecture explains how to solve various word problems involving fractions, including adding, subtracting, multiplying, and dividing fractions in real-life scenarios.
Adding and Simplifying Fractions
- To find total hours Juliana worked (6 + 5 + 3 = 14), express as 14/24, then simplify to 7/12 of a day.
- When adding mixed numbers (e.g., 5 1/4 + 3 1/3), add whole numbers and fractions separately.
- Use the least common multiple (LCM) to add fractions with different denominators.
Subtracting Fractions and Mixed Numbers
- To subtract a fraction from a mixed number, convert both to improper fractions if needed.
- Example: 3 1/4 - 5/4 = 13/4 - 5/4 = 8/4 = 2 meters.
- You can also convert improper fractions to mixed numbers before subtracting.
Combined Operations with Mixed Numbers
- For sums and differences involving more than one mixed number or fraction, combine like terms and use LCM for denominators.
- Example: For meat usage, sum two mixed numbers, then subtract from the total to find the remaining.
Multiplying Fractions (Area Problems)
- Area = length × width, convert mixed numbers to improper fractions before multiplying.
- Multiply numerators and denominators; convert the result to a mixed number if necessary.
Word Problems Involving Fractional Expenses
- Multiply salary by each expense fraction to find the amount spent per category.
- Add all expenses to get total spending.
- Subtract total expenses from salary to get savings.
- Express savings as a simplified fraction of total salary.
Dividing Fractions and Mixed Numbers
- To divide a mixed number by a whole number, convert to an improper fraction, then multiply by the reciprocal of the divisor.
- Simplify the result and convert to a mixed number if possible.
Multi-step Fraction Word Problems
- For scenarios with sequential spending and saving, work step-by-step: calculate amount spent, subtract to find remainder, allocate savings, then divide the rest as required.
Key Terms & Definitions
- Mixed Number — a number made up of a whole number and a fraction (e.g., 3 1/4).
- Improper Fraction — a fraction where the numerator is larger than the denominator (e.g., 13/4).
- LCM (Least Common Multiple) — the smallest number that is a multiple of two or more numbers, used to find common denominators.
- Reciprocal — swapping the numerator and denominator of a fraction, used during division.
Action Items / Next Steps
- Practice similar fraction word problems.
- Review methods for simplifying, adding, subtracting, multiplying, and dividing fractions.
- Complete any assigned homework on real-life fraction problems.