1. Bellwork: Solve for x. 1. 2.

2. 8.1 Ratio and Proportion Students will be able to: 1. Recognize and work with ratios and proportions. 2. Find a fourth proportional. 3. Be able to apply the means/extremes product theorem. 4. Calculate the geometric mean.

3. Ratio (Defn) A quotient of two numbers Please note: A ratio can be written in 3 different ways. Ratios can (and should) be reduced.

4. Proportion (Defn) An equation stating that two ratios are equal. Means Extremes

5. Means-Extremes Products Theorem (Toolbox!) The product of the means is equal to the product of the extremes.

6. Example 1 Find the fourth proportional for each set of three terms. 1. 2, 3, 8 2. a, 3b, 6

7. Example 2 Find the ratio of x to y if

8. Toolbox: A “mean” proportion (Defn) or Geometric mean (x in this case). A proportion in which the means are the same. Ex.

9. Example 3 Find the geometric and arithmetic means between 3 and 27. Note which is greater. What is an arithmetic mean?

10. Example 4 Find the mean proportional between 4 and 12.

11. Example 5 6 is the geometric mean between 12 and what number.

12. Example 6 Show that is equivalent to.

13. Ticket to Leave Find the geometric mean between 5 and 20. 9 is the geometric mean between 27 and what number?

14. Homework Pg. 329 # 4 – 15, 17, 18, 24 Show work for credit!