Mathematics Quarter 3 – Module 4: Representing, Comparing and Arranging Dissimilar Fractions 3
Mathematics – Grade 3 Alternative Delivery Mode Quarter 3 – Module 4: Representing, Comparing and Arranging Dissimilar Fractions 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. Published by the Department of Education Secretary: Leonor Magtolis Briones Undersecretary: Diosdado M. San Antonio Printed in the Philippines by ________________________ Department of Education – Region XI Office Address: F. Torres St., Davao City Telefax: (082) 291-1665; (082) 221-6147 E-mail Address: [email protected] * [email protected] Development Team of the Module Authors: Vanessa Mae A. del Monte, Mary Luz O. Fullo, Noel T. Porquillo Editors: Jeremias C. Ceniza, Gina G. Silvestre, Elma C. Prudente, Annie Fel Lingatong, Edgardo Dondon S. Lorenzo Reviewers: Melissa Keith A. Sarilla, Jeremias C. Gumanoy, Marites L. Caluban, Neil Edward D. Diaz, Ana Lorma A. Dahiroc Illustrators: Dennis Macaubos, Alfie Valenteros, Christian Loyd Alfuerto, Pit Ybanez Layout Artist: Ailyn Verula-Ponce Management Team: Allan G. Farnazo Alona C. Uy Mary Jeanne B. Aldeguer Maria Gina F. Flores Analiza C. Almazan Arnel S. Zaragosa Ma. Cielo D. Estrada Jeremias C. Ceniza Renato N. Pacpakin Illuminado T. Boiser
3 Mathematics Quarter 3 – Module 4: Representing, Comparing and Arranging Dissimilar Fractions
ii 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 sheet 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.
1 This module was designed and written with you in mind to help you read and write fractions that are equal to one and greater than one. The scope of this module permits it to be used in many different learning situations. The language used recognizes your diverse vocabulary backgrounds. 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 Mathematics Grade 3 learning materials you are using. After going through this module, you are expected to: 1. represent, compare and arrange dissimilar fractions in increasing or decreasing order. Enjoy your journey. Good luck! What I Need to Know
2 What I Know Choose the letter of the correct answer. Write the chosen letter on a separate sheet of paper. 1. What is the first step in ordering dissimilar fractions? a. Find the greatest common denominator b. Find the least common denominator c. Reduce the fractions to lowest term d. Compare the denominators, the greater the denominator, the greater the fraction 2. Which of the following models show the least fractional part? 3. Which of the following fractions is arranged in increasing order? a. 3 8 2 6 9 12 1 2 c. 2 6 3 8 1 2 9 12 b. 1 2 2 6 3 8 9 12 d. 9 12 3 8 2 6 1 2 a. d. c. b.
3 4. Which of the following fractions is arranged in decreasing order? a. 4 5 7 10 1 4 1 8 c. 1 4 7 10 1 8 4 5 b. 1 8 1 4 7 10 4 5 d. 7 10 4 5 1 4 1 8 5. It takes Nicole one-fifth of an hour to cook his lunch, fivesixths of an hour to wash the clothes, and two-thirds of an hour to clean his room. What is the order of Nicole’s time spent to complete by chore in ascending order? a. washing, cooking, cleaning b. cooking, washing, cleaning c. cleaning, washing, cooking d. cooking, cleaning, washing
4 Lesson Represents, Compares and Arranges Dissimilar Fractions in Increasing or Decreasing Order Fractions can be classified in different ways. There are two kinds of fractions when classified according to the relationship of the denominators in the set. When the denominators are the same, it is called Similar Fractions. When the denominators are not the same, it is called Dissimilar Fractions. In this module, you will learn how to represent and arrange dissimilar fractions in increasing or decreasing order. What’s In Let’s Review Activity 1 A. Find the Least Common Multiple (LCM) of numbers below. Follow the directions. 1. Multiples of 9 = ….. Multiples of 6 = ….. The common multiple is __________. The LCM is __________. 9 18 6 12
5 2. Multiples of 5 = ….. Multiples of 10 = ….. The common multiple is __________. The LCM is __________. 3. Multiples of 3 = ….. Multiples of 5 = ….. Multiples of 15 = ….. The common multiple is __________. The LCM is __________. 4. Multiples of 4 = Multiples of 10 = Multiples of 20 = The common multiples are __________. The LCM is __________. 5. Multiples of 6 = Multiples of 8 = Multiples of 12 = Multiples of 24 = The common multiples are __________. The LCM is __________. 5 10 10 20
6 B. Encircle the equivalent fraction of the given fraction. 1.) 2 3 ( 4 9 10 15 11 12 ) 4.) 15 35 ( 6 21 3 7 5 14 ) 2.) 4 8 ( 16 24 20 40 8 12 ) 5.) 12 20 ( 3 4 3 5 2 10 ) 3.) 1 6 ( 4 24 3 15 2 9 ) What’s New Modelling is one way to present fractions. When there is a visual representation you can easily determine the value of each fraction. Thus, arranging the fractions in increasing (least to greatest) or decreasing order (greatest to least) will be easier for you. Consider the problem below. Jimboy, Jaja and Via were given a pizza each. Jimboy was able to finish of the pie. Jaja consumed of the pie, while Via ate of the pie. Who ate less? You can draw a model and order the fractions , and . The model can help you decide which fraction comes first, next and last. 3 4 1 2 2 3 3 4 1 2 2 3
7 From the illustration, you can see that is less than and is less than . Thus the order of the fractions in increasing order is , , . So, who ate less? It’s Jaja since she only ate of the pizza. Activity 2 Answer the following activity by looking at the fraction strip. 3 4 2 3 1 2 1 2 2 3 2 3 3 4 1 2 2 3 3 4 Jimboy Jaja Via 1 2
8 How to use the fraction strip? Fraction strips are rectangular strips that represent different part of the fraction that when added make up a whole. The example below shows how to use the fraction strips. Example: Arrange 2 12 , 3 8 and 4 6 in increasing order. 3 8 is 2 12 is 4 6 is Therefore, the arrangement is , and from least to greatest. Order the fractions in increasing order. 1.) 1 3 4 9 3 10 1 12 ___________________________ 2.) 11 12 3 4 7 8 2 3 ___________________________ 3.) 2 9 3 6 4 5 2 8 ___________________________ Order the fractions in decreasing order. 4.) 1 4 2 9 3 8 1 2 ___________________________ 5.) 9 12 8 10 4 6 3 5 ___________________________
9 What is It A. Representing Dissimilar Fractions We can represent dissimilar fractions through visualization as shown below. Error! Error! Error! As shown, the three rectangles are of the same size divided into different number of parts. The first rectangle is divided into two equal parts with one shaded portion (Error!), the second one is divided into four equal parts with three shaded portions (Error!) and the third one is divided into three equal parts, with two portions shaded (Error!). You will see that when a whole is divided into several equal parts, each part becomes smaller. Notice that the divided parts of each figure are dissimilar in sizes compared to the divided parts of the other two figures. The three different ways of dividing the parts of a rectangle above demonstrate dissimilar fractions. Different Number of Divided Parts
10 B. Comparing Dissimilar Fractions We can compare dissimilar fractions using the symbols “>” greater than or “<” less than. It is easy to compare dissimilar fractions when fractions are illustrated in figures. See example below. Compare the following fractions: 1 2 1 3 1 4 1 5 Look at the fractions. You may say that each of them has a numerator of 1 while their denominators are different. From the illustration, we can clearly say that, 1 2 > 1 3 or 1 4 < 1 3 or 1 3 > 1 5 . We can also use the Cross Product Method when comparing dissimilar fractions especially dealing with greater number.
11 Steps of the Cross Product Method Step 1. Write the fractions vertically, next to each other with an ‘X’ between the two fractions. This helps remind you which numbers to multiply with each other. 1 3 x 1 5 Step 2. Multiply the numerator and denominator that each line of the ‘X’ connects. Write the product above the numerator you multiplied. 1 3 x 1 5 Step 3. Compare the products. The fraction in line with the greater product is the greatest among the two fractions. In our example, the product of 1 and 5 which is 5 is greater than 3 which is the product of 1 and 3. Therefore, > . C. Ordering Dissimilar Fractions In ordering dissimilar fractions without models, find the equivalent fraction using the Least Common Denominator (LCD)of the set of fractions. Example 1: Arrange , and in increasing order. i. Find the LCD using the LCM. 10 = 10, 20, 30 40 , 50 8 = 8, 16, 24, 32, 40 5 = 5, 10, 15, 20, 25, 30, 35, 40 LCD= 40 5 10 1 5 3 8 5 3
12 ii. Find the Equivalent Fraction to make the fractions Similar. Use the LCD as the denominator. 5 = 5 x 4 = 20 10 10 x 4 40 LCD 3 = 3 x 5 = 15 8 8 x 5 40 LCD 1 = 1 x 8 = 8 5 5 x 8 40 LCD iii. Compare the numerators. The lesser the numerator, the lesser the fraction. Therefore, the order of the given fractions in increasing order is 1 , 3 , 5 5 8 10 Example 2: Arrange , , and in decreasing order. i. Find the LCD using the LCM. 4 = 4, 8, 12, 16, 20, 24 24 = 24, 48, 72, 12 = 12, 24, 36, 48, 60 8 = 8, 16, 24, 42, 40 LCD= 24 3 4 7 24 5 8 11 12
13 ii. Find the Equivalent Fraction to make the fractions Similar. Use the LCD as the denominator. 3 = 3 x 6 = 18 4 4 x 6 24 LCD 7 = 7 x 1 = 7 24 24 x 1 24 LCD 11 = 11 x 2 = 22 12 12 x 2 24 LCD 5 = 5 x 3 = 15 8 8 x 3 24 LCD iii. Compare the numerators. The greater the numerator, the greater the fraction. Therefore, the order of the given fractions in decreasing order is 11 , 3 , 5 , 7 12 4 8 24
14 What’s More Activity 3 Using the shapes provided below, create a pair of dissimilar fractions for each number by dividing each given shape into equal parts and shading some parts then write the fraction of the shaded parts and compare the two fractions using > or < in the box provided. Shape 1 Shape 2 1. _____ _____ 2. _____ _____ 3. _____ _____
15 Activity 4 A. Write the fraction of the shaded parts of each figure and arrange them in increasing order. 1.) ______ _____ _____ _____ ________________________________________________________ 2.) ______ _____ _____ _____ ________________________________________________________ 3.) ______ _____ _____ _____ ________________________________________________________ B. Arrange the fraction of each models in decreasing order. 4.) ______ _____ _____ _____ ______________________________________________________ 5.) ______ _____ _____ _____ _____________________________________________________
16 Activity 5 A. Arrange the fractions in increasing order. 1.) 1 12 8 9 2 6 2 3 ___________________________ 2.) 2 3 1 2 4 4 9 12 ___________________________ 3.) 1 2 3 4 5 8 2 10 ___________________________ B. Arrange the fractions in decreasing order 4.) 4 6 7 12 9 24 1 4 ___________________________ 5.) 8 10 23 25 74 100 4 20 ___________________________ What I Have Learned To arrange dissimilar fractions through visualization, we can use fraction models or fractions strips for representation of each fraction. To arrange dissimilar fractions, follow the following step. 1. Find the Least Common Denominator (LCD) of the given fractions. 2. Find the equivalent fractions of the given fraction using the LCD as the new denominators. 3. Compare the numerators of the new formed fractions. The lesser the numerator, the lesser the value of the fraction. The greater the numerator, the greater the value of the fraction.
17 What I Can Do I. Arrange the fractions in increasing order. 1.) 1 3 3 8 3 12 5 7 2.) 3 5 5 10 2 6 7 9 ____________________ __________________ __________________ II. Shade the given fractions using the fraction strips. Arrange the fractions in decreasing order. 1. 1 2 7 8 2 7 3 5 2.) 9 12 5 6 3 8 4 9 ____________________
18 III. Put a check (√ ) mark on the box provided in each set of fractions that are arranged properly. If it is arranged properly, identify if it is in increasing or decreasing order. 1___________________ 2___________________ 3___________________ 4___________________ 5___________________ 7 7 7 7 6 5 4 2 4 7 9 10 5 15 10 12 4 2 1 3 5 3 2 8 1 3 6 5 6 4 7 3 9 1 1 3 10 8 5 4
19 Assessment Choose the letter of the best answer. Write the chosen letter on a separate sheet of paper. 1. Which of the following models show the least fractional part? a. 1 3 b. 2 8 c. 4 6 d. 3 10 2. Which fraction is the greatest? a. 3 4 b. 9 10 c. 2 3 d. 3 7 3. Identify the set arranged in increasing order. a. 1 4 2 3 3 5 2 6 c. 2 6 1 4 3 5 2 3 b. 2 3 3 5 1 4 2 6 d. 3 5 2 3 2 6 1 4 4. Which of the following fractions is arranged in decreasing order? a. 2 5 3 8 1 4 c. 2 4 4 8 6 10 b. 5 30 3 12 4 15 d. 6 8 1 4 1 2 5. JJ, RJ, PJ and LA raced a distance of 1 mile. Here is their time record in fractions of an hour: JJ - , RJ - , PJ - , LA - . Give the names in increasing order of finishing time. a. JJ, PJ, LA, RJ c. LA, RJ, PJ, JJ b. JJ, RJ, PJ, LA d. JJ, LA, RJ, PJ 1 4 5 12 4 15 , 6 20
20 Additional Activities Solve the following problems. 1.) Mrs. Padla bought kg of beans, kg of cabbage and Kg of carrots. Which kind of vegetable did she buy the most? 2.) Tina ran the 200 – meter dash in minutes, Chelsea ran it in minutes and Erica ran it in minutes. Who ran the slowest? 3.) Mang Pepe planted of his garden plot with squash, with eggplant and with tomatoes. Which among the three plants has the largest area in the plot? 4.) It takes Chen four-fifths of an hour to complete his math homework, one-sixth of an hour to complete his reading homework, and two-thirds of an hour to complete his science homework. Arrange the time spent to complete Chen's homework by subject in decreasing order. 5.) Sehun jogged for one-third of a mile, Luhan jogged for one-half of a mile, and Kai jogged for one-fifth of a mile. Arrange these distances in increasing order. 4 5 5 3 8 9 4 15 5 12 12 4 5 4 8 9 24 2 6
21 Answer Key Assessment B 1. B 2. C 3. C 4. A 5. Additional Activity carrots 1.) Tina 2.) squash 3.) Math, science, 4.) Reading 1 , 1 , 1 5.) 3 2 5 What I Can Do I 5 , 3 , 1 , 3 1. 12 3 8 7 7 , 3 , 5 , 1 2. 10 5 9 6 II 2 , 1 , 3 , 7 1. 5 2 7 8 4 , 3 , 6 , 5 2. 12 8 9 6 III decreasing / 1. 2. decreasing / 3. increasing / 4. 5. What’s More Activity 5 1 , 2 , 2 , 8 1. 9 3 6 12 1 , 2 , 9 , 4 2. 4 12 3 2 2 , 1 , 5 , 3 3. 4 8 2 10 1 9 7 4 4. 6 12 24 4 4 , 8 , 74 , 23 5. 25 100 10 20 What’s New 1. 1 12 3 10 1 3 4 9 2. 2 3 3 4 7 8 11 12 3. 2 9 2 8 3 6 4 5 4. 1 2 3 8 1 4 2 9 5. 8 10 9 12 4 6 3 5 What’s More Activity 3 Answers may vary Activity 4 1. ¼, 3 7 ൗ , ½, 5 5 ൗ 2. 1 5 ൗ , 2 7 ൗ , 3 8 ൗ , 5 6 ൗ 3. 1 4 ൗ , 5 5 ൗ , 6 12 ൗ , 2 3 ൗ , 5 6 ൗ 4. 7 8 ൗ , 2 3 ൗ , 1 4 ൗ , 2 9 ൗ 5. 3 4 ൗ , 7 10 ൗ , 1 2 ൗ , 2 5 ൗ n Cont. What's I 28, , 24 , 20 , 16 , 12 , 8, 4 4. 4 0 , 36 , 32 , 60 , 50 , 40 , 30 , 20 , 10 100 90, 80, , 70 100 , 80 , 60 , 40 , 20 , 140 , 120, 130 , 110 , 180, , 160, 170 150, 200 20 LCM 20 40 CM , 36 , 30 , 24 , 18 , 12 , 6 5. , 48 42, , 48 , 40 , 32 , 24 , 16 , 8 64 , 56 72, , 60 , 48 , 36 , 24 , 12 96 , 84 48, 72, 96, 120, , 24 168, 192 144, 24 LCM 24 48 CM ctivity 1 B A 1. 10 15 2. 20 40 3. 4 24 4. 3 7 5. 3 5 What I Know B 1. C 2. B 3. A 4. D 5. n What's I ctivity 1 A A 45 , 36 , 27 1. 30 , 24 , 18 18 LCM 18 CM 15, 20, 25 2. 30, 40, 50 10 LCM 10 20 CM 18 , 15 , 12 , 9, 6, 3 3. 30 , 52, 20 , 15 , 10 , 5 90 , 57, 60 , 45 , 30 , 15 15 LCM 15 CM
22 References Mathematics – Grade 3, Learner’s Manual. First Edition. Visualizing Dissimilar Fractions. Retrieved from https://www.slideshare.net/edithahonradez/3-math-lm-q3 Mathematics – Grade 3, Learner’s Manual. First Edition. Arranging Dissimilar Fractions. Retrieved from https://www.slideshare.net/edithahonradez/3-math-lm-q3
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