Unit 5 Resources & Lessons
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Part 1: Ratios, Rates, & Proportions
Objective: To use ratios, rates, unit rates, and proportions to solve problems.
Key Concepts
Ratios & Rates: A ratio compares two quantities. A rate is a ratio with different units (e.g., miles per hour).
Ratio of 3 boys to 5 girls: \( \frac{3}{5} \) or 3:5
Unit Rate: A rate where the second quantity is 1. To find it, divide the first quantity by the second.
120 miles in 2 hours \(\rightarrow\) \( \frac{120 \text{ miles}}{2 \text{ hours}} = 60 \) miles per hour
Solving Proportions: Two equal ratios form a proportion. Use cross-multiplication to solve for a missing value.
\( \frac{x}{10} = \frac{3}{5} \rightarrow 5x = 30 \rightarrow x = 6 \)
Part 2: Percent Applications
Objective: To solve real-world problems involving percents, including discounts, tax, and tips.
Key Concepts
Finding Percent of a Number: Change the percent to a decimal (divide by 100) and multiply.
20% of 80 \(\rightarrow\) \(0.20 \times 80 = 16\)
Discounts: Calculate the discount amount (percent of the price) and subtract it from the original price.
25% off $40 \(\rightarrow\) \(0.25 \times 40 = \$10\) discount. New price: \(\$40 - \$10 = \$30\).
Tax & Tip: Calculate the tax or tip amount (percent of the bill) and add it to the original total.
8% tax on $50 \(\rightarrow\) \(0.08 \times 50 = \$4\) tax. Total cost: \(\$50 + \$4 = \$54\).