Ratios & Rates

1. Ratios & Rates

2. Ratios & Rates Objective: 7.1.01 Develop and use ratios, proportions, and percents to solve problems. Essential Questions: • What are the differences between ratios, rates, and unit rates?

3. Ratios & Rates Vocabulary: • Ratio:a comparison of two numbers by division. • Equivalent Ratios:two or more ratios that form equivalent fractions. (Example: 1/2 = 5/10) • Rate:a ratio of two measurements having different kinds of units. (Example: buy 7 pencils for $2) • Unit Rate:a rate that has been simplified so it has a denominator of 1. (Examples: $9 per pound; 6 ounces per serving)

4. Ratios & Rates So What Do We Really Use Ratios for In The Real World… RATES & UNIT RATES But Before We Can Look At Rates And Unit Rates We Have To Understand Ratios

5. Ratios & Rates Real World: Two different packages of batteries are shown below. Determine which is less expensive per battery, the 4-pack or the 8-pack. 4-pack $3.60 8-pack $6.80 We know the 8-pack is a better deal per battery

6. Ratios & Rates But Before We Can Really Understand Rates And Unit Rates We Have To Understand Ratios

7. Ratios & Rates (1) What is the ratio of soccer balls to the total number of balls? 6 to 14 6:14 6 out of 14 6/14 • 3 to 7 3:7 3 out of 7 3/7 • (2) What is the ratio of basketballs to the total number of balls? • 8 to 14 8:14 8 out of 14 8/14 • 4 to 7 4:7 4 out of 7 4/7

8. Ratios & Rates Lets Look At Some… Ratios

9. Ratios & Rates Example 1:Write a ratio that compares the number of footballs to the number of soccer balls. # of Footballs TO # of Soccer Balls 4 to 6 OR 4:6 OR 4/6 2 to 3 OR 2:3 OR 2/3

10. Ratios & Rates Example 1:Write a ratio that compares the number of footballs to the number of soccer balls. Footballs 4 2 Soccer Balls 6 3 ▪ The ratio of footballs to soccer balls is 2:3, 2/3 or 2 to 3. • ▪ For every 2 footballs there • are 3 soccer balls.

11. Ratios & Rates Example 2:Write a ratio that compares the number of hamburgers to the number of snacks. # of Hamburgers TO Total # of Snacks 4 to 12 OR 4:12 OR 4/12 1 to 3 OR 1:3 OR 1/3

12. Ratios & Rates • Example 2:Write a ratio that compares the number of hamburgers to the number of snacks. Hamburgers 4 1 Snacks 12 3 ▪ The ratio of hamburgers to snacks is 1:3, 1/3 or 1 to 3. • ▪ There is 1 hamburger for every 3 snacks. • ▪ For every 3 snacks 1 is a hamburger.

13. Ratios & Rates Example 3:The ratio of the number of bones in a human’s ears to the total number of bones in the human skull is 3:11. If there are 21 bones in the human ear, how many bones are in the human skull? 6 bones in the human ear

14. Ratios & Rates Example 4:The ratio of the number of games won to the number of games lost last season was 3:2. If the basketball team won 18 games last season, how many did they lose? The team lost 12 games

15. Ratios & Rates Lets Look At Some… Rates & Unit Rates

16. Ratios & Rates What about the G-UNIT RATE: (1) When a rate contains a denominator of 1, we call this a unit rate. • (2) We can use unit rates to determine whether deals are good or bad. • (3) For instance, is it better to buy four individual rolls of paper towels for $1.29 each, or a pack of four for $5.04.

17. Ratios & Rates Example 5:Dr. Rodriguez drove 391 miles on 17 gallons of gas. How many miles could he have driven with just one gallon of gas? ÷17 391 miles w miles 17 gallons 1 gallon • ÷17 • Answer: 23 miles/gallon

18. Ratios & Rates Example 6:Mr. Williams was at Wal-Mart buying some wrapping paper to wrap his Christmas presents. The paper he bought was $2.73 for 7 yards of paper. What was the cost per yard? ÷7 $2.73 x dollars 7 yards 1 yard • ÷7 • Answer: $0.39 per yard

19. Ratios & Rates • Example 7:Is it better to buy four single rolls of paper towels for $1.29 each, or a pack of four for $5.04? By how much? The 4-Pack is Cheaper By $0.06

20. Ratios & Rates Example 8:Jacob filled his 60 gallon fish tank in 5 minutes. How fast was water being poured into the tank? ÷5 60 gallonsw gallons 5 minutes 1 minute • ÷5 • Answer: 12 gallons per minute

21. Ratios & Rates Independent Practice: • Express as a ratio in simplest form. • 1. 3 sailboats to 6 motorboats • 2. 14 lions to 10 tigers • Express each as a unit rate. • 3. $18 for 3 CDs • 4. 8 tomatoes for $4.40

22. Ratios & Rates Independent Practice: • Answers. • 1. 3/6 or 3:6 or 3 to 6 • 2. 7/5 or 7:5 of 7 to 5 • Answers. • 3. $6 per CD • 4. 1 tomato for $0.55 or $0.55/tomato

23. Ratios & Rates Independent Practice: • Express as a ratio in simplest form. • 1. 5 ducks to 10 geese • 2. 15 roses to 10 carnations • Express each as a unit rate. • 3. 48 televisions on 4 trucks • 4. $5.28 for 24 pencils

24. Ratios & Rates Independent Practice: • Answers. • 1. 1/6 or 1:6 or 1 to 6 • 2. 5/4 or 5:4 of 5 to 4 • Answers. • 3. 12 televisions/truck • 4. $0.22/pencil

25. Ratios & Rates Real World: As you all know, cans of Coca-Cola are sold in different size packages. For instance, Piggly Wiggly currently has the following Coca-Cola packages on sale for the following prices. Which of the four is the best deal? If I wanted to buy 48 cans of Coke, what would be the best to do it? $0.65 $2.99 $4.08 $9.12

26. Ratios & Rates HOMEWORK