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Homework 1 Name: _____________________________________________ Chapter 4 Pages 114 - 150 Practice 4.1 – Comparing Two Quantities Write two ratios to compare the quantities. 1) ________________________________ _______________________________ 2) Catherine has 23 video game disks and Dylan has 37 video game disks. ________________________________ _______________________________ 3) In a school, there are 8 classes in the sixth grade and 7 classes in the seventh grade. Each class has an equal number of students. ________________________________ _______________________________ Homework 2 State whether each of the following can be expressed as a ratio. Explain why or why not. (length, capacity, mass) 4) 6 cm and 60 g _______________________________________________________ ______________________________________________________________________ 5) 54kg and 54 cm ______________________________________________________ ______________________________________________________________________ 6) 12 g and 45 kg _______________________________________________________ ______________________________________________________________________ 7) 87 ft and 93 yd _______________________________________________________ ______________________________________________________________________ Solve. Show your work. 8) There are 123 students in a drama club. 65 of them are girls. a) What is the ratio of the number of boys to the number of girls? b) What is the ratio of the number of boys to the total number of students? 9) There are 37 clarinet players and 150 trumpet players who tried out for a music competition. a) Find the ratio of the number of clarinet players to the number of trumpet players. b) Find the ratio of the number of trumpet players to the total number of players. Homework 3 10) Carl had $43 when he entered the museum gift shop. After spending some money, he had $18 left. a) Find the amount of money Carl spent. b) Find the ratio of the amount of money Carl spent to the amount of money he had when he entered the gift shop. 11) Kelvin’s monthly allowance is $42 and Mike’s monthly allowance is $63. How many times Mike’s monthly allowance is Kelvin’s monthly allowance? 12) The ratio of the weight of vegetables sold to the weight of fruits sold is 45 : 144. a) How many times the weight of vegetables sold is the weight of fruits sold? b) What fraction of the total weight of vegetables and fruits sold is the weight of vegetables sold? Homework 4 13) The ratio of the length to the width of a rectangle is 5 : 2. a) Express the difference between the length and the width of the rectangle as a fraction of the length of the rectangle. b) Express the width of the rectangle as a fraction of the perimeter of the rectangle. Write a situation that each ratio could represent. 14) 5 : 16 ______________________________________________________________________ ______________________________________________________________________ 15) 98 : 3 ______________________________________________________________________ ______________________________________________________________________ Homework 5 Practice 4.2 – Equivalent Ratios Express each ratio in simplest form. 1) 13 : 39 2) 16 : 40 3) 25 : 15 4) 56 : 21 5) 30 : 54 6) 72 : 48 7) 26 cm : 4 m 8) 9 kg : 36 g 9) 35 min : 2 h State weather each pair of ratios are equivalent. If yes, show/explain why. 10) 11 : 17 and 17: 11 11) 7 : 11 and 21 : 33 12) 15 : 35 and 25 : 45 13) 15 : 20 and 20 : 25 14) 38 : 19 and 2 : 1 15) 12 : 8 and 18 : 12 Homework 6 Find the missing term in each pair of equivalent ratios. 16) 7 : 9 = 49 : ______ 17) 12 : 5 = 144 : ______ 18) 4 : 15 = 48 : ______ 19) 7 : 13 = 77 : ______ 20) 45 : 36 = ______ : 12 21) 30 : 48 = ______ : 8 22) 72 : 84 = ______ : 7 23) 121 : 88 = ______ : 8 Find the equivalent ratios. 24) Use multiplication to find three equivalent ratios to 8 : 12. 25) Use division to find all the whole number ratios equivalent to 168 : 56 (There are 7 equivalent ratios using division) Homework 7 Complete the table. 26) A manufacturer’s instruction states that 3 cups of cleaning agent should be diluted with 5 cups of water before use. Amount of Cleaning Agent (cups) 3 Amount of water (cups) 5 9 12 35 Find the missing term in each pair of equivalent ratios. Hint – Simplify first. (Divide by the GCF, and then multiply by the correct factor) 27) 63 : 27 = 49 : ______ 28) 81 : 18 = 36 : ______ 29) 24 : 96 = 5 : ______ 30) 72 : 24 = 15 : ______ 31) 60 : 144 = ______ : 60 32) 125 : 80 = ______ : 48 33) 90 : 15 = ______ : 7 34) 98 : 112 = 63 : ______ 45 Homework 8 35) Judy uses 5 ounces of lemonade concentrate for every 9 ounces of orange juice concentrate to make a fruit punch. a) Find the ratio of the number of ounces of orange juice concentrate to the number of ounces of lemonade concentrate she uses. b) If Judy uses 36 ounces of orange juice concentrate to make the fruit punch, how many ounces of lemonade concentrate does she use? c) If Judy uses 45 ounces of lemonade concentrate to make the fruit punch, how many ounces of orange juice concentrate does she use? 36) In a science experiment, Farah mixed a salt solution and vinegar in the ratio 3 : 7. a) If she used 262.8 milliliters of salt solution, how much vinegar did she use? b) If 0.56 liter of vinegar was used, how much salt solution did she use? Homework 9 37) A fruit seller packs different fruits into baskets of the same size. The ratio of the weight of bananas to the weight of apples to the weight of pears is the same for all the baskets. The table shows the different weights of fruits in the baskets. Complete. Baskets Bananas Apples (lbs) 1 6 2 (lbs) 8 3 12 18 Pears (lbs) 15 Practice 4.3 – Real – World Problems: Ratios Solve. Show your work. 1) A rope is cut into three pieces P, Q, and R. The lengths of the pieces are in the ratio 3 : 5 : 7. If the rope is 33 feet 9 inches long, find the lengths of P, Q, and R. 2) Alice, Bernice, and Cheryl shared some stamps in the ratio 8 : 9 : 18. Alice received 184 stamps. Find the number of stamps that Bernice and Cheryl each received. Homework 10 3) Alan, Gil, and Deb’s point score in a video game was in the ratio 2 : 3 : 4. Deb scored 114,400 points. a) How many points did Gil score? b) How many points did they score in all? 4) Lara has three cats: Socks, Princess, and Luna. The ratio of Sock’s weight to Princess’s weight is 4 : 5. The ratio of Princess’s weight to Luna’s weight is 6 : 7. What is the ratio of Sock’s weight to Luna’s weight? Homework 11 5) Danny poured 78 liters of water into containers X, Y, and Z. The ratio of the volume of water in Container X to the volume of water in Container Y is 5 : 2. The ratio of the volume of water in Container Y to the volume of water in Container Z is 8 : 11. a) How much water was poured into Container X? b) How much more water was poured into Container X than Container Z? 6) The ratio of the number of mystery books to the number of science fiction books is 4 : 3. The ratio of the number of science fiction books to the number of biographies is 4 : 5. If there are 48 science fiction books, find the total number of books. Homework 12 7) In a music room, the ratio of the number of clarinets to the number of flutes was 3 : 4. After the school bought another 24 flutes, the ratio became 3 : 8. How many clarinets were there in the music room? 9) The ratio of the number of men to the number of women on a bus was 2 : 3. At a bus stop, 4 women got off and the ratio became 4 : 5. a) How many men were on the bus? b) How many women were on the bus in the end? Homework 13 10) The number of chickens to the number of ducks on a farm was 6 : 5. After 63 ducks were sold, there were 3 times as many chickens as ducks left. a) How many chickens were there on the farm? b) How many chickens and ducks were there altogether on the farm in the end?