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Ratios & Rates

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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? Ratios & Rates

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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) Ratios & Rates

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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 Ratios & Rates

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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 $3.608-pack $6.80 4-pack $3.608-pack $6.80 We know the 8-pack is a better deal per battery Ratios & Rates

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

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(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 Ratios & Rates

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Lets Look At Some… Ratios Ratios & Rates

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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 Ratios & Rates

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Example 1: Write a ratio that compares the number of footballs to the number of soccer balls. Footballs4 2 Soccer Balls63 ▪ The ratio of footballs to soccer ▪ The ratio of footballs to soccer balls is 2:3, 2/3 or 2 to 3. balls is 2:3, 2/3 or 2 to 3. ▪ For every 2 footballs there ▪ For every 2 footballs there are 3 soccer balls. are 3 soccer balls. Ratios & Rates

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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 Ratios & Rates

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Example 2: Write a ratio that compares the number of hamburgers to the number of snacks. Hamburgers 4 1 Snacks12 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. Ratios & Rates

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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 Ratios & Rates

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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 Ratios & Rates

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

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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. Ratios & Rates

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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 ÷17 391 miles w miles 391 miles w miles 17 gallons 1 gallon 17 gallons 1 gallon ÷17 ÷17 Answer: 23 miles/gallon Answer: 23 miles/gallon Ratios & Rates

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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 ÷7 $2.73 x dollars $2.73 x dollars 7 yards 1 yard 7 yards 1 yard ÷7 ÷7 Answer: $0.39 per yard Answer: $0.39 per yard Ratios & Rates

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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 Ratios & Rates

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

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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 Ratios & Rates

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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 Ratios & Rates

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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 Ratios & Rates

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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 Ratios & Rates

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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 $0.65 $2.99 $4.08 $9.12 Ratios & Rates

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HOMEWORK

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