(,u. SKILL): Rates and Unit Rates. I Cost in dollars I LIMIT. MPH Example 1. Example 2. Guided Practice days per year miles per gallon

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1 Name Date Class SKILL): Rates and Unit Rates A ratio that compares quantities that have two different units is called a rate. A unit rate compares a quantity with one unit of the other quantity. Two examples of unit rates are $.25 per ounce(~ ;;) and 55 miles per hour ( 5 ~ ~i). /'.. SPEED LIMIT 55 MPH Example I J I (,u Example 2 : Find three rates equal to 6 carar! apples. Find the unit r~te. Make a table of equal ratios. The unit rate compares the cost in dollars to 1 apple. I Cost in dollars I 3 Apples 6 3 X 2 3-:-3 3 -:- 6 Three rates equal to $3 6 caramel apples are $ 6 ll and $ ' 2 ' 1. The unit rate, 1!ggle' may be written as $.50 per apple. This is an example of a unit price because it shows the price of one unit of the item. I Guided Practice Is the ratio a rate? Write yes or no and tell why. l 1. 5 circles to 2 circles days per year., Is the rate a unit rate? Write yes or no students 5 groups miles per gallon eggs in a dozen ~. $ h $85.00 for 1 0 people ----' Section A: Ratio and Proportion 250 calories 4 3 servings 36 inches 6 3feet ounces in a cup 10. $8.50 for each person book every 2 weeks Ratio, Proportion, and Percent. 5

2 Name Date Class SKILL l: Practice Is the ratio a rate? Write yes or no gallons in 10 minutes 2. 3 teaspoons to 1 teaspoon quarters in $ car wash every 15 minutes 5. 3 daisies for $ $20 out of every $50 Is the rate a unit rate? Write yes or no. If not, write the rate as a unit rate weeks per year 8. $4.50 for 2 pounds 9. $10 for 5 books minutes for each quarter per ounce pages 6 days 13. Every 3 days, Miguel has a total of 90 minutes of softball practice. Give three more rates that describe 90 minutes to 3 days. ( ' Which vehicle has a mileage rate equal to each ofthe following? Use the chart for exercises 14 through mi Gas Mileage of Passenger Vehicles 14 5 gal Vehicle Type Gas Mileage 100 mi 15 4 gal 60 mi 16 4 gal ini 2 gal Compact car Mid-sized car Mini-van Sport utility 30 mi/gal 25 mi/gal 20 mi/gal 15 mi/gal ~. ~j?l'i':j;jij~ -~ 18. Which ratio is a unit rate? Ski/13 A 2 mi in 3 h C $7 to $1 B 3 lb for $2 D 30 mi per h 19. Which ratio is equal to~~ ~? F G H 3 J 2 3 Skill 2. <) E 6 Ratio, Proportion, and Percent Section A: Ratio and Proportion

3 Name Date Class SKILL 4: Meaning of Proportion Two equal ratios form a proportion. Both ratios in a proportion h. F I 1 3 IS. a propo rt 10n. must use t e same un1ts. or examp e, 2 6 Example 1... i Do~ and ~;form a proportion? ~ ]_ ~ ~ 4 X ~ 5 X 3 15 Multiply both terms of one ratio by the same number and get the second ratio. Because the ratios are equal, they do form a proportion. Example 2 A grocery store sells three oranges for $.49 and a bag of a dozen oranges for $?.00. Are these price rates equal? Make a table of equal ratios to find the cost of a dozen (12) oranges at the rate of 3 for $.49. Oranges Dollars 3 oranges 12 oranges less than the $2 00 for a bag of~ dozen $.49 $1.96,... The prices are not equal rates. They do not form a proportion Guided Practice Do ;~ and ~ form a proportion? 1. What do you divide 72 by to get 8? 2. What do you divide 24 by to get 3? 3. Do the ratios form a proportion? Why or why not? 0 c Do the ratios form a proportion? Write yes or no. 4 _gj_ ]_ l boys. 20 girls. t t U th" f t" t t rt" 4 1 b 25 1s no rue. se 1s 1n orma 1on o wn e a propo 1on. g1r s oys Section A: Ratio and Proportion Ratio, Proportion, and Percent 7

4 Name Date Class SKILL 4: Practice Do the ratios form a proportion? Write yes or no. 7? ]_.:!1_ _ ] :! _ ? ]_. _ ]_ ]_ 11_ ? ]_.:!:Q_ Complete the table of equal ratios for the Pep Club's Lemonade Sale. 14. What does the ratio for 10 cups sold tell you? 15. Write a proportion that gives the unit rate for a cup of lemonade. 16; Write a proportion that could ; be used to find the profit if 300 cups of lemonade are sold. 17. Which ratio forms a proportion with i? A c D 20 Skill Which ratio is a unit rate? F ~ H 1 em 10 5m 5m 10 G J 1 em 1 Skill 3 t.i E / ' i ' 8 Ratio, Proportion, and Percent Section A: Ratio and Proportion

5 Name Date Class SKILL 5: Cross Products in Proportions In a proportion, the cross products are eqwal. The cross products are the results of multiplying the numbers in the proportion as. shown at the right. Since the cross products are equal, we 5 15 know that w ~ 5 X X ) Example 1 Do the ratios form a proportion? l ] R X X The cross products are equal, 3 12 so 5 20' Guided Practice Example 2 :. Oo the ratios form a proportion? 40 ]_ JL X X The cross products are not equal, so cig (Recall that the symbol means is not equal to.). '. ' Use the cross products to decide whether the ratios form a proportion. Write or f.. 10? 2 1. ~:?: ~ ' X X X X ~o~ 5 3 ~g :?: % 9 X X u E y Use the table at the right. 4. For which two teachers are the ratios of boys to girls equal? Class Enrollment Teacher Boys Girls Ms. Hong ~ Mr. Munoz ""' Mrs. Bruno 12 8 '" Mr. Ryan 15 8 Section A: Ratio and Proportion Ratio, Proportion, and Percent 9

6 Name Date Class SKILL S: Practice Do the ratios form a proportion? Write yes or no lo ~~ ? ~ 36 4 "6_8 5 D_ Q ~ ~ ? , ? ~ _11_ 1.. ± 2 tsp ~ 6 tsp 13 7 gal - 21 gal cm 1.. ~ 20 g - 25 em $ $84 3 hr - 18 hr lb lb. $21 - $ sec ~ 10 in. 21 sec - 15 in ~ 1.. _l!!_ 13 gal - 14 gal---- Use the data given in the table. 19. Which two students ran at the same rate? 20. Larry ran 200 meters in 16 seconds. Did he run 200 meters at the same rate that he ran 500 meters? Runner Distance Time Joyce loom 12 sec Larry 500m 55 sec Tanya 10m 1 sec Alan 200m 24 sec 21. At the rate given for 1 0 meters, how long would it take Tanya to run 100 meters? u E 22. What is the cross product for th. rt". _ _ 24? IS propo 10n Skill 5 A 120 c 192 B 75 D Which shows a true proportion? _ Ski/ H F G J Ratio, Proportion, and Percent Section A: Ratio and Proportion

7 Name Date Class I. I SKILL 6: Solving Proportions Using Cross Products To solve a proportion, you must find the missing number that makes the proportion true. You can use cross products to find this missing value. Example 1 r " ~ ~~ ~;~~ ~ ~ ~~~~~~ ~ ~~ ~~ ~~ ~~~.. ~;~ ~~ ~~ ~ ~~ ~ ~ ~~.. r... r : "3"'' l 21 7 D X 7 21 X 3 If the proportion is true, its cross products must be equal. D X 7 63 Multiply: 21 x Use division to undo multiplication. So, the value of the missing number is 9. Example 2 Find the unit rate equal to $12 for 4 pounds. 12 dollars n dollars.:...:...:c--'---'-'-"- 4 pounds 1 pound 12 X 1 : 4 X n The unit rate is an equal ratio that compares the cost, n dollars, to one pound. Write the cross products. ) 124 X n Multiply: 12 X x n 4-4 Use division to undo multiplication. 3n 12 3 So, 4 1 The unit rate, or unit price, is 3 dollars for 1 pound. c.i E Guided Practice Use cross products to solve each proportion n s-n n 36 2 X n X X 10 X n 6 x n x 2 X n n n n ) 4. Write a proportion to find the unit rate for 35 miles on 1 0 liters of gasoline. Write cross products. Solve the proportion. miles~ D. n liters ~ D 1 X X n Write the unit rate. _ Section A: Ratio and Proportion Ratio, Proportion, and Percent 11

8 Name Date Class SKILL 6: Practice Solve each proportion n ~ n 3. n n c ---- n n n 6. n n n 7 n n 4 n n ! l.1 7 n h / Find the unit price. 16. $1.20 for 24 ounces of juice. per ounce 17. $12 for 8 pounds of peanuts. per pound quarts of milk cost $3.88. perquart ~iif'ii;u;j?a ~ 19. Find n: ~ A 1.3 B 12 Ski/16 c 3 D Give the ratio of As to all letters. ABBCAACC F 8 3 G 3 5 H 3 8 J 5 3 Skill 1 12 Ratio, Proportion, and Percent Section A: Ratio and Proportion

9 Name Date Class Example SKILL 7: PROBLEM SOLVING: Solving Proportions Ron found that a dripping faucet filled 4 cups every hour. At this rate, how many cups of water would drip from the faucet in orie day? Read ~a,ch hour, 4 cups of water drip from the faucet. Plan One ratio is 4 ~u:s. So, two equal. ratios that form. 4 cups x cups a proportion are 1 hour and 24 hours. cups ~ 4 n --- hours ~ I ) Solve Find the cross products. 4 X 24 1 X n 96 n :- ' So, in one day, 96 cups of water would drip from the faucet. Look Back 4 cups per hour.is 40 cups in 10 hours, or 80 cups in 20 hours. The answer makes sense. Guided Practice 1. How many quarts is 96 cups of water? a. How many cups are there in one quart? b. Write a proportion. cups ~ D D quarts ~ D D c. Find the missing value in the prop9rtion. f. cj c:: 2. Lea found she walked 1 0 feet in 6 steps. At this rate, how many.steps would she need to walk one mile? (There are 5,280 feet in a mile.) a. Write a proportion you can use to find the answer. steps feet ~D D ~o o J b. How many steps would Lea need to walk one mile? Section A: Ratio and Proportion Ratio, Proportion, and Percent 13

10 Name Date Class SKILL 7: Practice Use a proportion to find each missing number days weeks 2. 9 dozen items items minutes, hours 4. 3 tons pounds Solve each pro~lem. 5. Kurt gets an $800 paycheck every 2 weeks. At this rate, how much does he earn in 1 year (52 weeks)? 6. A newborn baby's heart beats about 7 times every 3 seconds. At this rate, how many times does a baby's heart beat in 60 seconds? 7. During a test, 3 out of 1 00 cars selected at random were found to be defective. Use this ratio to estimate the number of defective cars if 1,500 cars are tested. 8. At Super Stores a 12-exposure roll of film costs $2.34 and a 20-exposure roll costs $3.80. Which roll of film costs less per exposure? 9. Sleeping 8 hours a day is the same as sleeping about 10 days a month. a. About how many days is this per year? b. About how many days in this in a 75-year lifetime? ~ ~'aiii:j;j~~ -~ 10. Four quarts of water weighs about 8 pounds. About how much does 2 quarts of water weigh? A 1 lb B 41b c 161b. D 21b Skill Which ratio is not equal to 1 35? 6 F G 150 H 1 5 J 45 9 Skill Ratio, Proportion, and Percent Section A: Ratio and Proportion

11 Name Date Class...'!:P') l: SKILL 8: Similar Figures Similar figures are the same shape but not necessarily the same size. Congruent figures are the same size and the same shape. B Polygons A, B, and C are all similar, but only polygons A and C are congruent. In similar figures, matching angles have the same measure, and matching sides are proportional. The two triangles are similar. Find the length of side k. The triangles are similar, so the corresponding sides are proportional. 6cm ) Write a proportion using corresponding sides. 'The side that corresponds to k has a length of 4 em. Another pair of corresponding sides k 6 has lengths of 6 em and 3 em. 4 3 Find cross products to solve the proportion. 3 X k 24 3 X k 24 Divide to undo multiplication. 3 3 Side k measures 8 em. k 8 k 3cm~ 4 em, Guided Practice Find a pair of triangles that appear to be: 1. Congruent _ 2. Similar ' '-- Use the similar triangles in the Example. Find the length of side m. 3. Find the length of the side that corresponds to side m. 4. Find another pair of corresponding sides. -: Write a proportion using corresponding sides. _ 6. Solve to find the length of side m. Section A: Ratio and Proportion Ratio, Proportion, and Percent 15

12 Name Date Class SKILL 8: Practice Tell o whether the figures appear to be congruent, similar, or neither. D 0 The polygons in each exercise are similar. Find the missing lengths in. 12in.D a De 12 in. b s. ~18ft.. m~10ft~ n 14ft I ' a m b n c em s {} 6.5cmLJ6cm 5cm 6cm 7. X z """. ) ~ I I; " r x s y t z The sizes of rectangular screens are given Hand TV 2 in. by 3 in. in the table. Which screens are similar in size? Computer 12 in. by 15 in. TV 15 in. by 21 in. Movie 20ft by 28ft 9. The triangles are similar. Find the length of h. 9m~ 6m A 3m c 6m 8 9m D 27m h~ 2m Skill 8 d Solve for d: F 3.5 G 7 H 5 J 0.5 Skill 6 () E (ii I () cb :;:; c.(i! ) 16 Ratio, Proportion, and Percent Section A: Ratio and Proportion

13 Name Date Class SKILL 9: PROBLEM SOLVING: Scale Drawings A scale drawing is used to illustrate something that is too large or too small to show the actual size. The scale is the ratio of a length in the drawing to the actual length it represents. If the units are the same, they may be omitted from the scale. For example, 1 em : 4 em may be written as 1 : 4 pr Example Find the actual height of the motorcycle. Read What information do you know? The scale of the drawing is 1 in. 3 ft. The height of the motorcycle in the drawing is 1.5 in. Plan What proportion can you write? scale ~ actual ~ 3 x Solve Find the cross product. x 4.5 The actual height of the motorcycle is 4.5 feet. 2 in. Look Back Check to see that your answer makes sense. If 1 inch on the drawing represents 3 feet, then 1.5 inches would represent 3 feet plus half of 3 feet (1.5 feet), or a total of 4.5 feet. The answer makes sense. Guided Practice 1. Find the actual length of the motorcycle represented in the drawing. a. How many inches long is the motorcycle in the drawing? b. Write a proportion you can use to find the length in feet. ti c c. What is the actual length of the motorcycle? 2. A house is 60 feet long. Find the length of the house in a scale drawing for each scale given. a. 1 in. 15ft b. 1 in. 40 ft c. 1 in. 16ft _ d. 1 in. 300 ft Section A: Ratio and Proportion Ratio, Proportion, and Percent 17

Name SKILL 9: Practice Date Class Find the actual length of the locomotive for each scale. 1. 1 em 1 m 2. 1 em 0.7 m 3. 2 em 1 m. Solve each problem. 4. Sammy created a model of a frontier fort.

She uses a scale of 1 in. 6 in. The actual sculpture will be 48 inches tall. What is the height of the scale model? 6. In Barry's classroom, the scale on the globe is 1 em : 250, km.

14 Name SKILL 9: Practice Date Class Find the actual length of the locomotive for each scale em 1 m 2. 1 em 0.7 m 3. 2 em 1 m. Solve each problem. 4. Sammy created a model of a frontier fort. He used a scale of 1 in. to 2ft. The walls of his model were 9 inches tall. How tall were the walls of the actual frontier fort? 5. An artist makes a scale model of a sculpture of a child. She uses a scale of 1 in. 6 in. The actual sculpture will be 48 inches tall. What is the height of the scale model? 6. In Barry's classroom, the scale on the globe is 1 em : 250, km. Barry used a tape measure. He found that it was about 40 centimeters from Dallas to Singapore. Find the estimate of the air distance between Dallas and Singapore. 7. On a scale drawing, the width of a room is 6 in. and its length is 9 in. The actual length of the room is 18 ft. What is the actual width of the room? ~ ~~?i'iii:jij?ab -~ I' ' 8. Find the length of the hex nut in a drawing that was made using a scale of 8 : 3. The actual length of the hex nut is 1.5 em. Skill 9 A 0.56 em C 4.5 em B 4 em D 12 em 9. The actual distance between Alta Vista and Bonita is 16 miles. Use the map to find the actual distance between Bonita and Carleton. Skill 7 0 c F 4 mi G 8 mi H 32 mi J 64 mi 18 Ratio, Proportion, and Percent Section A: Ratio and Proportion

15 Name Date Class Circle each correct answer. 1. The model of a building is 5 in. long. The scale is 2 in. 15 ft. What is the actual length of the building? A 2.5 ft B 6ft c 37.5ft D.30ft 2. Which shows a proportion? 20 5 F H G J Which ratio does not show 7 students to 10 adults? A 10 c B 7 to 10 D 7: 10 Skill9 Skill4 Skill 1 it\, 4~ During a test, 3 out of 200 television sets were found to be defective. About how many defective sets would you expect out of 4,000 television sets? Skill 7 F 266 sets H 60 sets G 20 sets J 30 sets, 7. Which figures appear to be similar? W X A W and Y B X and Z C X and Y D W and Z 8. Which ratio is equal to ~? F 8 H G 16 J y z Skill 8 Skill The rectangles are similar. Find the length of side r. Skill 8 2cml Bcm A 0.75 em B 51 em 3 3cml c 12 em D 24 em 1 Q. Find the cross product: } 5 %- F 18 G 27 H 40.5 J 2 r Skill 5 <.i E 5. Solve:~ { 0. A 45 C 180 B 30 D Which is a unit rate? F 12 limes $1 2 L G $1.19 $1 H $10 J 8 tokens $10 Skill6 Skill3 11. Use the scale 3 in. to 10 ft to find the scale length of a car that is 17ft long. Skill9 A 2 in. C 56.6 in. B 5.1 in. D 3.1 in. 12. If 24 identical prints cost $5.04, how much does each print cost? Skill 7 F $.21 H $ G $2.10 J $12 Section A: Ratio and Proportion Ratio, Proportion, and Percent 19

16 Name Date Class Mixed Review for Section A I I. Match each exercise with its answer by drawing a line from the exercise star to the answer star. Write the letter the line goes through on the blank beside the answer. You will name a famous person. The units are not given in the answers. 30 n 1. Solve: s 2. Is $5 for 6 tickets a rate? 3. If 3 COs cost $42, what do 2 COs cost? 4. Solve:~~ 5. 4 qt 1 gal M 20 qt 1_gal s 6. Give the ratio of As to Bs: ABAABBAA: 7. Find the unit rate for 12 for $4. 8. Find the cross product: " 9. Find n. The triangles 5~ 7~ 14 are similar. s M mi in 2 h is the same as? mi in 6 h. 11. Solve: t ~ 12. A scale of 3 em to 8 m is the same as 9 em to? m. 13. Is % ~ a proportion? A A s y 0 T Yes No 'ly ~ c.i E (ij I cb (.) :;:; c ~ " )) ~I 20 Ratio, Proportion, and Percent Section A: Ratio and Proportion

2 : 5. 5 to 16 or 5:16 or. The 8 parts represent $40

2 : 5. 5 to 16 or 5:16 or. The 8 parts represent $40 Unit Two - Ratio Relationships 5.1 Ratios *I can understand ratios and language used to describe two different quantities. Discuss with your group How do you THINK you would write the ratio of stars to