1. Understanding & Solving Proportions Learning Goal: I will use proportions to solve problems.

2. *Fold paper into 16 parts Understanding Ratios *Shade 12 grids (from the left) *What is the ratio of the shaded squares to total squares? *Divide your paper into eighths. What is the ratio of the shaded eights to the total number of eighths? * What is another way to divide into equal parts? What is the ratio of the shaded parts to the total number of parts?

3. Ratio A ratio is the comparison of two numbers by division. A classroom has 16 boys and 12 girls. Also written as16 boys, 16:12 or 16 to 12 12 girls Generally, ratios are in lowest terms: 16 = 16/4 = 4 12 12/4 3

4. Ratio, continued Ratios can compare two unlike things: Joe earned $40 in five hours The ratio is 40 dollars or 8 dollars 5 hours 1 hour When the denominator is one, this is called a unit rate.

5. Ratio, continued Let’s look at a classroom: Ratios can be part-to-part 16 boys 15 girls Ratios can be part-to-whole 16 boys or 15 girls 31 students 31 students

6. Ratio, continued If a ratio is part-to-whole, you can divide and find a decimal or a percent. 16 boys 31 students 31/16.00 = 0.516, or 51.6% are boys

7. Proportion Proportion is a statement that says two ratios are equal called equivalent ratios. In an election, Damon got three votes for each two votes that Shannon got. Damon got 72 votes. How many votes did Shannon get? Damon 3 = 72 so 3 x 24 = 72 Shannon 2 n 2 x 24 48 n = 48, so Shannon got 48 votes.

8. Proportion, continued Tires cost two for $75. How much will four tires cost? # of tires 2 = 4 so 2 x 2 = 4 tires cost 75 n 75 x 2 $150 n = 150, so four tires cost $150

9. Proportion, continued One more way to solve proportions: Cross products 2 = 6 2 x n = 6 x 8 2n = 48 8 n 2 2 n = 24

10. Proportion, continued Now you try! Three cans of soup costs $5. How much will 12 cans cost? # of cans 3 = 12 3 x 4 = 12 cans cost 5 n 5 x 4 20 dollars n = 20, so 12 cans cost $20

11. Classwork Worksheet page 35 (odds) Exit Pass – white boards Reminder: study your notes and do practice problems on Fractions and Mixed Numbers…..TEST on Friday 9/20