Math-G6-Q1-Mod6-v2.pdf

6 Mathematics Quarter 1 – Module 6: Subtracting Decimals and Mixed Decimals Through Ten Thousandths CO_Q1_Mathematics6_Module6 Mathematics – Grade 6 Alternative Delivery Mode Quarter 1 – Module 6: Subtracting Decima...

6 Mathematics Quarter 1 – Module 6: Subtracting Decimals and Mixed Decimals Through Ten Thousandths CO_Q1_Mathematics6_Module6 Mathematics – Grade 6 Alternative Delivery Mode Quarter 1 – Module 6: Subtracting Decimals and Mixed Decimals Through Ten Thousandths 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 book 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. Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio Development Team of the Module Author: Charlyn Joy Alingalan Estimera Editors: Ma. Portia G. Galanto, Rebecca O. Billones, and Collin G. Sales Reviewers: Rosemarie D. Aclan and Collin G. Sales Illustrator: Charlyn Joy A. Estimera Layout Artist: Felizardo S. Valdez III Management Team: Ramir B.Uytico Pedro T. Escobarte, Jr. Elena P. Gonzaga Donald T. Genine Ma. Roselyn J. Palcat Nordy D. Siason, Jr. Rowena S. Carillo Rosemarie D. Aclan Arthur J. Cotimo Felizardo S. Valdez III Marve E. Gelera Printed in the Philippines by ________________________ Department of Education – Region VI Office Address: Duran Street, Iloilo City_________________________ ____________________________________________ Telefax: (033)336-2816, (033)509-7653___________________ E-mail Address: [email protected]_________________________  6 Mathematics Quarter 1 – Module 6: Subtracting Decimals and Mixed Decimals Through Ten Thousandths Introductory Message This Self-Learning Module (SLM) is prepared so that you, our dear learners, can continue your studies and learn while at home. Activities, questions, directions, exercises, and discussions are carefully stated for you to understand each lesson. Each SLM is composed of different parts. Each part shall guide you step-by- step as you discover and understand the lesson prepared for you. Pre-tests are provided to measure your prior knowledge on lessons in each SLM. This will tell you if you need to proceed on completing this module or if you need to ask your facilitator or your teacher’s assistance for better understanding of the lesson. At the end of each module, you need to answer the post-test to self-check your learning. Answer keys are provided for each activity and test. We trust that you will be honest in using these. In addition to the material in the main text, Notes to the Teacher are also provided to our facilitators and parents for strategies and reminders on how they can best help you on your home-based learning. Please use this module with care. Do not put unnecessary marks on any part of this SLM. Use a separate of paper in answering the exercises and tests. And read the instructions carefully before performing each task. If you have any questions in using this SLM or any difficulty in answering the tasks in this module, do not hesitate to consult your teacher or facilitator. Thank you.  What I Need to Know This module was designed and written with you in mind. It is here to help you master the skills in subtracting decimals and mixed decimals through ten thousandths. 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. The module is divided into two lessons, namely:  Lesson 1 – Subtracting Decimals and Mixed Decimals through Ten Thousandths without Regrouping  Lesson 2 – Subtracting Decimals and Mixed Decimals through Ten Thousandths with Regrouping After going through this module, you are expected to: 1. subtract decimals and mixed decimals through ten thousandths without regrouping; (M6NS-Id-106.2) 2. subtract decimals and mixed decimals through ten thousandths with regrouping; (M6NS-Id-106.2) and 3. solve one or more steps routine and non-routine problems involving addition and/or subtraction of decimals and mixed decimals using appropriate problem-solving strategies and tools. (M6NS-Id-108.2) 2 CO_Q1_Mathematics6_Module6  What I Know Find the value of N. Write in column and subtract. Write your answers on your answer sheet. Example: 89.3926 – 16.0103 = N Solution: 89.3926 - 16.0103 73.3823 1.) 23.6739 – 2.3219 = N 2.) 56.9035 – 22.8012 = N 3.) 229.5629 – 118.0019 = N 4.) 5 009.2896 – 1 008.1154 = N 5.) 59.0391 – 48.02 = N 6.) 31.5069 – 21.4041 = N 7.) 78.0919 – 23.0010 = N 8.) 52.7306 – 3.0004 = N 9.) 639.7901 – 308.680 = N 10.) 56.9270 – 22.9170 = N 3 CO_Q1_Mathematics6_Module6  Subtracting Decimals and Lesson Mixed Decimals through 1 Ten Thousandths Without Regrouping In this lesson you will learn how to subtract decimals through ten thousandths without regrouping. What’s In Subtract the following. Write your answers on your answer sheet. 1) 0.973 3) 9.698 - - 6.540 0.540 2) 0.489 4) 298.830 - - 120.200 0.270 What’s New Read the problem and try to understand it. Joyce loves to take a walk from home to school every morning. The distance of school from their home is 2.6793 kilometers. Before going to school, her mother asked her to deliver the bread to her aunt on the next block which is 1.3201 kilometers away from their home. How many kilometers she needs to walk from her aunt’s house to school? 4 CO_Q1_Mathematics6_Module6  What is It What is asked in the problem? Can you solve the given problem? What process will you use to find the answer? Here are the steps to solve it.  Write and arrange the numbers vertically. Align the decimal points. 2.6793 - 1.3201  Subtract the ten thousandths place. 2.6793 - 3 1  2 1.3201 2  Subtract the thousandths place. - 2.6793 90 9 1.3201 92  Subtract the hundredths place. 2.6793 - 725 1.3201 592 5 CO_Q1_Mathematics6_Module6  Subtract the tenths place. 2.6793 - 63 3 1.3201 3592  Place the decimal point. 2.6793 - 1.3201.3592  Subtract the whole numbers. Subtract the ones. 2.6793 - 2 1  1 1.3201 1.3592 So, 2.6793 – 1.3201 = 1.592 Therefore, 1.3592 kilometers is the distance that Joyce needs to walk. 6 CO_Q1_Mathematics6_Module6  What’s More Find the value of N. Arrange the decimals vertically and perform the indicated operation. Write your answers on your answer sheet. Example: 345.6789 – 231.5702 = N Solution: 345.6789 - 231.5702 114.1087 1.) 32.569 – 21.231 = N 2.) 5.0971 – 3.0450 = N 3.) 86.789 – 2.56 = N 4.) 23.9062 – 13.8061 = N 5.) 132.9998 – 10.5390 = N What I Have Learned When two decimals are subtracted,  align the decimal points in a straight column.  use 0 as placeholder if needed.  subtract just like subtracting whole numbers.  place a decimal point in the difference.  align the decimal point in the difference with the decimal points in the minuend and subtrahend. 7 CO_Q1_Mathematics6_Module6  What I Can Do A. Find the value of N. Write your answers on your answer sheet. 1.) 28.8967 – 13.7601 = N 2.) 97.8949 – 25.0320 = N 3.) 56.3929 – 31.3008 = N 4.) What is the difference if 2.3160 subtracted from 6.5165? 5.) If 63.9813 subtracted from 93.9986, what is the difference? B. Read and solve. Show your solutions on your answer sheet. 6.) Geovy Marielle savings account balance earned ₱253.41 interest and her balance now is ₱8 998.76. How much was the balance in her savings account before she earned the interest? 7.) If you add 34.2576 to the difference of 75.6974 and 34.6671, what will be the result? Assessment Find the value of N. Write in column and subtract. Write your answers on your answer sheet. 1.) 56.9830 – 23.450 = N 6.) 329.4598 – 210.2321 = N 2.) 45.7834 – 44.7822 = N 7.) 131.0637 – 30.0527 = N 3.) 6 790.6397 – 450.5246 = N 8.) 349.3281 – 221.1140 = N 4.) 37.9076 – 4.8060 = N 9.) 0.9821 – 0.7820 = N 5.) 147.8206 – 23.6004 = N 10.) 459.0957 – 213.0931 = N 8 CO_Q1_Mathematics6_Module6  Additional Activities A. Find the value of N. Write your answers on your answer sheet. 1.) 42.8986 – 2.3783 = N 2.) 65.9341 – 22.9231 = N 3.) 562.9120 – 430.6010 = N 4.) 72.1274 – 12.0021 = N 5.) 1 432.5228 – 21.422 = N B. Solve the following problems. Show your solution on your answer sheet. 6.) Mang Jose needs ₱8 569.98 to buy plane tickets for a family vacation in Manila. He has saved ₱4 318.75 for the plane ticket. How much more does he need for the plane ticket? 7.) The highest temperature yesterday was 19.99oC? The lowest temperature was 14.66oC. Find the difference between these two temperatures. 8.) Flor a fruit vendor buys 56.205 kilograms of mangoes to increase her stocks. She has now a total stock of 97.6081 kilograms of mangoes. How many kilograms are there on her stocks before adding her new stocks? 9.) The narra tree is 25.789 meters tall. The mango tree is 3.362 meters shorter than the narra tree. How tall is the mango tree? 10.) Portia deposits ₱234.85 in her savings account. She has now a total of ₱1,479.97 in her account. How much was her account before the deposit? 3 CO_Q1_Mathematics6_Module6 CO_Q1_Mathematics6_Module6 4 What I Know What's More Assessment 1) 21.3520 1) 11.338 1) 33.533 2) 34.1023 2) 2.0521 2) 1.0012 3) 111.5610 3) 84.229 3) 6 340.1151 4) 4 001.1742 4) 10.1001 4) 33.1016 5) 11.0191 5) 122.4608 5) 124.2202 6) 10.1028 6) 119.2277 7) 55.0909 8) 49.7302 What I Can Do 7) 101.011 9) 331.1101 8) 128.2141 A. 9) 0.2001 10) 34.01 10) 246.0026 1) 15.1366 What’s In 2) 72.8629 Additional Activities 3) 25.0921 1) 0.433 4) 4.2005 A. 2) 0.219 3) 3.158 5) 30.0173 1) 40.5203 4) 178.630 2) 43.0110 B. 3) 132.311 4) 60.1253 6) ₱8 745.35 5) 1 411.1008 7) 75.2879 B. 6) ₱4 251.23 7) 5.33oC 8) 41.4031 kilograms 9) 22.427 meters 10) ₱1 245.12 Answer Key  What I Know Find the value of N. Write in column and subtract. Regroup if necessary. Write your answers on your answer sheet. Example: 79.3216 – 16.0107 = N Solution: 01 79.3216 - 16.0107 63.3109 1.) 96.8902 – 23.7810 = N 2.) 390.1289 – 210.3860 = N 3.) 9.2896 – 8.1159 = N 4.) 56.9012 – 29.8901 = N 5.) 99.0391 – 48.12 = N 6.) 321.4041 – 316.3029 = N 7.) 689.092 – 345.191 = N 8.) 639.7901 – 308.680 = N 9.) 22.8012 – 13.0092 = N 10.) 3 890.23 – 26.2369 = N 5 CO_Q1_Mathematics6_Module6  Subtracting Decimals and Lesson Mixed Decimals through 2 Ten Thousandths With Regrouping This lesson will help you understand the skills in subtracting decimals and mixed decimals through ten thousandths with regrouping. What’s In “Climb the Ladder” Find the value of n by getting the difference of the given numbers. Write your answers on your answer sheet. Congratulations! 5.) 17.395 – 9.267 = n 4.) 90.475 – 0.383 = n 3.) 22.750 – 0.249 = n 2.) 109.868 – 1.094 = n 1.) 26.793 – 0.026 = n What’s New Read and understand the problem. Jacob went to the department store to buy a pair of shoes. He bought a pair of shoes for ₱245.78. He gave the cashier the amount of ₱250.00. How much change did he receive? 6 CO_Q1_Mathematics6_Module6  What is It What information is given in the problem? How are you going to solve for it? Here are the steps to solve it.  Write and arrange the numbers vertically. Align the decimal points. Fill in the empty spaces with zero. 250.00 - 245.78  Subtract from right to left, column by column. Regroup if necessary. 4 9 9 10 250.00 - 245.78 004.22 Subtract the decimal numbers.  Start with hundredths.  tenths  Write the decimal point. Subtract the whole numbers.  ones  tens  hundreds So, ₱250.00 – ₱245.78 = ₱4.22. Therefore, Jacob’s change is ₱4.22. 7 CO_Q1_Mathematics6_Module6 Now that you are already familiar with the steps on how to subtract decimals without or with regrouping, you can move on studying the problem below. Example 1: Mrs. Aligado has ₱2 457.95 in her purse. Her daughter asked her to buy their food supply and she spent ₱1 236.05. How much money had she left? To solve the problem above, follow these steps: Understand: a. What is asked? Answer: The amount of money that is left. b. What are the given facts? Answer: ₱2 457.95 - the money in her purse ₱1 236.05 - the money spent for the food supply Plan: a. What is the operation to be used? Answer: subtraction b. What is the number sentence? Answer: ₱2 457.95 – ₱1 236.05 = N Solve: Show your computation: Subtract ₱2 457.95 – ₱1 236.05 = N 1. Line up the decimal points 2457.95 - 1236.05 8 CO_Q1_Mathematics6_Module6  2. Subtract the numbers. Regroup if needed. 2457.95 - 1236.05 1221.90 Answer: ₱1 221.90 is the amount of money left with Mrs. Aligado. Check: Check your answer. This is one way on how to check if the answer is correct. 1236.05 the money spent for food supply + the money left with Mrs. Aligado 1221.90 2457.95 the money inside her purse Example 2: The cost of apples and grapes is ₱235.50. The grapes cost ₱93.50 more than the apples. Find the cost of the grapes. To solve the problem above, follow these steps: Understand: a. What is asked? Answer: The cost of the grapes b. What are the given facts? Answer: ₱235.50 - the cost of apples and grapes ₱93.50 - the cost of grapes more than the apples Plan: a. What is the word/phrase clue? Answer: cost of the grapes c. What is the operation to be used? Answer: subtraction, division and addition 9 CO_Q1_Mathematics6_Module6  d. What strategy you are going to use? Answer: Block Model Strategy Solve: To find for the cost of the grapes you will solve the problem by using the block model strategy. Apple = ₱235.50 Grapes = ₱93.50 In the illustration above, the total cost of two equal units and the other bigger unit which is P93.50 is P235.50. 2 of + ₱93.50 = ₱235.50 Notice that out of 3 units, the bigger unit is ₱93.50 while the other 2 equal units don’t have value yet. That’s what you will solve for. To solve for the 2 equal units, you need to take away ₱93.50 from ₱235.50. 2 of = ₱235.50 – ₱93.50 2 of = ₱142.00 Then, for the value of 1 unit, you need to divide P142.00 by 2. 1 = ₱142.00 ÷ 2 1 = ₱71.00 So, you can say now that each unknown or equal unit is ₱71.00. This time you place value to each block and solve for the cost of each fruit. To get the cost of each fruits, you need to substitute the value of each unit. For the apples, it is understood that 1 unit is equal to ₱71.00. For the grapes, add the value of the smaller unit which is ₱71.00 to the bigger unit which is ₱93.50. Apples ₱71.00 = ₱71.00 Grapes ₱71.00 ₱93.50 = ₱164.50 Therefore, the cost of grapes is ₱164.50. 10 CO_Q1_Mathematics6_Module6  Check: This is one way on how to check if the answer is correct. ₱164.50 Cost of the grapes + ₱ 71.00 Cost of apples ₱235.50 Total cost of apples and grapes ₱164.50 Cost of the grapes - ₱ 71.00 Cost of apples ₱ 93.50 Therefore, the cost of grapes is ₱93.50 more than the cost of apples. What’s More Arrange the decimals vertically and subtract the following mixed decimals. Write your answers on your answer sheet. Example: 397.6819 – 242.2348 = N Solution: 71 397.6819 - 242.2348 155.4471 1.) 34.9849 – 0.5923 = N 2.) 76.9078 – 65.4079 = N 3.) 139.9619 – 36.2835 = N 4.) 114.983 – 23.8646 = N 5.) Jessie has 8.5 kilograms of fish more than Shiela. They have 39.5 kilograms of fish altogether. Find the weight of fish Jessie has. 11 CO_Q1_Mathematics6_Module6  What I Have Learned When two decimals are subtracted,  align the decimal points in a straight column.  use 0 as placeholder if needed.  subtract just like subtracting whole numbers. Regroup if necessary.  place a decimal point in the difference.  align the decimal point in the difference with the decimal points in the minuend and subtrahend. What I Can Do A. Subtract the following mixed decimals. Write your answers on your answer sheet. 1.) 89.8996 – 43.9697 = N 2.) 28.5692 – 17.4980 = N 3.) 96.8405 – 90.6914 = N 4.) Subtract 2.523 from 5.094. 5.) What is 34.9639 decreased by 21.8991? B. Read and solve the problems. Write your answers on your answer sheet. 6.) Marvie saved ₱1 755.45 from her earnings from selling calamansi juice each month. On the first month, she saved ₱585.45. On the second month, she saved ₱195.45 less than the first month. And on the third month she saved twice as much as the second month. How much money did she save in the second month? And on the third month? 7.) A working table is 5.3854 feet long. It is to be extended just a little to 8.0732 feet. How long does it extend? 12 CO_Q1_Mathematics6_Module6  Assessment Find the value of N. Write in column and subtract. Write your answers on your answer sheet. 1.) 98.30 – 23.9045 = N 2.) 7.8354 – 4.7822 = N 3.) 970.6937 – 450.5246 = N 4.) 67.6709 – 29.8915 = N 5.) 127.2866 – 23.6974 = N 6.) 674.9145 – 219.2328 = N 7.) 182.6032 – 109.0527 = N 8.) 493.8321 – 227.1140 = N 9.) 45.9021 – 20.7829 = N 10.) Zyah, Kara and Shaina have ₱457.75 together. Kara has ₱15.25 more than Zyah, and Shaina has twice as much money as Kara. How much money does each of them have? Additional Activities A. Subtract the following mixed decimals. Write your answers on your answer sheet. 1.) 52.8982 – 22.3783 = N 2.) 56.4391 – 33.9831 = N 3.) 1 562.8340 – 40.6719 = N 4.) 291.2304 – 82.0921 = N 5.) 2.5268 – 1.432 = N 13 CO_Q1_Mathematics6_Module6 B. Solve the following problems. Write your answers on your answer sheet. 6.) Lalyn has ₱550.75 but she owes Collin ₱1100.55. She received a certain amount as gift. After paying her debt, she had ₱1 200.00 left. How much did she receive? 7.) A pail holds 7.23 liters of water. A water container holds 4.96 liters less water than the pail. What is the volume of water in the water container? 8.) You are craving for mango float. Your recipe needs 3.5 kilograms of mangoes. If you have 1.783 kilograms of mangoes, how many more kilograms do you need? 9.) The textile store had to restock their supply of materials. The store owner ordered 320.25 meters of new materials which were delivered on Saturday. On Monday, they sold 35.473 meters of the new stock. On Tuesday, they sold 44.599 meters, and on Wednesday 63.756 meters. How many meters of materials were left for the next day/s? 10.) The distance between two consecutive nails in the inner and outer square frames is 1.35 centimeters. Alice used 20 equidistant nails around the bigger frame. What is the difference in the perimeter of the outer frame and the inner frame? (Figures are not drawn to scale.) 1.35 cm 14 CO_Q1_Mathematics6_Module6 CO_Q1_Mathematics6_Module6 15 Most Essential Learning Competencies (MELC) in Mathematics 6  Reference: What I Know What's More Assessment 1) 73.1092 1) 34.3926 1) 74.3955 2) 179.7429 2) 11.4999 2) 3.0532 3) 1.1737 3) 103.6784 3) 520.1691 4) 27.0111 4) 91.1184 4) 37.7794 5) 50.9191 5) 24 kilograms 5) 103.5892 6) 5.1012 6) 455.6817 7) 343.901 7) 73.5505 8) 331.1101 8) 266.7181 9) 9.792 What I Can Do 9) 25.1192 10)3 863.9931 A. 10)Zyah-₱103.00 Karah-₱118.25 What’s In 1) 45.9299 Shaina-₱236.50 2) 11.0712 1) 26.767 3) 6.1491 Additional Activities 2) 108.774 4) 2.571 3) 22.501 5) 13.0648 A. 4) 90.092 1) 30.5199 5) 8.128 B. 2) 22.456 3) 1 522.1621 6) 2nd month-₱390.00 4) 209.1383 3rd month-₱780.00 5) 1.0948 7) 2.6878feet B. 6) ₱1 749.80 7) 2.27 liters 8) 1.717 kilograms 9) 176.422 meters 10)10.8 centimeters Answer Key For inquiries or feedback, please write or call: Department of Education - Bureau of Learning Resources (DepEd-BLR) Ground Floor, Bonifacio Bldg., DepEd Complex Meralco Avenue, Pasig City, Philippines 1600 Telefax: (632) 8634-1072; 8634-1054; 8631-4985 Email Address: [email protected] * [email protected] 16 CO_Q1_Mathematics6_Module6