2. Understanding Ratios Proportions We will solve problems using ratios and proportions.

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. Ratios A ratio can be written three ways: 3:53/5 3 to 5 Say “Three to Five”

5. 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.

6. Ratios are often expressed as fractions in simplest or as a decimal. BACK

7. 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 31 students

8. A ratio is the comparison of two numbers with the same units by division. A ratio may be written in three ways. What ratios can we form from the tiles above? 12 to 8 BACK

9. Create as many ratios as possible. Write each ratio three different ways. BACK

10. Simplest Form Write the ratio 50 to 300 in simplest form. BACK

11. Unit Rate To find the Unit Rate, you would find the cost or amount for 1. Or the rate when the denominator is 1. “How much for just 1?” BACK

12. If it costs $78 for 13 sandwiches, What is the unit rate? Unit Rate BACK

13. Mile per Gallon M.P.G. stands for miles per gallon and is usually used for gas mileage in cars. BACK

14. 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 =.516, or 51.6% are boys

15. Proportion Proportion is a statement that says two ratios are equal. 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.

16. Two ways to solve proportions Multiplicative Property of Equality Cross Products Property The cross products of a proportion are equal.

17. 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

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

19. 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