Overview
This lecture covered problem solving involving addition and subtraction of decimal and mixed decimal numbers, focusing on step-by-step strategies and practical word problem examples.
Problem Solving Steps
- Understand the problem by identifying what is being asked and the given facts.
- Plan by choosing the appropriate operation(s) to use: addition or subtraction (or both).
- Solve using the chosen operation, with or without regrouping.
- Check your answer by reversing the operation (e.g., addition after subtraction).
Sample Problems & Solutions
Liquid Weights Table
- To find weight for multiple gallons, multiply the per-gallon weight by the number of gallons.
- To compare weights, subtract the smaller weight from the larger to find the difference.
- Example: 4 gallons of kerosene at 6.664 lbs/gallon equals 26.656 lbs.
- Example: Sea water (8.58 lbs) minus drinking water (8.33 lbs) equals 0.25 lbs more.
Word Problems with Money and Land
- When a price is reduced, add the reduction back to the sale price to find the original.
- For differences in land size, subtract the smaller area from the larger.
- Example: Microwave costing 2,999.99 pesos after a 500 peso reduction originally cost 3,499.99 pesos.
- Example: 15-hectare banana plantation is 2.1433 hectares larger than a 12.8567-hectare sugarcane plantation.
Application Problems
- To find a new total after a withdrawal, add all withdrawals then subtract from the initial amount.
- When buying items in multiples, multiply the unit price by the quantity before adding other items.
- To find change, subtract the total bill from the amount paid.
Multiple Choice Practice
- Apply correct addition or subtraction of decimals to select the best answer.
- Sample: Adding 28.58, 30.55, and 25.48 kg gives a total weight of 84.61 kg.
Key Terms & Definitions
- Decimal Number — A number that includes a decimal point to show values less than one.
- Mixed Decimal — A number with both whole and decimal parts (e.g., 12.8567).
- Regrouping — Rearranging numbers when carrying or borrowing during addition or subtraction.
Action Items / Next Steps
- Complete written solutions to practice problems in your notebook.
- Practice the four-step problem solving method on additional word problems.
- Review key terms and decimal operations for upcoming assessments.