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Ratios, Rates, Distance and Proportions

Ratios, Rates, Distance and Proportions. TSW write and simplify ratios. TSW determine unit rate. TSW calculate rates involving cost per unit to determine the best buy. DO NOW (not later):. Compare the number of boys to girls in the class. The number of boys = The number of girls =

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Ratios, Rates, Distance and Proportions

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  1. Ratios, Rates, Distance and Proportions TSW write and simplify ratios. TSW determine unit rate. TSW calculate rates involving cost per unit to determine the best buy.

  2. DO NOW (not later): Compare the number of boys to girls in the class.

  3. The number of boys = The number of girls = If we compare boys to girls we get ___ boys to _____ girls.

  4. What do we call a comparison between two or more quantities? We just found the RATIO of boys to girls. RATIO Is the ratio of girls to boys the same ? No, when writing a ratio, ORDER matters.

  5. How many basketballs to footballs are there? For every 4 basketballs there are 6 footballs. The ratio is 4 to 6.

  6. What are some other ways we can write the ratio of basketball to footballs? Every ratio can be written in 3 ways: First quantity to Second quantity Careful!! Order matters in a ratio. 4 to 6 Is NOT the same as 6 to 4 First quantity : Second quantity First quantity divided by the second quantity (as a fraction). 4 to 6 4 : 6 4 6

  7. Practice problem # 1 (1) You have 100 different shirts. The ratio of blue to black shirts is 20 . 30 a) Write the ratio of blue to black shirts 3 different ways. b) Write the ratio in simplest form. c) Explain what this ratio tells us. d) How many black shirts do you have?

  8. Solution - # 1  You have 100 different shirts. The ratio of blue to black shirts is 20 / 30 a) Write the ratio of blue to black shirts 3 different ways. 20 to 30 , 20 : 30, 20 30 b) Write the ratio in simplest form.2 3 c) Explain what this ratio tells us. For every two blue shirts, there are 3 black shirts. d) How many black shirts do you have? 2x + 3x = 100 5x = 100 x = 20 There are 2x black shirts so 2 (20) = 40 black shirts

  9. Practice Word Problems Mindy has 72 candy bars. If the ratio of Mars to Snickers is 8:4, Find the number of each type of candy. Explain what this ratio tell us.

  10. Rate In a ratio, if the numerator and denominator are measured in different units then the ratio is called a rate. A unit rate is a rate per one given unit, like 60 miles per 1 hour.

  11. Example: You can travel 120 miles on 6 gallons of gas. What is your fuel efficiency in miles per gallon. 120 miles = 20 miles 6 gallons 1 gallon Your fuel efficiency is 20 miles per gallon

  12. Unit Price • A unit rate involving money is a unit price • Unit price is used to determine the best buy Example: A 24 ounce box of cereal costs $5.28. What is the unit price of the cereal? Just divide 5.28 by 24. Therefore, you are paying $0.22 per ounce of cereal.

  13. Additional Example 4A: Finding Unit Prices to Compare Costs Pens can be purchased in a 5-pack for $1.95 or a 15-pack for $6.20. Which pack has the lower unit price? Divide the price by the number of pens. price for package number of pens $1.95 5 = = $0.39 price for package number of pens $6.20 15 =  $0.41 The 5-pack for $1.95 has the lower unit price.

  14. price for bottle number of ounces price for bottle number of ounces Check It Out!Example 4B John can buy a 24 oz bottle of ketchup for $2.19 or a 36 oz bottle for $3.79. Which bottle has the lower unit price? Divide the price by the number of ounces. $2.19 24 =  $0.09 $3.79 36 =  $0.11 The 24 oz jar for $2.19 has the lower unit price.

  15. Determine the better buy Six rolls cost $0.90. Twelve rolls cost $1.68. What is the better deal?

  16. Determine the best buy The big can held 16 ounces and cost 80 cents. The small can held 12 ounces and cost 72 cents. Which can was the better buy?

  17. Distance Speed uses the formula: d = r · t D = distance R = rate/speed T = time

  18. Example A train has traveled 238 miles in 3.5 hours. How many miles per hour has the train traveled?

  19. Examples A delivery truck drove an average rate of 30 miles per hour in the city. At that rate, how long did it take the truck to drive 75 miles?

  20. Solution D = 75 R = 30 T = ? d = rt 75 = 30t 75 = 30t30 30 2.5 = t The truck took 2.5 hours to drive 75 miles.

  21. Examsple Mr. Lucas has driven 12 miles in 15 minutes. What is his speed in miles per hour? The winning car finished a race of 400 miles in exactly 2 hours and 30 minutes. What was the car’s speed in miles per hour?

  22. Objectives TSW solve real world problems involving rat/time/distance. TSW find the missing value of a proportion.

  23. Distance Problem Kayla drove 288 kilometers in 4 hours. At this rate, how many hours will it take her to drive 432 kilometers? Mr. Cipriati has driven 700 miles in 4 days. At that rate, how many miles will he drive in 22 days?

  24. Proportion 2 = 6 x 9 2 · 9 = 6 · x 18 = 6x 6 6 3 = x Statement that says two ratios are equal In order to solve for a missing value, cross multiply Example:

  25. Proportion Problem Shawn ate 4 tadpoles to every frog that Nicole ate. If Shawn ate a total of 48 tadpoles, how many frogs did Nicole eat?

  26. Proportion Problem Justin was a great chef. He worked at a fabulous restaurant in Paris. His customers ate snails to snake skins at a ratio of 3 to 7. If they ate 40 snake skins, how many snails did they eat?

  27. Homework 1 • Find the unit price: • 1. Andrea bought 6 candles for $19.50 • 2. Jorge bought a crate of 20 clementines for $8.00 • 3. Mrs. Litka purchased 7 yards of fabric for $31.15 • 4. Jacob paid $22.00 for 4 cases of soda • 5. Nishia earned $156 in 12 hours. • 6. Hannah rented 2 video games for $16.28 • 7. Couscous costs $4.50 for a 3 pound bag at the local market. At the Mega-Mart, couscous costs $14 for an 8 pound bag. Which store has the better buy?

  28. Homework 2 1. Adam ran 3 miles in 18 minute. At the same rate, how long will it take him to run 5 miles? 2. A passenger train traveled 212 miles from Nashville to Memphis in 6 hours. At what rate was the train traveling? 3. It took Dustin 9 hours to drive 432 miles. What was his hourly rate of speed? 4. Ashley sold 15 bracelets for $52.50. What was the unit price? 5. One store sold packages of 1 dozen for $1.44 a package. The other store sold packages of 3 dozen for $4.68. Which price is the better buy?

  29. Homework 3 20 = 4 15 x p = 4 9 3 s = 4 5 3 t = 9 11 44 1. 2. 3. 4. 5. Jimmy could cap 60 bottles in 7 hours. How long would it take to cap 420 bottles? 6. The ratio of the bumptious to the gracious was 7 to 3. If 1400 were bumptious, how many were gracious?

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