Overview
This lesson covers solving routine and non-routine problems involving multiplication, addition, and subtraction of fractions and mixed numbers, with a focus on translating word problems into mathematical phrases and solving them step-by-step.
Multiplication Phrases and Translation
- Multiplication phrases include: times, product of, multiplied by, of, twice, thrice.
- Translate verbal phrases into mathematical expressions using parentheses and appropriate operators.
Steps in Problem Solving
- Identify given facts and needed data.
- Determine what is being asked.
- Decide on the correct operation(s) and write the number sentence.
- Solve the problem using appropriate strategies (e.g., cancellation method).
- Check your answer for correctness.
Example Problem Translations
- "Twice the sum of 3/5 and 2/3 less 1/2" becomes 2 × ((3/5 + 2/3) - 1/2).
- "The product of 5 and 7 9/27 and 27/56" requires converting mixed numbers to improper fractions before multiplying.
- When multiplying mixed numbers, convert them to improper fractions first.
Solving Fraction Problems
- Use the cancellation method to simplify fractions before multiplying (find common factors to reduce).
- Multiply numerators and denominators directly when no further simplification is possible.
- After multiplication, convert improper fractions to mixed numbers as needed.
Word Problem Applications
- Find area by multiplying length and width expressed as mixed numbers (convert, simplify, multiply, and write as mixed number).
- When dealing with totals, multiply quantity by unit value, then add, subtract, or compare as the problem requires.
- For subtraction problems (like making change), calculate the total spent then subtract from the amount given.
Key Terms & Definitions
- Routine Problem — a standard problem with a direct solution method.
- Non-routine Problem — requires creative or multi-step approaches.
- Cancellation Method — simplifying fractions by dividing numerators and denominators by common factors.
- Improper Fraction — a fraction where the numerator is greater than or equal to the denominator.
- Mixed Fraction — a whole number and a proper fraction combined.
Action Items / Next Steps
- Complete all practice problems and translate word problems into mathematical phrases.
- Practice converting mixed numbers to improper fractions and apply the cancellation method.
- Check notebook for assigned problems from the lesson to solve.