11 Business Mathematics Quarter 1 – Module 4: Solving Problems Involving Kinds of Proportion Business Mathematics – Grade 11 Self-Learning Module (SLM) Quarter 1 – Module 4: Solving Problems Involving Kinds of Proportion First Edition, 2020 Republic Act 8293, section 176 states that: No copyright shall subsist in any work of the Government of the Philippines. However, prior approval of the government agency or office wherein the work is created shall be necessary for exploitation of such work for profit. Such agency or office may, among other things, impose as a condition the payment of royalties. Borrowed materials (i.e., songs, stories, poems, pictures, photos, brand names, trademarks, etc.) included in this module are owned by their respective copyright holders. Every effort has been exerted to locate and seek permission to use these materials from their respective copyright owners. The publisher and authors do not represent nor claim ownership over them. Development Team of the Module Writer: Sherwin P. Uy Editors: Joecel S. Rubinos, Adam Julian L. Che, Chery Lou F. Bacongco Reviewers: Zaida N. Abiera, Floramae A. Dullano Illustrators: Maria Angelica T. Garcia, Sherwin P. Uy Layout Artist: Sherwin P. Uy Cover Art Designer: Ian Caesar E. Frondoza Management Team: Allan G. Farnazo, CESO IV – Regional Director Fiel Y. Almendra, CESO V – Assistant Regional Director Romelito G. Flores, CESO V – Schools Division Superintendent Mario M. Bermudez, CESO VI – Assist. Schools Division Superintendent Gilbert B. Barrera – Chief, CLMD Arturo D. Tingson Jr. – REPS, LRMS Peter Van C. Ang-ug – REPS, ADM Jade T. Palomar – REPS, Mathematics Juliet F. Lastimosa – CID Chief Sally A. Palomo – Division EPS In- Charge of LRMS Gregorio O. Ruales – Division ADM Coordinator Zaida N. Abiera – Division EPS, Mathematics Printed in the Philippines by Department of Education – SOCCSKSARGEN Region Office Address: Telefax: E-mail Address: Regional Center, Brgy. Carpenter Hill, City of Koronadal (083) 2288825/ (083) 2281893 region12@deped.gov.ph 11 Business Mathematics Quarter 1 – Module 4: Solving Problems Involving Kinds of Proportion Introductory Message For the facilitator: Welcome to the Business Mathematics for Grade 11 Self-Learning Module (SLM) on Solving Problems Involving Kinds of Proportion! This module was collaboratively designed, developed and reviewed by educators both from public and private institutions to assist you, the teacher or facilitator in helping the learners meet the standards set by the K to 12 Curriculum while overcoming their personal, social, and economic constraints in schooling. This learning resource hopes to engage the learners into guided and independent learning activities at their own pace and time. Furthermore, this also aims to help learners acquire the needed 21st century skills while taking into consideration their needs and circumstances. In addition to the material in the main text, you will also see this box in the body of the module: Notes to the Teacher This contains helpful tips or strategies that will help you in guiding the learners. As a facilitator you are expected to orient the learners on how to use this module. You also need to keep track of the learners' progress while allowing them to manage their own learning. Furthermore, you are expected to encourage and assist the learners as they do the tasks included in the module. 2 For the learner: Welcome to the Business Mathematics - Grade 11 Self-Learning Module (SLM) on Solving Problems Involving Kinds of Proportion! The hand is one of the most symbolized part of the human body. It is often used to depict skill, action and purpose. Through our hands we may learn, create and accomplish. Hence, the hand in this learning resource signifies that you as a learner is capable and empowered to successfully achieve the relevant competencies and skills at your own pace and time. Your academic success lies in your own hands! This module was designed to provide you with fun and meaningful opportunities for guided and independent learning at your own pace and time. You will be enabled to process the contents of the learning resource while being an active learner. This module has the following parts and corresponding icons: What I Need to Know This will give you an idea of the skills or competencies you are expected to learn in the module. What I Know This part includes an activity that aims to check what you already know about the lesson to take. If you get all the answers correct (100%), you may decide to skip this module. What’s In This is a brief drill or review to help you link the current lesson with the previous one. What’s New In this portion, the new lesson will be introduced to you in various ways such as a story, a song, a poem, a problem opener, an activity or a situation. What is It This section provides a brief discussion of the lesson. This aims to help you discover and understand new concepts and skills. What’s More This comprises activities for independent practice to solidify your understanding and skills of the topic. You may check the answers to the exercises using the Answer Key at the end of the module. What I Have Learned This includes questions or blank sentence/paragraph to be filled in to process what you learned from the lesson. What I Can Do This section provides an activity which will help you transfer your new knowledge or skill into real life situations or concerns. 3 Assessment This is a task which aims to evaluate your level of mastery in achieving the learning competency. Additional Activities In this portion, another activity will be given to you to enrich your knowledge or skill of the lesson learned. This also tends retention of learned concepts. Answer Key This contains answers to all activities in the module. At the end of this module you will also find: References This is a list of all sources used in developing this module. The following are some reminders in using this module: 1. Use the module with care. Do not put unnecessary mark/s on any part of the module. Use a separate sheet of paper in answering the exercises. 2. Don’t forget to answer What I Know before moving on to the other activities included in the module. 3. Read the instruction carefully before doing each task. 4. Observe honesty and integrity in doing the tasks and checking your answers. 5. Finish the task at hand before proceeding to the next. 6. Return this module to your teacher/facilitator once you are through with it. If you encounter any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator. Always bear in mind that you are not alone. We hope that through this material, you will experience meaningful learning and gain deep understanding of the relevant competencies. You can do it! 4 What I Need to Know This module was designed and written with you in mind. It is here to help you master the solving problems involving kinds of proportion. The scope of this module permits it to be used in many different learning situations. The language used recognizes the diverse vocabulary level of students. The lessons are arranged to follow the standard sequence of the course. But the order in which you read them can be changed to correspond with the textbook you are now using. In this module, you will be able to: ο· solve problems involving direct, inverse and partitive proportion. ABM_BM11RP-If-4 Specifically, you are expected to: 1. translate verbal statements involving proportions into mathematical statements; 2. describe direct, inverse and partitive proportions; and 3. solve problems involving direct, inverse and partitive proportion. 5 What I Know Before we begin this lesson, let us find out how much you already know on this module. After taking and checking this short test, take note of the items that you were not able to answer correctly and look for the right answer as you go through this module. Direction: Encircle the letter of the correct answer. 1. A car travels a distance of d km in t hours. The formula that relates d to t is π = ππ‘. What type of proportion is it? a. combined b. direct c. inverse d. partitive 2. What type of proportion is involve when one quantity (x) increases, the other quantity (y) decreases or vice versa? a. direct b. inverse c. joint d. partitive 3. What concept is involved when a whole portion is divided into parts that is proportional to the given ratio? a. combined proportion c. inverse proportion b. direct proportion d. partitive proportion 4. If Aleng Puring needs 4 liters of juice for 50 kids and 6 liters for 75 kids, what type of proportion is being illustrated? a. combined proportion b. direct proportion c. inverse proportion d. partitive proportion 5. Which of the following mathematical statements represents cost (c) which is directly proportional to the number (n) of pencils? a. π = ππ b. π = ππ c. π= d. π= π π π π 6 6. What mathematical statement represents the speed (r) of a moving object which is inversely proportional to the time (t) travelled? a. π‘ = ππ b. π = ππ‘ c. d. π= π‘ π π π‘ =π 7. Which of the following problems represents an inverse proportion? a. Divide a 81-m rope into 3 with the ratio 1:2:5. What is the measure of each rope? b. The exchange rate of peso to a dollar in 2019 is β±51.00 to $1. How much will you get for $6.50? c. Three men can complete a project in 3 weeks. How many men will be needed if the project is to be completed in a week? d. When Mrs. Cruz went to abroad for an educational tour, she noticed that each guide goes along with three tourists. If there are 4 guides, how many tourists would they bring around? 8. Which of the following problems represents a partitive proportion? a. Divide a 81-m rope into 3 with the ratio 1:2:5. What is the measure of each rope? b. The exchange rate of peso to a dollar in 2019 is β±51.00 to $1. How much will you get for $6.50? c. Three men can complete a project in 3 weeks. How many men will be needed if the project is to be completed in a week? d. When Mrs. Cruz went to abroad for an educational tour, she noticed that each guide goes along with three tourists. If there are 4 guides, how many tourists would they bring around? 9. The verbal phrase “the ratio of a number (x) and four added to two” is equivalent to which of the following mathematical statements? a. π₯: 4 + 2 b. π₯ = 4+2 c. π₯+2 d. π₯ 4 4 +2 10. Which is an example of an inverse proportion? a. 1 ππ’πππ 3 π‘ππ’πππ π‘π = 4 ππ’πππ π b. 3 πππ‘πππ 5 ππππππ = π 20 ππππππ c. π΅ 3 πππ¦π 3 π€ππππ 1 π€πππ d. 1π₯+2π₯+3π₯ = β±50.00 = β±600.00 π₯ 7 11. Juanita spends her working hours (8 hours) in filing, typing, placing and receiving calls. If she approximately performs these functions in the ratio of 1:3:4, which among the mathematical statements best represents the time spent for each function? a. 8π₯ = 8 b. 1+3+4 c. 1π₯ + 3π₯ + 4π₯ = d. 1π₯ + 3π₯ + 4π₯ = 8 π₯ =8 1 8 12. Which of the following problems DOES NOT belong to the group? a. If 10 laptops cost β±200,000.00, then how much do 8 laptops cost? b. A basket of food is sufficient to feed 15 persons for 3 days. How many days would it last for 10 persons? c. Three boys sold garlands in the ratio of 2:3:4. Together they sold 225 garlands. How many garlands did each boy sell? d. How many tea bags (B) are needed to make 15 liters of iced tea when eight tea bags are needed to make 5 liters of iced tea? 13. Carla will spend β±3,920.00 for her birthday party if she will invite 14 guests. If the cost is directly proportional to the number of invited guests, how much will she spend if she will invite 56 guests? a. β±15,680.00 b. β±15,685.00 c. β±15,780.00 d. β±15,880.00 14. If 3 men can do a portion of a job in 8 days, how many men can do the same job in 6 days? a. 4 b. 5 c. 6 d. 7 15. If Mang Gorio wants to give β±5,000 to his four children in the ratio of 1:2:3:4 for their weekend allowance, how much will each of the four children receive? a. β±500: β±1,000: β±1,500: β±2,000 b. β±450: β±1,050: β±1,450: β±2,050 c. β±500: β±1,000: β±1,250: β±2,250 d. β±450: β±1,000: β±1,500: β±2,050 8 Lesson 4 Solving Problems Involving Kinds of Proportion Hello! Do you still remember these lines, “if two ratios are equal, then their reciprocals are also equal” or “the product of the extremes is equal to the product of the means”? Right now, let us deal with these statements more in-depth as go through with this module. What’s In Let us review on the following terms using a concept map for you to better understand the lessons in this module. Activity 1: Refresh Your Mind Direction: Fill in the blanks with right word/s to make each statement correct. Base your answer on the illustrations below. 9 1. It is comparison of two numbers or measurement known as _________________. 2. A relationship between two variables when their ratio is equal to a constant value is called _________________. 3. _________________ represents a relationship of two values x and y such when x increases, then y decreases or vice versa. 4. A/an _________________ is a ratio in which the two terms are different in units. 5. A whole is divided into parts that is proportioned into equal or unequal ratios refers to the _________________. Alright! You are now ready to explore kinds of proportion and solve real-life problems. What’s New How are you coping with our lesson? I hope you are curious about the following activities that we will discussing in this module. The next activity will test your readiness on pre-requisite skills on translating verbal statements involving proportions into mathematical statements. Activity 2: Match It, Translate It! Direction: In this activity, you will: A. Match the following phrases translated into mathematical expressions or statements by connecting it through lines: Mathematical Expressions/Statements Verbal Sentences/Phrases 1. There are twice as many partners (P) as corporations (L). A. π/π(π³ – π·) + π 2. There are half as many profit (P) as loss (L). B. ππ· = π³ 3. The number of Php100 bills (L) is twice as many as Php500 bills (P). C. π· = 4. One less than twice the salaries of Pedro (P) & Lito (L) D. π(π· + π³) – π 5. Two more than half the difference of certain mobile phones sales (L) and power bank sales (P) E. π· = ππ³ 10 π π³ π B. Translate the following problems to mathematical statement: Given Problem Mathematical Statement 6. It takes Andy 30 minutes to burn 200 calories in jogging. How long (T) will it take Andy to burn 400 calories? 7. How many tea bags (B) are needed to make 15 liters of iced tea when eight tea bags are needed to make 5 liters of iced tea? 8. Assuming they work at the same rate, how long (S) will it take 2 housekeepers to clean an entire house if it takes 4 days for 8 housekeepers to clean it? 9. Four machines can recopy 25000 books in 6 days. How many machines (M) are needed to copy 25000 books in 3 days? 10. Mr. Covito donated β±5,000.00 as a club fund for the upcoming ABM strand fair. The Accountancy Club, Business Club and Management Club will share the amount in the ratio of 2:3:5. How much (x) will each group receive? Great Job! Keep the fire burning! Let’s unlock some difficulties. What is It You are already knowledgeable in translating worded problems to mathematical statements. Now, let us process and classify those translated problems to the three (3) kinds of proportions. How do we recognize whether a given proportion problem involves a direct proportion, an inverse proportion, or a partitive proportion? The definitions below determine the kinds of proportion considering the following problem: 11 1.) If 10 laptops cost the number of β±200,000.00, then how much do 8 laptops cost? We see that the greater the number of laptops, the higher is the total cost (x). Setting up the ratio, we obtain: Given: Number of laptops: a= Total cost: 10 laptops b = β±200,000.00 c= 8 laptops d= x * 10 laptops for β±200,000.00 Mathematical Statement: ∗ πΏπππ‘πππ βΆ π‘ππ‘ππ πππ π‘ = πΏπππ‘πππ βΆ π‘ππ‘ππ πππ π‘ 10 ππππ‘πππ 8 ππππ‘πππ = β±200,000.00 π₯ Solution: 10 8 = 200,000 π₯ 10π₯ = 8(200,000) 10π₯ 10 = 1,600,000 10 π = β±πππ, πππ In the problem, the number of laptops and total cost are directly proportional since the more laptops you buy, the higher is the cost or the lesser laptops you buy, the lower is the cost. Thus, the problem involves Direct Proportion. 2.) In a T-shirt factory, 5 employees can finish designing 20 T-shirts in two hours. How long will it take 10 people to design 20 T-shirts? We see that the more employees on a job, the lesser time (x) needed to finish the job. Setting up the ratio, we obtain: Given: No. of employees: Time spent: a= b= 5 employees 1 2βππ . c = 10 employees d= 1 π₯ * 5 employees for 2 hours Mathematical Statement: * ππππ ππππππ¦πππ βΆ πππ π ππππππ¦πππ = ππππ π‘πππ βΆ πππ π π‘πππ 10 ππππππ¦πππ 2 βππ’ππ = 5 ππππππ¦πππ x 12 Solution: 10 2 = 5 x 10(π₯) = 5(2) 10π₯ 10 = 10 10 10 π₯= 10 π = π ππ. In the problem, the number of employees and time to finish the job are inversely/indirectly proportional since the more employees you hired, the lesser the time to spend to finish the job. Thus, the said problem involves Inverse/Indirect Proportion. 3.) Quarantina wants to donate her collection of figurines to her four friends in the ratio of 1:3:3:5. She has a total of 96 figurines. If her best friend wants the most number of figurines, how many figurines will she get? We see that the whole collection of figurines is being divided into parts (x) and distributed to them with specified ratio. Setting up the partition, we obtain: Given: Let x be the constant number of figurines 1x = number of figurines for her 1st friend 3x = number of figurines for her 2nd friend 3x = number of figurines for her 3rd friend 5x = number of figurines for her best friend (the most) 96 = total number of figurines Mathematical Statement: 1π₯ + 3π₯ + 3π₯ + 5π₯ = 96 Solution: 12π₯ = 96 12π₯ 96 = 12 12 π = π πππππππππ 5x = number of figurines for her 4th friend (the most) 5x = 5(8) = 40 figurines for her best friend When a whole is partitioned into equal or unequal ratios, such concept involves Partitive Proportion. In the problem, the total number of figurines is partitioned into the ratio of 1:3:3:5, thus making use of partitive proportions. 13 What’s More Alright! We have already unlocked your difficulties in classifying, differentiating and defining kinds of proportions. At this moment, be ready for our next activity. Here, your will be able to use what you have learned from our previous discussions. You can do this! Activity 3: Answer Me: Where do I belong? Direction: Solve the following problems and identify the kind of proportion involved. 1. An artisan bread maker uses 2,000 grams of flour to make 4 loaves of handcrafted bread. How many grams of flour is needed to make 2 loaves of bread? Solution Kind of Proportion: 2. It takes 4 mechanics to repair a car for 6 hours. How long will it take 7 mechanics to do the repair if they work at the same rate? Solution Kind of Proportion: 14 3. If Mang Orly wants to give β±5,000 to his four children in the ratio of 1:2:3:4 for their weekend allowance, how much is the least amount of allowance? Solution Kind of Proportion: 4. A box of pencil costs β±30 pesos. How much do 4 boxes cost? Solution Kind of Proportion: 5. Three men can finish doing the interior designing of a house in 3 weeks. How many men are needed to finish the interior designing in a week? Solution Kind of Proportion: 15 What I Have Learned Now, let us summarize what you have learned. Let’s do this activity! Activity 4: Write About Me Direction: Write an essay briefly and concisely to process your knowledge on how to solve problems involving kinds of proportions. 1. What are the steps in solving problems involving direct proportions? ____________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ _________________________________________________________________________________. 2. What are the steps in solving problems involving indirect/inverse proportion? ____________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ _________________________________________________________________________________. B. 3. What are the steps in solving problems involving partitive proportions? ____________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ __________________________________________________________________________________ _________________________________________________________________________________. 16 What I Can Do Let us now apply what you have learned in solving problems involving kinds of proportion in real-life situations. Activity 5: I am Being Solved! Direction: Solve the following problems involving kinds of proportion. 1. The ratio of boys to girls in a badminton tournament game is 4:3. Mariel counted that there are 12 more boys than girls. How many boys and girls are there in the tournament? 2. It takes 3 salesmen 8 days to sell 5,000 boxes of soap. If 2 more salesmen are added, how long will it take them to sell the same number of boxes of soap? 3. Mr. Faustino allocates his monthly salary for bills, food, transportation, and other expenses at the ratio of 3:6:7:9, respectively. If he receives β±28,450.00 each month, how much is his budget for food? 17 Assessment Job well done! Let’s test what you have learned from the very start of our lesson. Direction: Read carefully and answer the questions below. Encircle the letter of your correct answer. 1. It relates between the time it takes to dig a well and install a water pump to supply the house with water and the number of people need to build it. What types of proportion is being portrayed? a. combined b. direct c. inverse d. partitive 2. What type of proportion is involve when the total amount is distributed into two or more equal or unequal parts which is proportional to the given ratio? a. combined proportion b. direct proportion c. inverse proportion d. partitive proportion 3. What type of proportion is involve when one quantity (x) increases, the other quantity (y) increases or vice versa? a. joint b. direct c. inverse d. partitive 4. If a cake recipe uses 20 cups of water for every 8 cups of chocolate and 10 cups of water for 4 cups of chocolate, what kind of proportion is being illustrated? a. combined proportion b. direct proportion c. inverse proportion d. partitive proportion 5. Which of the following mathematical statements represents the total cost (c) which is directly proportional to the sales revenue (r)? a. π = ππ b. π = ππ c. π= π π 18 d. π= π π 6. What mathematical statement represents the time (t) travelled which is inversely proportional to the speed (s) of a moving object? a. π‘ = ππ π π b. π‘= c. d. π‘ = ππ‘ π =π‘ π 7. Which of the following is NOT an example of direct proportion statement? a. b. c. d. 30 ππππ 200 ππππππππ 2 πππ‘πππ = 55 ππππ = π π 5 ππππππ 10 ππππππ π΅ 4 π€ππππ 4 πππ¦π = 1 πππ¦ π₯ + 2π₯ + 4π₯ = β±700.00 1 8. Which of the following problems represents a partitive proportion? a. Divide a 75-m rope into 4 with the ratio 1:2:5:7. What is the measure of each rope? b. The exchange rate of peso to a dollar in 2019 is β±51.20 to $1. How much will you get for $8.50? c. Three men can complete a project in 6 weeks. How many men will be needed if the project is to be completed in a week? d. When Mrs. Reyes went to abroad for an educational tour, she noticed that each guide goes along with five tourists. If there are 5 guides, how many tourists would they bring around? 9. Which of the following problems represent an inverse proportion? a. Divide a 75-m rope into 4 with the ratio 1:2:5:7. What is the measure of each rope? b. The exchange rate of peso to a dollar in 2019 is β±51.20 to $1. How much will you get for $8.50? c. Three men can complete a project in 6 weeks. How many men will be needed if the project is to be completed in a week? d. When Mrs. Reyes went to abroad for an educational tour, she noticed that each guide goes along with five tourists. If there are 5 guides, how many tourists would they bring around? 10. Which of the following problems DOES NOT belong to the group? a. A government-donated food pack is sufficient to feed 15 persons for 3 days. How many days would it last for 10 persons? b. If 10 tablet-PC cost he number of β±100,000.00, then how much do 8 tablet-PCs cost? c. How many tea bags (B) are needed to make 10 liters of iced tea when eight tea bags are needed to make 5 liters of iced tea? 19 d. Three boys sold rosary necklaces in the ratio of 2:3:4. Together they sold 225 rosary necklaces. How many rosary necklaces did each boy sell? 11. The verbal phrase “the ratio of a three and number (x) added to four” is equivalent to which of the following mathematical statements? a. π₯+4 3 b. c. 3: π₯ + 4 π₯ = 3+4 d. 3 π₯ +4 12. Mr. Ramon allocates his monthly salary for bills, food, transportation, and other expenses at the ratio of 3:3:2:2. If he received β±28,450.00 last month, which among the mathematical statements represent an answer to solve the various allocations for payment? a. 10π₯ = β±28,450.00 b. 3π₯ + 3π₯ + 2π₯ + 2π₯ = 28,450.00 c. 3+3+2+2 π₯ d. 3π₯ + 3π₯ + 2π₯ + 2π₯ = = β±28,450.00 28,450.00 1 13. Junjun will spend β±5,500.00 for his birthday party if he will invite 15 guests. If the cost is directly proportional to the number of invited guests, how much will it cost is he invites 30 guests? a. β±11,000.00 b. β±11,100.00 c. β±11,150.00 d. β±11,190.00 14. If 4 men can do a portion of a job in 9 days, how many men can do the same job in 6 days? a. 5 b. 6 c. 7 d. 8 15. If Mang Inasal wants to give β±10,000 to his four children in the ratio of 1:2:3:4 for their weekend allowance, how much will each of the four children receive? a. β±450: β±1,050: β±1,450: β±2,050 b. β±500: β±1,000: β±1,250: β±2,250 c. β±1,000: β±2,000: β±3,000: β±4,000 d. β±1,000: β±2,000: β±2,500: β±4,500 Good Job! You did well on this module! Keep going! 20 Additional Activities Congratulations! You’ve come this far. I know you’ve learned a lot in this module. Now for your additional activities, just do this. Activity 6: “My 3-2-1 Chart” Direction: Complete the 3-2-1 chart below. My 3-2-1 Chart Three things I found out: 1. 2. 3 Two interesting things: 1. 2. One question I still have: : 1. Here’s your 3 stars for a job well done. You are now ready to answer the next module on Buying and Selling. 21 What 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 22 Teaching Guide for Senior High School Business Mathematics, pp. 65-68 Business Mathematics Textbook, pp. 65-68 References I Know b b d b a c c a d c d c a a a What I Have Learned Activity 4 Answer will vary on the learners capacity answering essay type question. What’s More Activity 3 1. 100 grams; Direct 2. 3 hrs. 25 mins.; Indirect 3. β±500.00; Partitive 4. β±120.00; Direct 5. 9 men; Indirect What’s In Activity 1 1. Ratio 2. Direct Proportion 3. Inverse/Indirect Proportion 4. Rate What’s New Activity 2 1. E 2. C 3. B 4. D 5. A 6. 7. 8. 5. Partitive Proportion 9. ππ ππππ. π» = πππ πππ. πππ πππ. π© π πππ ππππ = ππ ππππππ π ππππππ π ππππππππππππ πΊ = π ππππππππππππ π π πππ π π πππ π΄ = π π πππ π ππππππππ 10. ππ + ππ + ππ = β±π, πππ. ππ π β±π, πππ. ππ = π ππ What I Can Do Activity 5 1. Kind: Direct PS: π ππππ π πππππ = (ππ+π)ππππ π Ans: ππ ππ¨π²π¬; ππ π π’π«π₯π¬ 2. Kind: Indirect/Inverse PS: π ππππππππ π ππππππππ = π π πππ π Ans: π. π πππ²π¬ 3. Partitive; ππ + ππ + ππ + ππ = β±ππ, πππ. ππ; Ans:β±π, πππ. ππ (foods) Assessment 1. c 2. d 3. b 4. b 5. b 6. b 7. d 8. a 9. c 10. d 11. d 12. b 13. a 14. b 15. c Answer Key DISCLAIMER This Self-learning Module (SLM) was developed by DepEd SOCCSKSARGEN with the primary objective of preparing for and addressing the new normal. Contents of this module were based on DepEd’s Most Essential Learning Competencies (MELC). This is a supplementary material to be used by all learners of Region XII in all public schools beginning SY 2020-2021. The process of LR development was observed in the production of this module. This is version 1.0. We highly encourage feedback, comments, and recommendations. For inquiries or feedback, please write or call: Department of Education – SOCCSKSARGEN Learning Resource Management System (LRMS) Regional Center, Brgy. Carpenter Hill, City of Koronadal Telefax No.: (083) 2288825/ (083) 2281893 Email Address: region12@deped.gov.ph 23
