1. Thursday, April 14 th, 2005 Unit 8—Using Proportional Reasoning Day 1—Writing Ratios and Simplifying Ratios Homework—Worksheet 8.1

2. Overview of Unit 8 Equal Ratios Rates Proportions Scale Drawings Expressing Fractions as Decimals Fractions, Decimals, and Percents Percents Greater than 100% and Less than 1% Percent of a number Percent Proportion

3. 3 Ways to Write a Ratio A : B A to B

4. Simplifying Ratios Steps to Simplify: 1. Find the Greatest Common Factor (GCF) between the two numbers. 2. Divide the GCF into both numbers. 3. Check to make sure that the ratio is simplified.

5. Let’s Find the GCF! Find the GCF of: 3 and 9 10 and 22 6 and 27 GCF is 3 GCF is 2 GCF is 3

6. Now Let’s Simplify Using the GCF you just found, simplify these ratios! 3:9 = 10:22 = 6:27 =

7. Your Turn! Simplify: 1. = 2. = 3. =

8. Caution!!!: *Do Not get rid of the denominator if it equals 1! * We want to keep the 1 as the denominator, so the simplified ratio is:

9. Equivalent Ratios How can we determine if two ratios are equivalent? Simplify both ratios and see if they are equal! 1. Are 8:24 and 7:21 equivalent ratios? 2. Is the ratio 5 inches to 3 feet equivalent to the ratio 12 inches to 5 feet? (hint: there are 12 inches in 1 foot)

10. Let’s See if we have Equivalent Ratios! Example 1 1. 8:24 = and 7:21 = Both of these ratios simplify to so 8:24 and 7:21 are equivalent ratios!

11. Example 2 2. 5 in. to 3 ft and 12 in. to 5 ft = 5 in. to 36 in. = 12 in. to 60 in. == These ratios do not simplify to the same ratio, so 5 in. to 3 ft. and 12 in. to 5 ft. are NOT equivalent ratios!

12. Homework: Worksheet 8.1 due Tomorrow Have a great day!