Name Period Date. are equivalent because they both simplify to 43. Two fractions are equivalent when they simplify to the same value.

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1 Lesson C ~ Ratios 3 6 Two fractions are equivalent when they simplify to the same value. For example, 4 and 8 are equivalent because they both simplify to 43. This means the ratios 3 : 4 and 6: 8 are equivalent ratios because they both simplify to 3 : 4.. Write two ratios equivalent to 0 :.. Write two ratios equivalent to 5 to The ratio of girls to all students in a class is 53. a. Write the ratio of boys to all students in the class. b. Write the ratio of girls to boys in the class. c. There are 5 girls in the class. How many students are in the class? d. In a different class, the ratio of girls to all students is also 53, but there are not 5 girls in the class. However, there are more than 5 girls. Give one example of how many girls and boys there might be in the class. 4. The ratio of dogs to cats at a kennel is 3 :. There are 0 total dogs and cats at the kennel. a. How many dogs are at the kennel? b. How many cats are at the kennel? c. Another kennel has a ratio of dogs to cats that is also 3 :. However, it does not have 0 total dogs and cats. It also has more than 5 animals. Give one example of how many dogs and cats might be in that kennel. 5. Three sides of a triangle have sides of length 6 inches, 8 inches, and 0 inches. One way to write the ratio of the sides of the triangle is 6 : 8 : 0. This ratio can be simplified to 3 : 4 : 5. a. How was the ratio simplified from 6 : 8 : 0 to 3 : 4 : 5? b. Another triangle also has side lengths in a ratio of 3 : 4 : 5. The largest side of the triangle is 30 inches. What are the lengths of the other two sides of the triangle? 6. A triangle has side lengths in a ratio of : :. a. What does this ratio mean? b. What type of triangle has side lengths in a ratio of : :? c. Draw two different triangles that have side lengths in a ratio of : :. Label their side lengths.

2 Lesson C ~ Geometric Sequences Write the first five terms of a geometric sequence that uses the first term given and has a fourth term that follows the rule given. Write the ratio used to create your sequence.. first term: 3. first term:, first term: fourth term less than fourth term less than 0 fourth term greater than 00 An infinite geometric series is a sum of infinitely many terms in a geometric sequence. For example, is an infinite geometric series. The means it extends forever. Since it extends forever it has a large sum! However, if the ratio of the terms is less than, the sum of the first term series can be found by computing. ratio The infinite geometric series has a ratio of which is less than. This means it has a sum of = = 00 = = 00. Determine whether or not you can find the sum of each infinite geometric series. If it is possible, find the sum. If it is not possible, explain why The number of bacteria in a petri dish doubles every hour. Tim put 4 bacteria in the petri dish to begin an experiment. After how many hours will there be 5 bacteria in the petri dish? 8. The population of a town is decreasing. Every 5 years the population is 0 its previous population. The town has 00,000 people. How many people will live in the town 0 years from now?

3 Lesson 3C ~ Customary Conversions Fill in each blank with the customary units that make each number a reasonable estimate.. height of a van: 6. weight of a medium sized watermelon: 3. time to run miles: 6 Complete each conversion yards = inches hours = seconds 6. 7 inches = feet 7. 3 cups = quarts days = weeks 9. miles = inches 0. Suzie wanted to build a shed in her backyard. She had to choose between the two models shown below that would fit in her yard. Which one gives her the largest amount of space to fill? Be sure to write your work and explain your thinking. yards yards 84 inches.5 yards 84 inches 60 inches

4 Lesson 4C ~ Metric Conversions Fill in each blank with the metric units that make each number a reasonable estimate.. height of an apple tree: 0. weight of a marble: 6 3. length of a garter snake: 5 Complete each conversion meters = millimeters liters = milliliters centimeters = meters grams = kilograms kilometers = centimeters 9. 5 kilometers = millimeters 0. Write three different measurements that are equivalent to 3 kilometers.. Naomi looked at a map online to find out how far she was going to have to walk. The map said it was.5 kilometers to the library and then 300 meters from the library to the grocery store. Her house was.5 kilometers from the grocery store. Naomi needed to walk to the library, then the grocery store, and then home. How far was she going to walk? Be sure to include units in your answer.

5 Lesson 5C ~ Perimeter and Area. a. Find the perimeter of the square in yards. 9 ft b. Find the perimeter of the square in inches.. 5 cm a. Find the area of the triangle in square meters. cm 9 cm b. Find the area of the triangle in square millimeters. 3. Kevin wanted to put a fence around a section of his yard matching one of the shapes below. He wanted to put the fence around the shape with the larger area. The fence costs $0.00 per foot. How much will it cost to fence the shape with the largest area? 3yd 4 yd 40 in 40 in 9 in 44 in 4. How many square millimeters are in one square meter? m m

6 Lesson 6C ~ Fractions and Decimals Match the answer to each sum, difference, product or quotient with its decimal equivalent A B C D E F G H I J. 0.5 Write each set of numbers in order from least to greatest.. 8 3, 0.3, 0.5, ,.5,., 0

7 Lesson 7C ~ Repeating Decimals and Rounding. Tim cut a pentagon out of a piece of paper. He measured each of the sides as shown below. a. Write each of the measurements as a decimal rounded to the nearest hundredth. b. Find the perimeter of the pentagon and write your answer as a mixed number. c. Find the perimeter of the pentagon and write your answer as a decimal. Measurements as Decimals 3 inch 5 6 inch inch inch 6 inch 3 inch inch inch 7 9 inch inch Perimeter = Perimeter = For questions # 5, convert each fraction to a decimal. a. Write the answer using the bar over the repeating digits. b. Round the answer to the nearest hundredths place Write a repeating decimal between the two values given and and and Does 0. 9 =? Find the answer to part a and part b and then write your reasons for why you think 0.9 may or may not equal. a = b = c. Does 0. 9 =? Explain your thinking.

8 Lesson 8C ~ Rates and Unit Rates Find each unit rate miles hours. $ jackets apples 6 crates 4. David put a quarter into a gumball machine and two gumballs came out. Find his cost per gumball. Max is writing a novel. He has written 40 pages and would like to have a complete story that is 360 pages long. 5. How many pages will he have to write per day in order to have a finished rough draft in a. one week? (Round to the nearest hundredth.) b. two weeks? (Round to the nearest hundredth.) c. one month (30 days)? 6. Does the rate of pages per day increase or decrease as the length of time increases? 7. To finish the novel in three weeks, Max needs to write about 6 pages per day. The table below shows the number of pages Max wrote each day for the first week. Is Max meeting his goal of 6 pages per day? Explain why or why not using the information in the table. Day Number of Pages Tina delivers meals to people. The table below shows the number of meals she delivered and the time it took her to deliver those meals. Number of Meals Minutes Worked Look at the day Tina delivered 3 meals. What was her rate of delivery (minutes per meal)? 9. Look at the day Tina delivered 4 meals. What was her rate of delivery (minutes per meal)? 0. On average, what is Tina s rate of delivery (minutes per meal)? Explain how you found this rate.

9 Lesson 9C ~ Rate Problem Solving Complete each equivalent rate.. 0 miles 70 miles =. gallon gallons $4.65 $ = 5 mints 4 mints 3. Write three rates equivalent to 600 miles. 0 hours Use equivalent fractions or unit rates to solve each problem. 4. Monica rode her bike 7 miles in hours. How long will it take her to bike 5 miles at the same rate? 5. Julie paid $49.00 for four tickets to a musical production. Her friend is buying three tickets for the same musical production. How much money will her friend pay for the three tickets? 6. Kim s new car travels 378 miles using 9 gallons of gas. At this rate, how many miles can the car travel using 5 gallons of gas? 7. Phillip drove at a speed of 45 miles per hour. At this rate, a. how far will he drive in 0 minutes? b. how long will it take him to drive 60 miles? 8. Sometimes rates are approximations. The table below shows the number of words Shelby typed and the number of minutes it took Shelby to type the words. She told her boss she can type 00 words per minute. Is this an accurate statement? Explain why or why not using the information in the table. Number of Words Minutes of Typing

10 Lesson 0C ~ Comparing Rates Use unit rates to determine which of the two rates is larger.. $4.00 candies or $ candies. 7.6 miles or 3 hours 63.7 miles 7 hours Write a rate less than the given rate and a rate greater than the given rate. Be sure to use the same units as in the rate given Smaller Rate Rate Larger Rate 5 kilometers 3 hours $ tokens Solve each problem. Show all thinking. 5. Martin burns 360 calories running for 30 minutes. Paul burns 65 calories for every 5 minutes he runs. If Kara runs for 0 minutes, how many calories would she have to burn to have a rate of calories burned per minute of running that is between Martin and Paul? 6. Kay needs to fix part of her fence. She can buy 6 feet of fencing for $3.00 at a fencing store or 0 feet of fencing for $5.50 at a home store. She visits another store that sells 8 feet of fencing for a certain cost. The cost per foot is between that at the fencing store and the home store. How much might the store charge for 8 feet of fencing? 7. Manny can buy pounds of watermelon for $9.00 at a local fruit stand. He can buy 0 pounds of watermelon for $8.00 at the grocery store. How much would each store charge for 5 pounds of watermelon? 8. Kylie brought 9 tennis balls to practice and lost of them. Tara brought 0 tennis balls to practice and lost 3 of them. Which tennis player lost the fewest number of tennis balls per tennis balls brought to practice?

11 Lesson C ~ Motion Rates. Carmen drove her car at a rate of 55 miles per hour. At this rate, how far will she travel in 3.5 hours?. Kyle walks miles in 30 minutes. How many hours will it take him to walk 9 miles? 3. Identify the faster rate: 30 miles 40 minutes or 40 miles 5 hours 4. Tommy ran a half marathon (3 miles) in.65 hours. Alisha ran 8 miles in 0.8 hours. Which person ran at a faster rate? Write the equivalent rate by converting the rate on the left to the rate on the right miles? inches = 6. hour hour meters = hour? millimeters hour 7. 3 miles hours? ft = 8. hour 4 kilometers = 5 hours? centimeters hour 9. Tao rode his bike from his home to the library in 0 minutes at a speed of miles per hour. Next, he rode for hour and 30 minutes at a speed of 0 miles per hour to the county fair. He returned home riding hour and 5 minutes at a speed of miles per hour. What total number of miles did he bike?

12 Lesson C ~ Introducing Percents For each shaded grid, write the ratio of the shaded squares to 00 (a fraction) and the percent of squares shaded as a number with the % sign Each large square shows 00%. a. Shade the small squares to show 50%. b. What percent does each small square represent? Write the shaded number of squares as a percent, decimal and fraction If a shirt is on sale for 5% off, what percent of the original price will the customer pay? 9. Use the 0 by 0 grid below. Design a yard with the following guidelines: 0% of the yard is a deck 50% of the yard is grass % of the yard is a garden What percent of the yard is left over to landscape?

13 Lesson 3C ~ Percents, Decimals and Fractions For problems # 3: a. Shade each figure so it shows a percent between the two percents given. b. Write the shaded part of each shape as a fraction in simplest form, a decimal and a percent a. Between 0% and 30%. a. Between 30% and 45%. a. Between 55% and 70% b. b. b. Write the shaded part of each shape as a fraction in simplest form, a decimal and a percent Write each decimal or fraction as a percent Order the numbers from least to greatest: 60%, 0.67, 4 6. At a park, out of every 0 students were playing basketball. What percent of the students were NOT playing basketball?. Carmen walked 3 3 miles. What percent of a mile did Carmen walk?

14 Lesson 4C ~ Percent of a Number. Sam is going to buy a stereo for 0% off the original price. The stereo had an original price of $300. a. What percent of the original price will Sam pay for the stereo? b. How much will Sam pay for the stereo?. Kyle is going to buy a pencil for $.00. However, it is discounted 40% off the original price. How much will Kyle pay for the pencil? Solve each percent problem. 3. a. Which number is 5% of 0? 4. a. Which number is 66 % of 60? 3 b. What percent of the number from b. What percent of the number from part a is 9? part a is 80? 5. is 450% of % of 50 is 7. 50% of is 8. Draw a square that has a perimeter which is 50% of the perimeter in the square drawn. Measure using inches. 9. Draw a rectangle that has an area which is 50% of the area in the rectangle drawn. Measure using inches. 0. What percent of meter is 4 centimeters?. What percent of meter is 5 millimeters?

15 Lesson 5C ~ Percent Applications. Lyle collected marbles. He had 50 marbles and 0 of them were blue. His friend had 00 marbles and the same percent of blue marbles as Lyle. How many blue marbles did his friend have?. Martin needed to buy a new bookcase. At the store, he found a bookcase to buy that had a price of $99. However, the bookcase also had a sign which said it was 0% off the original price. How much did Martin pay for the bookcase? 3. Colin can buy a video game console in Oregon for $ He can buy the same video game console in Washington for $ However, Washington has a 6% sales tax. In which state should he buy the video game console, so he pays the least amount of money possible? 4. Kevin bought a music CD in California which had a price of $5.00. However, he paid $6.0 for the music CD. What was the percent of tax in California? 5. Tommy bought a new car in Texas. The price tag on the car was $6,000. However, the car was on sale for 5% off the original price. In Texas, there was a 7% sales tax. How much did Tommy finally pay for the new car? 6. Wyatt owns a new store on the boardwalk by the beach. He plans to sell beach balls in his store. Each one costs him $4.95. He wants to charge close to $0 for each beach ball to make a profit. However, there is an 8% sales tax in his area and he does not want customers to have to pay more than $0 total for a beach ball. How much should he charge customers for a beach ball? Explain your reasoning.

16 Lesson 6C ~ Introduction to Probability. There is a 0.75 chance it will rain on Thursday. a. Write the probability it will not rain on Thursday as a decimal, fraction and percent. b. Do you think it will rain? Why or why not?. There is a 5 4 probability Martin will run for class president. There is a 0.85 probability Sam will run for class president. There is a 75% probability Karen will run for class president. Who is most likely to run for class president? 3. Tom asked 40 people which sport they preferred. Ten people chose basketball, 5 of the people chose baseball, and 35% chose football. a. How many people chose baseball? b. How many people chose football? c. What percent of the people chose basketball? d. What is the probability a person will not choose football? Write a probability as a fraction that has a value between the two probabilities given %,, ,, 30% 6. Shade the spinner so there is a 00% chance of landing in the shaded part. 7. You are making a 6-sided cube out of paper. You want there to be a 33 3 % chance of rolling a star. On how many sides should you draw a star? You have a jar of jelly beans to fill with red, white and pink jelly beans. You want to have between 70 and 90 jelly beans in the jar. You want the probability of choosing a red jelly bean to be 0%, the probability of choosing a white jelly bean to be 50% and the probability of choosing a pink jelly bean to be 30%. a. How many red jelly beans will you put in the jar? b. How many white jelly beans will you put in the jar? c. How many pink jelly beans will you put in the jar?

17 Lesson 7C ~ Experimental Probability. Carmen has four friends she likes to ride bikes with: Mary, Shawna, Kate and Leslie. a. Identify the sample space if she randomly chooses one friend to ride bikes with. b. Suppose she chooses two friends to ride bikes with. What are all the possible combinations of friends she might ride bikes with? List all possible pairs of people. (Example: Mary and Leslie) c. The answer to part b is the sample space for choosing two friends to ride bikes with. How many pairs of friends are in the sample space? d. Identify the sample space if Carmen picks three friends to ride bikes with. Solve each problem.. Gary has a pet frog. He recorded the lengths of its jumps 40 times. He noticed the frog jumped farther than one foot 5 times. a. What is the experimental probability the frog will jump farther than one foot? b. If Gary records the next 6 jumps the frog makes, how many of those 6 jumps would you expect the frog to jump farther than one foot? 3. Penny practiced putting a golf ball into the hole from 0 feet away. Of the 5 times she practiced, she put the ball in the hole 0 times. a. What is the experimental probability she will put her next practice putt from 0 feet into the hole? b. If Penny practices the putt 35 more times, how many of those 35 putts would you expect her to make? 4. Kendra randomly chose a card from a stack of cards. She put the card back and chose again. Each time she recorded the color of the card: red, blue, yellow, or green. Her results are shown below. Color of Card Red Blue Yellow Green Number of Times Card Picked a. Find the experimental probability of picking each color. Color of Card Red Blue Yellow Green Experimental Probability b. If Kendra randomly chooses a card from the stack of cards 00 times, how many of those 00 times would you expect her to choose each color based on her experiment? Color of Card Red Blue Yellow Green Number of Times Card Picked

18 Lesson 8C ~ Theoretical Probability. Rich has a bag with four sticks inside. They are inch, inches, 3 inches and 4 inches long. He randomly picks one, puts it back, and then chooses a second one. He then draws a rectangle using the two stick lengths one is the height and one is the base of the rectangle. a. Write the possible combinations of ways Rich could choose the two lengths from the bag. For this problem, choosing a inch stick and then a inch stick is the same as choosing a inch stick and then a inch stick because the rectangles would be congruent. b. How many of the combinations in part a make a rectangle with an area greater than 8 square inches? c. What is the theoretical probability Rich will choose two lengths that make a rectangle with an area greater than 8 square inches?. Draw a spinner so that a person has a 50% chance of landing on red and a 33 % chance of landing on blue. The rest of the spinner is yellow. 3 What percent of the spinner is yellow? 3. You choose a card randomly from a deck of cards numbered through 40. a. Describe one example of card(s) that you would have a 40 probability of choosing. b. Describe one example of card(s) that you would have a probability of choosing. 4. Gene has a red, blue and green shirt and a black and brown shorts with which to make an outfit. The tree diagram below shows his options. Red Shirt Blue Shirt Green Shirt Black Shorts Brown Shorts Black Shorts Brown Shorts Black Shorts Brown Shorts Red Shirt and Black Shorts Red Shirt and Brown Shorts Blue Shirt and Black Shorts Blue Shirt and Brown Shorts Green Shirt and Black Shorts Green Shirt and Brown Shorts a. What is the probability he will choose a red shirt and brown shorts? b. What is the probability he will choose a red shirt and black or brown shorts? c. Suppose Gene also had a yellow shirt. What would be the probability of choosing the yellow shirt and black or brown shorts?

19 Lesson 9C ~ Geometric Probability. Tami is painting the railing around her garden which is in the shape of a triangle. She has painted 4 feet of the railing. What is the probability a bird that lands on the railing will land on the painted part of the railing? 9 feet 8 feet feet Use each figure below to find the geometric probability that a dart landing on each board will land on the shaded part m m 0 inches 4 inches 5 inches m 3 inches ft 0 ft 6 cm 4 cm 3 ft 4.5 ft 4 cm 8 cm 6. Find the probability that the dart will not land in the shaded part of each dart board in # Draw your own board with shading so the probability a dart landing on the board will land on the shaded part is 4. Include dimensions on your board and show why the probability of landing on the shaded part is 4.

20 Lesson 0C ~ Parts of Circles. The diameter of the circle is 5 inches. What is the length of each side of the central angle drawn? When two chords intersect in a circle, the product of each part of one chord is equal to the product of each part in the second chord. This means: AC BC = EC DC A E C D B Use this information to find the length of the missing part of each chord ?? 4 3? = Find the degree measurement of angle in each circle Find the probability that a dart that randomly lands on the circle will land on the shaded area

21 Lesson C ~ Circumference of a Circle Find the circumference of each circle. Round each answer to the nearest tenth. Use 3.4 for π.. diameter = in. radius = 6. cm 3. radius = 3 miles 4. Kyle bounced a ball along the path shown. Each time, his ball bounced an equal distance. Janet threw a ball that landed where Kyle s ball finally rested. Which ball traveled a farther distance? Use 3.4 for π. Path of Janet s ball. Path of Kyle s ball. 3 feet 5. How much longer is the circumference of the larger circle than the smaller circle? 3 m m 6. Draw and label the diameter of a circle whose circumference is more than 4 feet and less than 8 feet. 7. a. Mike runs around a circular track with a radius of 0 feet. Find the distance he runs in one lap. b. If he runs one lap in minutes, about how many feet per minute is he running?

22 Lesson C ~ Perimeter and Circumference The perimeter for each shape is given. Find the length of the missing side with a?. Use 3.4 for π and round to the nearest hundredth.? in.. 3. in in 6 yd 4 in? yd 4 in 6 in m? m perimeter 35.4 yd perimeter = 60 in perimeter m? cm 3 cm? in cm in 4 cm 6. in 6. in 5.8 ft 4 ft? mft 5.8 ft perimeter = 0 cm perimeter.8 in perimeter 7.45 ft 7. Tom ran around the track shown to the right. a. About how far did Tom run each lap? b. If Tom wanted to run mile, about how many laps should he run? 00 ft 370 ft c. Tom ran 0 laps in 6 minutes. How many miles per hour did he run?

23 Lesson 3C ~ Similar and Congruent Figures. Draw two rectangles that are similar, but not congruent.. ΔBOY is similar to ΔLIV. B a. Find the ratio of each side in ΔBOY to the corresponding side in ΔLIV. b. Find the perimeter of ΔBOY. 5 in Y 8 in 6 in O c. Find the perimeter of ΔLIV. L d. What is the ratio of the perimeter of ΔBOY to the perimeter of ΔLIV? 0 in 6 in e. If two similar shapes have a ratio of : 3 for their corresponding sides, what is the ratio of their perimeters? V in I 3. Use square A to the right to answer the following questions. a. Measure a side of square A using inches. Label the length of the side. A b. Draw a square B below square A so the ratio of the side of square A to the side of square B is : 3. Label the length of the side. c. Find the perimeter of square A. d. Find the perimeter of square B. e. What is the ratio of the perimeter of square A to square B? 4. A map uses a scale. Suppose you are looking at a map that has a scale such that centimeter on the map represents 5 miles. This scale is inch : 5 miles. a. Suppose the distance from your home to the zoo on the map is 4 inches. How many actual miles is it from your home to the zoo? b. Suppose it is 35 miles from your home to the beach. How many inches is this distance on the map?

24 Lesson 4C ~ Ratios and Similar Figures. The two rectangles are similar. Their perimeters are shown. Find the ratio of their corresponding sides. perimeter = 9 ft perimeter = 5 ft. Use the similar rectangles to the right. a. What is the scale factor of the rectangles? b. What is the ratio of their perimeters? 8 in 0 in in c. Find the area of each rectangle. d. What is the ratio of their areas? When two figures are similar with a scale factor of : 3, their perimeters also have a ratio of : 3. However, their areas have a ratio of ( ) : (3 3) or 4 : 9. If two similar figures have a scale factor of : 7, their areas have a ratio of ( ) : (7 7) or : 49. For each pair of similar figures, find: a. their scale factor. b. the ratio of their perimeters or circumferences. c. the missing perimeter or circumference. d. the ratio of their areas. m ft 8 ft m circumference? m 3 in 4 in perimeter =? in perimeter = 5 ft circumference 6 m 5 in perimeter =? ft 0 in perimeter = 60 in Use ratios to find the missing corresponding side length for each pair of similar figures.? cm 6. 7.? m 8. 0 perimeter = 4 m perimeter = cm perimeter = 5 cm 5 m 8 m perimeter = 40 m perimeter = 80 m? m perimeter = 60 m