Overview
This lecture teaches how to solve routine and non-routine word problems involving multiplication of decimals and mixed decimals, including real-life money problems.
Problem Solving with Decimals
- Multiplying decimals helps solve real-life problems like calculating calories burned or earnings.
- Four steps for problem solving: understand the problem, identify given facts, create a number sentence and solve, check the answer.
Sample Calorie Problems
- Playing volleyball for 15 minutes (2.51 cal/min): 2.51 × 15 = 37.65 calories.
- Standing 1 hour (1.20 cal/min) and washing dishes 10 mins (2.55 cal/min): (1.2 × 60) + (2.55 × 10) = 72 + 25.5 = 97.5 calories.
- Running 20 miles (10.5 cal/mile, 16.5 minutes): Solution involves multiplying rates and times to find total calories.
Application to Money and Length Problems
- 125.75 pesos = 12,575 centavos (125.75 × 100).
- Cotton: 24.75 m total, 9.85 m sold; 24.75 - 9.85 = 14.9 m left.
- Cycling: 6.2 mins/km, 4 km; 6.2 × 4 = 24.8 minutes needed.
Multi-step Word Problems
- Clerk earns 45.25 pesos/hour (40 reg. hours, 5 overtime at 1.15× rate, 2 holiday at 2× rate). Total = 1,810 + 339.38 + 181 = 2,330.38 pesos.
- Programmer: 42.75 hours × 50 pesos = 2,137.5 pesos/week.
- Arthur saves 10% of 1,350 pesos/day for 30 days: 1,350 × 0.1 × 30 = 4,050 pesos/month.
- Mr. Fernandez’s net yearly salary: (5,450 - 543) × 12 = 58,884 pesos.
- Dian works 2.5 hours/day (Mon–Fri), 3.75 hours (Sat), paid 25 pesos/hour: (2.5 × 5 + 3.75) × 25 = 46.25 pesos/week.
Creating Your Own Word Problems
- Use provided data (e.g., 256.25 pesos/day earnings, 15 pesos per apple for 24 apples) to make solvable problems.
Key Terms & Definitions
- Decimal Number — A number that includes a decimal point to show values less than one.
- Mixed Decimal — A whole number and decimal combined (e.g., 3.75).
- Centavo — A monetary unit, 1/100th of a peso.
- Routine Problem — A standard word problem with clear, familiar steps.
- Non-routine Problem — A problem needing creative or multiple-step solutions.
Action Items / Next Steps
- Complete practice problems and word problems using multiplication of decimals in your notebook.
- Create your own word problems using the given data sets.