Overview
This lecture reviews multiple choice practice questions for Math 7, focusing on percentages, rates, discounts, commissions, simple interest, and unit rates.
Percentage Increase & Decrease
- Percentage increase measures how much a value rises compared to its original value.
- Original value is the starting amount; new value is the amount after change.
- Formula for percentage increase: (New Value - Original Value) ÷ Original Value × 100.
- Formula for percentage decrease is similar but involves a decrease in value.
Discounts & Sale Price
- Discount is the amount or percent deducted from the original selling price.
- Total cost is the purchase price plus sales tax.
- Discount formula: Original Price × Discount Rate (convert rate to decimal before multiplying).
- Rate of discount: (Original Price - Sale Price) ÷ Original Price × 100.
Solving Price and Rate Problems
- Given decreased value and percentage, original value = New Value ÷ (1 - Percentage Decrease in decimal).
- Sale price with percentage reduction: Original Price × (1 - Discount Rate in decimal).
- To find original price from sale price: Sale Price ÷ (1 - Discount Rate).
Sales Tax & Commission
- Sales tax = Purchase Price × Tax Rate (in decimal).
- Sales tax rate = Sales Tax ÷ Purchase Price × 100.
- Commission = Total Sales × Commission Rate (convert rate to decimal before multiplying).
- To find total sales from commission: Commission ÷ Commission Rate (in decimal).
Simple Interest
- Simple interest formula: Interest = Principal × Rate × Time.
- To find principal given yearly interest: Principal = Interest ÷ (Rate × Time).
Rates, Unit Rates & Ratios
- Rates compare two different units, e.g., kilometers per hour.
- Unit rate has a denominator of 1; simplify rates by dividing numerator and denominator.
- Find rate per unit: divide total by the given quantity, e.g., 150 words in 3 minutes = 50 words per minute.
- Multiply or divide rates using reciprocals to compute unit rates.
Problem-Solving Examples
- Decrease by percentage: reverse calculate using given new value and percent decrease.
- Savings calculation: Subtract total expenses from total allowance over the period.
- For fractions (like ¾ kg for 45 pesos), use reciprocals to find unit price.
- Speed (unit rate): total distance ÷ total time.
Key Terms & Definitions
- Percentage Increase — Amount of increase compared to original value, expressed as a percent.
- Discount — Amount or percent deducted from original price.
- Commission — Earnings based on a percentage of sales made.
- Sales Tax — Percentage added to purchase price by government.
- Simple Interest — Interest calculated on principal only, not on accumulated interest.
- Rate — Comparison between two different kinds of quantities.
- Unit Rate — Rate with a denominator of 1.
Action Items / Next Steps
- Practice similar multiple choice problems on percentages, rates, discounts, commissions, and interest.
- Review definitions and formulas for future periodical tests.
- Watch Part 1 of the reviewer if you haven't yet (Polygons).