1. Chapter 7 Proportional Reasoning Section 7.1 The Concept of Ratio

2. Definition of Ratio A ratio is an ordered pair of numbers used to show a comparison between like or unlike quantities, written x to y, A ratio is an ordered pair of numbers used to show a comparison between like or unlike quantities, written x to y, x, x ÷ y, or x : y (y  0). x, x ÷ y, or x : y (y  0). Y Example: A certain football team won 9 of the twelve games they played last season. Write the ratio of: wins to games played(part to whole) wins to games played(part to whole) games played to losses(whole to part) games played to losses(whole to part) wins to losses(part to part) wins to losses(part to part)

3. Equivalent Ratios Two ratios are equivalent ratios if their respective fractions are equivalent or if the quotients of the respective terms are the same. Two ratios are equivalent ratios if their respective fractions are equivalent or if the quotients of the respective terms are the same. Example: Example: Katrina makes 8 free throws every 10 attempts. At this rate, how many free throws can she expect to make in 15 attempts? 20 attempts? 75 attempts?

4. Rates A rate is a ratio comparing quantities that involve different units. The word “per” is often used to describe rates. A rate is a ratio comparing quantities that involve different units. The word “per” is often used to describe rates. Rates of speed, time Unit price

5. Example A recipe for biscuit mix calls for 8 cups of flour, 1 1/3 cups of nonfat dry milk, and 5 tablespoons of baking powder, along with other ingredients. If you had only 6 cups of flour, what would be the comparable amounts of nonfat dry milk and baking soda? A recipe for biscuit mix calls for 8 cups of flour, 1 1/3 cups of nonfat dry milk, and 5 tablespoons of baking powder, along with other ingredients. If you had only 6 cups of flour, what would be the comparable amounts of nonfat dry milk and baking soda?

6. Example Alisha finds that she uses 12 gallons of gasoline for every 250 miles that she drives. Her friend Nicole uses about 15 gallons of gasoline for every 300 miles that she drives. Alisha finds that she uses 12 gallons of gasoline for every 250 miles that she drives. Her friend Nicole uses about 15 gallons of gasoline for every 300 miles that she drives. Who gets the better gasoline mileage and why?