1. 8.1 Exploring Ratio & Proportion How to use proportions to solve problems. How to compute the ratio of two numbers.

2. 8.1 Exploring Ratio & Proportion Computing Ratios: If a and b are two quantities that are measured in the same units, then the ratio of a to b is: The ratio of a to b can also be written as:

3. 8.1 Exploring Ratio & Proportion 1) Suppose a class has 18 girls and 20 boys. What is the ratio of girls to boys? The ratio of girls to boys is: Note: the ratio of a to b is not equal to the ratio of b to a Girls:Boys = 9: 10 Girls to Boys = 9 to 10 2) What is the ratio of boys to girls? The ratio of boys to girls is: Computing Ratios: Boys:Girls = 10:9 Boys to Girls = 10 to 9

4. 8.1 Exploring Ratio & Proportion Comparing Two Ratios: Tran’s thumb circumference is 3.5 inches, his wrist circumference is 7 inches, and his neck circumference is 14 inches. The ratio of his wrist measurement to his thumb measurement is 7 to 3.5 or 2 to 1. The ratio of his neck measurement to his wrist measurement is 14 to 7 or 2 to 1. What is the ratio of his thumb measurement to his neck measurement? ? How would you compare the first two ratios

5. 8.1 Exploring Ratio & Proportion An equation that combines two ratios with a equal sign is a proportion. If is equal to, then the proportion is the statement of equality. This proportion is written as: Where a, b, c, and d are nonzero. And read as: “a is to b as c is to d.” Using Proportions:

6. 8.1 Exploring Ratio & Proportion Using Proportions: IfThen: Extremes Means So: Properties of Proportions 1.The product of the extremes equals the product of the means. If, then Cross Product Property 2. If two ratios are equal, then their reciprocals are also equal. If, then Reciprocal Property Cross product a:b = c:d ?

7. 8.1 Exploring Ratio & Proportion Solving Proportions: a. Reciprocal Property Multiply by ? Simplify

8. 8.1 Exploring Ratio & Proportion b. Solving Proportions Cross Product Property Distributive Property Subtract ? From both sides.

9. 8.1 Exploring Ratio & Proportion Using & Solving Proportions: The photo, below left, shows Bev Doolittle’s painting Woodland Encounter. Her actual painting, represented on the right, is 50.8 cm high. How wide is it? 6.5 cm 13cm ? Original Photo 50.8 cm

10. Exploring Ratio & Proportion Using & Solving Proportions: Width of Painting Width of Photo = Height of Painting Height of photo Substitute Multiply by ? Calculate

11. Exploring Ratio & Proportion Homework: