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Understanding Ratios, Rates, and Proportions

Learn about ratios, rates, and proportions and how to solve them. Explore real-life examples and understand the cross product property. Discover unit pricing and unit rates for cost comparison.

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Understanding Ratios, Rates, and Proportions

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  1. Section 3-4: Ratio and Proportion Objectives: To find ratios and rates To solve proportions

  2. Definitions Ratio: A relationship between two numbers through division Rate: In a ratio, when each term represents a quantity measured in different units Unit Rate: a rate with a denominator of 1. Unit Analysis: The process of converting from one unit to another Proportion: An equation that states that two ratios are equal Extremes of the Proportion: the numerator the 1st ratio and the denominator of the 2nd ratio. Means of the Proportion: the numerator of the 2nd ratio and the denominator of the 1st ratio

  3. Cross Product Property If , then means extremes Ex: Since 24 = 24, we know that the proportion is valid

  4. Unit Pricing …In Real Life

  5. Example: Using Unit Rates The table below gives prices for different sizes of the same brand of apple juice. Find the unite rate (cost per ounce) for each. Which has the lowest cost per ounce?

  6. Using Unit Rates Divide Divide This has the lowest cost per ounce. Divide

  7. Real-World Example In 2004, Lance Armstrong won the Tour de France, completing the 2291 km course in about 83.6 hours. Find Lance’s unit rate, which is his average speed. Write a rule to describe the distance he cycles d as a function of the time t he cycles. Cycling at his average speed, about how long would it take Lance to cycle 185km?

  8. Real-World Example Distance  Time 

  9. Another Cross Product Example Solve the proportion

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