Q1 ADM G6 MATH PDF

6 Mathematics Quarter 1 1  6 Mathematics Quarter 1 This instructional material was collaboratively developed and reviewed by educators from public. We encourage...

6 Mathematics Quarter 1 1  6 Mathematics Quarter 1 This instructional material was collaboratively developed and reviewed by educators from public. We encourage teachers and other education stakeholders to email their feedback, comments, and recommendations to the Department of Education at action@ deped.gov.ph. We value your feedback and recommendation. Department of Education Republic of the Philippines 2 Mathematics- Grade 6 Alternative Delivery Mode Quarter 1 – Fractions and Decimal Numbers 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 royalty. 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 – Division of Las Pinas City Schools Division Superintendent: Joel T. Torrecampo.CESO VI Development Team of the Module Management Team Chairperson: Joel T. Torrecampo, Ph.D., CESO VI Schools Division Superintendent Co-Chairperson: Juan C. Obierna Assistant Schools Division Superintendent- OIC Reviewer/s Gina I. Aguitez- EPS Mathematics AUTHORS: Lesson 1 Necie P. Valledor Lesson 5 Reyland O. Dumlao Ilaya Elementary School Moonwalk Elementary School Lesson 2 Resly F. Dumasapal Lesson 6 Annabelle S. Tenorio Pulanlupa Elementary School Mikesell Elementary School Lesson 3 Rowena B. Kis-ing Lesson 7 Richie Macalanda Talon Elementary School Golden Acres Elementary School Lesson 4 Liezle R. Bautista Lesson 8 Erwin O. Escalante Daniel Fajardo Elementary School Pamplona Elementary School Central Consultant: Joseph F. De Leon/ Nora Cepeda Content Validator: Amador R. Ayapana Language Validator: Mary Jane D. Ayapana Lay-out Artist: Myrrh Estela G. Ramirez Printed in the Philippines by Department of Education – Division of Las Pinas City Office Address: Padre Diego Cera, E. Aldana, Las Pinas City, E-mail Address: www.depedlaspinas.ph 3  Table of Contents Preface Lesson 1 Adds and subtracts simple fractions and mixed numbers without or with regrouping ,p. 6 Solves routine and non-routine problems involving addition and/or subtraction of fractions using appropriate problem solvingstrategies and tools. Lesson 2 Multiplies simple fractions and mixed fractions, p.12 Solves routine or non-routine problems involving multiplication without or with addition or subtraction of fractions and mixed fractions Lesson 3 Divides simple fractions and mixedfractions, p.17 Solves routine or non-routine problems involving division without or with any of the other operations of fractions and mixed fractions Lesson 4 Adds and subtracts decimals and mixed decimals through ten thousandths withoutor with regrouping, p.19 Solves 1 or more steps routine and non- routine problems involving addition and/or subtraction of decimals and mixed decimals Lesson 5 Multiplies decimals and mixed decimalswith factors up to 2 decimal places, p.21 Multiplies mentally decimals up to 2decimals places by 0.1, 0.01,10, and 100. Solves routine and non-routine problems involving multiplication of decimalsandmixed decimals including money Lesson 6 Solves multi-step problems involving multiplication and addition or subtraction of decimals, mixed decimals and whole numbers including money, p.27 Lesson 7 Divide whole numbers by decimals up to 2 decimal places and viceversa, p.32 Divide decimals/mixed decimals up to 2decimalplaces Divides decimalsup to 4 decimal places by 0.1, 0.01, and 0.001 Divides decimals up to 2 decimal places by 10, 100, and 1 000 mentall Lesson 8 Differentiates terminating from repeating,non-terminating decimal quotients, p.37 Solves routine and non-routine problems involving division of decimals, mixed decimals, and whole numbers including money 4  Preface Dear Pupils, This module, Mathematics 6 Quarter 1 - Module 1 is written to further enhance your critical thinking and develop the love of mathematics. This acquired skill would soon be applied in your everyday lives. This module covers the concepts of Addition and Subtraction of Decimals. These topics are presented in such a way that they are easy to understand and visualize. The following are the special and unique features of this module: WHAT I NEED TO KNOW. This part presents the competency or the objective that each learner should know and master. WHAT’S NEW. T. it his part of the module presents the content input of the topic that will be discussed. WHAT IS IT. This contains the discussions of the topic which include illustrative examples of the lesson. WHAT’S MORE. In this part, the first activity will be given to each learner. WHAT I HAVE LEARNED. Another activity will be answered by the pupils. ASSESSMENT. This is the last part of each topic in which another activity will be given and answered by the learners to assess if each of them learned and mastered the skill. Learning Mathematics is fun. It is not as difficult as you think. We hope this module can help you explore the world of mathematical concept in relation to your everyday life. Adding and Subtracting Fractions and 5  Lesson 1 Mixed Numbers without or with Regrouping Solving Routine and Non-Routine Problems involving Addition and/or Subtraction of Fractions What I Need to Know In this module, the learners will be dealing with adding and subtracting simple fractions and mixed numbers with regrouping. As pre-requisites, the learners will be able to master adding and subtracting fractions and mixed numbers without regrouping. It is also important that the learners must have the knowledge on how to find the LCM or least common multiple to get the LCD or least common denominator of the dissimilar denominators and change them to similar fractions. Furthermore, additional exercises should be provided in this lesson as needed particularly when reinforcing the concept and skill and application to new and other situation to ensure mastery and accuracy of addition and subtraction of fractions with regrouping. After going through this module, you are expected to: 1. Adds and subtracts simple fractions and mixed numbers without or with regrouping 2.. Solves routine and non-routine problems involving addition and/or subtraction of fractions using different strategies What I Know Perform the indicated operations. Express the answers in simplest form. 1. 3/5 + 1/7 = ____________ 4. 9/11 - 4/8 = ____________ 2. 1/6 + 2/3= ____________ 5. 11 2/5 - 8 5/6 = _________ 3. 6 3/5 + 5 1/4 = ________ Problem 1 Ana needs 1/3m of ribbon to be used for decorating her gift to her friend and another 2/5m of ribbon to be used for decorating another gift for her other friend. How many meters of ribbon does she need in all? What’s the Point? Divide a 1meter ribbon into 3 parts and take 1/3 of it. 6  1/3 1/3 1/3 Divide another 1meter ribbon into 5 parts and take 2/5 of it. 1/5 1/5 1/5 1/5 1/5 Combine the 1/3m and 2/5m of ribbon. 1/3 + 2/ 1/3 1/5 1/5 1 2 3 4 5 1 2 3 4 5 6 1 1 1 1 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 5/15 + 6/15 = 11/15 Therefore, the result when you combine 1/3 and 2/5 is 11/15. Hence, Ana needs 11/15m of ribbon for decorating her gifts for her friends. To add or subtract dissimilar fractions, use the following steps. Step 1: Make the fraction similar by finding the LCD. Step 2: Add or Subtract the similar fractions. Step 3: Express the answer in lowest terms if needed. Example: Find the sum of 4/8 + ¼. Solution Step 1: Rename into similar by finding the LCD. Make the denominator the same 1/4 = 2/8 4/8 = 4/8 so the LCD is 8 Step 2: Add the similar fractions = 6/8 Step 3: Express the answer in lowest term. 1 4 6 6 4 + 8 = 8 rename 8 𝑡𝑜 𝑙𝑜𝑤𝑒𝑠𝑡 𝑡𝑒𝑟𝑚 𝑏𝑦 𝑓𝑖𝑛𝑑𝑖𝑛𝑔 𝑡ℎ𝑒 𝐺𝐶𝐹 then divide both the numerator and denominator by the GCF. GCFactors of 6 are 2 and 3 Factors of 8 are 2 and 4 so the common factors of 6 and 8 is 2. 1 4 6 3 Therefore 4 + = 8 ÷ 2 is 4 8 Problem 2 Find the difference of 5 ¾ - 2 3/6. 7 Solution: Step 1: Rename the fraction to similar by Step 2: Subtract the Similar fractions = finding the LCD. 3/12 3 3 The denominators of 𝑎𝑛𝑑 is 4 4 6 and 6 the common denominators is Step 3: Subtract the whole numbers. 4 ----- 4, 8, 12,… 5 - 2 = 3 6 ----- 6, 12, 18, … LCD = 12 Combine the results = 3 3/12 Step 4: Express the answer in lowest term. 3 (12 ÷4 ) 𝑥 3 9 5 = = 5 12 3 3 3 1 4 12 54 − 2 = 312 ÷ 3 = 3 6 4 3 (12 ÷6 ) 𝑥 3 6 2 = = 2 12the fractions are 6 12 Therefore the difference of 5 ¾ and 2 now similar we can now subtract 3/6 is 3 1/4. To add and subtract simple fractions and mixed numbers with regrouping, you need to remember the following: Step 1: Rename to similar by finding the LCD. Step 2: Then add or subtract the similar fractions. Step 3: Express the answer in lowest term if needed. To add or subtract dissimilar mixed numbers use the following steps. Step 1: Rename to similar by finding the LCD. Step 2: Then, add or subtract the similar fractions. Step 3: Add or subtract the whole numbers and combine this with the resulting fraction. Step 4: Express the answer in lowest term if needed. Make the given pairs of fractions similar by writing the missing number inside the box. 2 = ( 8 ÷ 4 ) x 2 = ______ ->4/8 4 8 8 2 = ( 8 ÷ 8 ) x 2 = ______ ->2/8 8 8 8 8 To add and subtract simple fractions and mixed numbers with regrouping, you need to remember the following: To add or subtract dissimilar fractions use the following steps. Step 1: Make the fraction similar by finding the (LCD) Step 2: Then add or subtract the similar fractions. Step 3: Express the answer in lowest term if needed. To add or subtract dissimilar mixed numbers use the following steps. Step 1: Make the fraction similar by finding the (LCD) Step 2: Then, add or subtract the similar fractions. Step 3: Add or subtract the whole numbers and combine this with the resulting fraction. Step 4: Express the answer in lowest term if needed. What I Can do Give the LCD of the following fractions and make the fractions similar. Then add or subtract the resulting fractions. Express the answers in lowest term. Similar Fractions Sum/Difference 3 1 1. + = 5 10 5 3 2. − = 6 7 5 2 3. − = 11 5 1 5 4. + = 8 12 6 3 5. + = 10 10 9  Assessment Perform the indicated operation. Express the answers inlowest term. 1. 3/5 + 1/7 = 2. 1/6 + 2/3= 3. 6 3/5 + 5 1/4 = 4. 9/11 - 4/8 = 5. 11 2/5 - 8 5/6 = Solving routine and non-routine problems involving addition and/or subtraction of fractions using appropriate problem solving strategies and tools. Routine problems are problems which can be solved using simple step-by-step method. Non-routine problems are complex problems and can be solved using different methods or strategies. Sample Problem : Andrei spent 2/9 of his money for buying an E-tablet. He gave PhP 6 000.00 to his mother and had 1/3 of the original amount left. How much did he have at first? SOLUTION: Problem 1: E-tab 2/9 Php 6000 Money left 1/3 or 3/9 2 units for E-tablet = PhP 3 000 9 units = 9 x PhP 1 500 = PhP 13 500 4 units PhP 6 000 ÷ 4 = PhP 1 500 Andrei had PhP 13 500.00 at first Solve. Show the computation 1. Add the fractions of money she spent. 2/5 + 1/5 = 3/5 2. Subtract the total amount of money spent from her money at the beginning. 5/5 – 3/5 = 2/5 So, the fraction of money left with Lilet is 2/5. Check. Check your answer. This is one way to check if the answer is correct. 2/5 + 1/5 + 2/5 = 5/5 = 1 10  WHAT’S MORE Solve these problems. Be sure to reduce the answer to its lowest term. 1. Celia and her cousins ate 2 ¾ of a Hawaiian pizza, 7/8 of a vegetable pizza, and ½ of a pepperoni pizza. How much pizza did they eat in all? 2. Ron walked 3 ¾ km on Monday, 4 1/3 km on Tuesday and 2 7/12 km on Wednesday. What distance did he walk in all? 3. Stefanie swam four-fifths of a lap in the morning and seven-fifteenths of a lap in the evening. How much farther did Stefanie swim in the morning than in the evening? Assessment Solve the following routine problems involving addition of fractions. Be sure to reduce the answer to its lowest term. 1. John walked 1/2 of a kilometer yesterday and 3/4 of a kilometer today. How many miles has John walked? 2. Rachel rode her bike for one-fifth of a mile on Monday and two-fifths of a mile on Tuesday. How many miles did she ride altogether? 3. It took Nick five-thirds of an hour to complete his math homework on Monday, three- fourths of an hour on Tuesday, and five-sixths of an hour on Wednesday. How many hours did he take to complete his homework altogether? 4. The Cruz family drove their car for five and five-sixths days to reach their vacation home, and then drove for six and one-sixth days to return home. How much longer did it take them to drive home? 5. A carpenter had a piece of wood that was 15 feet in length. If he needs only 10 and five- twelfths feet of wood, then how much wood should he cut? 11  Multiplying SimpleFfractions and Mixed Fractions Lesson 2 Solving routine or non-routine problems involving multiplication without or with addition or subtraction of fractions and mixed fractions What I Need to Know After going through this module, you are expected to: 1. multiplies simple fraction by another simple fraction or by a mixed number. 2. solves non-routine problems involving multiplication without or with addition or subtraction of fractions and mixed fractions using appropriate problem-solving strategies and tools. What I Know Directions: Find the product of the following fraction and mixed fraction 1 2 1 1 2 1. 8 𝑥 6 3. 6 𝑥4 5. 3 𝑥2 2 3 4 4 5 1 1 6 1 2. 4 𝑥1 4. 1 𝑥3 3 8 8 5 What’s In Last time you have learned the process and the idea of subtracting fraction. You learn the process of solving routine and non-routine problems involving subtraction of fraction. In this lesson we are going to learn the process involving multiplication of fraction. The rules in multiplying fraction and the process we can relate in real life situation. 12  What is It 1. Multiplying Mixed Number by a Fraction 2. Multiplying Fraction by a whole Number Mang Jose has a piece of wood which Ana and her friend ate 1/3 of the guavas at her mother picked. If measure 3 1/5 meters. He used 3/4 of it to mother picked 6 baskets of guavas, how many baskets of guava did make a stall. How many meters of wood were they eat? left? Understand: Understand: 1 1 1 The equation is of 6 = N It means x6=N 3 3 Given: 3 5 number of meters of wood Jose has 3 fraction part of a meter to make a To solve the equation, study the given steps below. 4 stall Step 1. What is asked: Meters of wood used Express the whole number as a fraction by using 1 as its 1 6 Solve: Strategy A denominator. 3 𝑥 1 𝑇𝑦𝑝𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 ℎ𝑒𝑟𝑒. Step 1. Step 2. Change the mixed form to an improper Multiply the numerators and then multiply the 1 6 6 fraction. denominators 𝑥 = 3 𝑇𝑦𝑝𝑒 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 ℎ𝑒𝑟𝑒. 3 1 1 3 (3 𝑥 5) + 1 15 + 1 16 Step 3. 3 𝑥 = = = 5 4 5 5 5 Express your answer in lowest term, if needed or change it 6 to mixed form.3 = 2 What’s More Activity 1 Find the product then express your answer in lowest term if needed. 3 1 2 1. 10 𝑥 = 2. 2 𝑥 = 4 4 5 4 3 5 2. 𝑥 3 10 = 4. 8 𝑥 12 = 6 2 1 5. 5 7 𝑥 = 2 13 Activity 2 Multiply the fraction at the center by the fraction at the sides. Write the answer inside the box provided for. Express your answer in lowest term, if needed. 2 1 3._____ 4 3 3 4._____ 4 1 2._____ 1 3 1 5._____ 4 2 4 5 1._____ 1 4 2 What I Have Learned How do we multiply a fraction by a fraction? To multiply a fraction by a fraction a. Multiply the numerator b. Multiply the denominator c. Simplify the product to lowest term, if possible How do we multiply mixed number by a fraction? To multiply a mixed number by a fraction: a. Change mixed numbers to improper fractions b. Multiply the numerators and then multiply the denominators. c. Use cancellation, if possible. d. Express your answer in lowest term, if needed. How do we multiply a fraction by a whole number? To multiply a fraction by a whole number: a. Change the whole number into a fraction by using 1 as its denominator. b. Multiply the numerators and then the denominators. c. Use cancellation, if possible. d. Express the answer in lowest term, if needed. 14  What I Can Do Solve this Problem! Imagine that you are on your best friend’s birthday party. If there were 90 1 children at the birthday party and of them are boys, how many were girls? 3 Assessment Direction: Read and solve what is asked for 1 2 1. What is the product of 2 4 𝑥 5 =? 5 2. What is of 30? 6 4 4 3. Multiply 2 of ? 6 6 2 4. Find of 54? 3 6 5. The product if 12 and 10 is ____? Solving non-routine problems involving multiplication without or with addition or subtraction of fractions and mixed fractions What’s In To solve non-routine problems involving multiplication of fractions, you will need to remember these 4 steps Understand Plan Solve Check What is asked in the What operation/s needed to Perform the Look back if your answer problem? solve the problem? equation is correct or not What are the given facts? What is the mathematical sentence or equation? 15  What’s More Activity: Answer the following non-routine problems by using the guide questions. Problem 1 Questions: On December 13, 2019 the Grade VI -3 1. What is asked in the problem? pupils of Pulanlupa Elementary School celebrated their Christmas Party. If 2. What are the given facts? there are 50 pupils in the class, 2/5 of 3. What is the hidden question? them did not joined the party, how many 4. What operation/s are going to used? pupils joined the party? 5. What is the mathematical sentence or. equation? 6. How do you solve the problem? 7. Have you checked your answer? Problem 2 Questions The boy scouts of Pulanlupa 1. What is asked in the problem? Elementary School brought 12 meters of rope. They cut ½ of it into pieces of 2. What are the given facts? 2/3meter each. How many pieces 3. What is the hidden question? didthey make? 4. What operation/s are going to used? 5. What is the mathematical sentence or equation? 6. How do you solve the problem? Assessment Directions: Read each problem carefully. Write the letter of the correct answer on your notebook. 1. For each day of the week, Ana spends 2 1/2 hours helping in a family store. How many hours does she helps in a week? 2. In a Pulanlgupa Sari-sari Store, if 1/10 of 360 eggs were found to be rotten, how many rotten eggs were there? How many are not rotten? 3. Mr. Castro repaired two tricycles in 3 1/2 hours. He spent ½ of the time greasing the wheels. How many hours did it take him to grease the wheels? 16  Dividing Simple Fractions and Mixed Numbers Lesson 3 Solving Routine or Non-routine Problems involving Division without or with any of the other operations of Fractions and Mixed Fractions What I Need to Know After going through this module, you are expected to: 1. Divides simple fractions and mixedfractions 2. Solves routine or non-routine problems involving division without or with any of the other operations of fractions and mixed fractions using appropriate problem solvingstrategies and tools. What I Know Divide and simplify your answer. 𝟐 𝟏 𝟓 𝟒 1 1. 𝟓 ÷ 𝟖 = 3. 𝟏𝟎 ÷ 𝟏𝟔 = 5. 16 ÷ 4 5 = 3 1 2 1 2. 3 4 ÷ 2 = 4. 5 3 ÷ 3 = What’s In A. Change the following to improper fraction 2 1 4 2 3 1. 1 2. 6 3. 3 4. 11 5. 5 3 4 5 3 7 B. Give the reciprocal of the following: 2 3 2 3 1. 2. 9 3. 4. 1 3 5. 85 3 4 17  How do we divide fractions? Let’s find out…. Problem A. Solution Cora received half of a piece 𝟏 ÷𝟔 = of land. She has to divide it 𝟏 𝟔 𝟐 equaly among her 6 children. ÷ = Change whole number to improper 𝟐 𝟏 What fraction of the land will 𝟏 𝟏 𝒙 = 𝟏 Change the sign to multiplication 𝟐 𝟔 𝟏𝟐 each of her children receive? and invert the divisor (Keep the dividend , change the sign , flip the divisor.(KCF) 𝟏 𝟏 𝟔𝟏 𝟏 𝟏 𝟏 ÷ 𝟔 = ÷ 𝒙 = = 𝟐 𝟐 𝟏𝟐 𝟔 𝟏𝟐 𝟏𝟐 Problem B. Solution (KCF) 𝟑 𝟓 𝟑 𝟓 𝟑 𝟔 𝟏𝟖. ÷ = ÷ = 𝐱 = Keep the dividend, 𝟖 𝟔 𝟖 𝟔 𝟖 𝟓 𝟒𝟎 𝟑 𝟔 𝟏𝟖 𝒙 = Change division sign to 𝟑 𝟓 𝟑 𝟔 𝟗 𝟖 𝟓 𝟒𝟎 ÷ = 𝐱 = multiplication, flip the divisor 𝟑 𝟔 𝐱 = 𝟏𝟖 𝟖 𝟔 𝟖 𝟓 𝟐𝟎 𝟖 𝟓 𝟒𝟎 𝟗 or multiply and simplify if needed 𝟐𝟎 Problem C. Fatima wants to cut Solution ( KCF ) 3 3 15 3 𝟑 a ribbon into several equal 3 ÷ = 4 ÷ Change 𝟑 to an improper 4 4 4 𝟒 𝟑 pieces. If the ribbon is 3 𝟒meter = 15 𝑥 3 Change the division sign 4 4 in length, how many pieces of to multiplication 𝟑 15 4 meter of ribbon will she have ? = 𝑥 flip the divisor apply 𝟒 4 3 cancellation 3 3 5 1 3 ÷ 15 4 4 4 = 𝑥 = 5 Simplify if needed 4 3 1 1 2 Assessment Divide and simplify answer if possible 𝟐 𝟑 𝟓 𝟒 1 1. ÷ = 2. ÷ = 3. 12 ÷ 4 = 𝟑 𝟖 𝟏𝟓 𝟏𝟖 8 3 4. Maricel has a piece of cloth that is 10 m long. How many skirts can she make if each 4 1 skirt uses 1 4m cloth? 3 5. How many meter pieces of lace can be cut from 30 meters of lace? 8 18  Adding and Subtracting Decimals and Mixed Lesson 4 Decimals through ten thousandths without or with regrouping What I Need to Know After going through with this module, you are expected to: 1. Adding and subtracting decimals and mixed decimals through ten thousandths without or with regrouping 2. Solves 1 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 What I Know Directions: Copy the words and supply the missing word and corresponding number. Ex.: 472.95 The 5 in the hundredths place means 5 /100 1. 11.256 The 2 in the ________ place means _____ 2. 98.356 The 6 in the ________ place means _____ 3. 5.48193 The 9 in the ________ place means _____ 4. 15.15413 The 3 in the ________ place means _____ 5. 42 171.326 The 7 in the ________ place means _____ What’s In Do you know the birthdays of your loved ones? What gift do you give them? What does it show when you give them a present or gift? Is it nice to be thoughtful? Why? __________________________ How are you going to find the answer? To find out, add 0.845 and 0.750. Since thousandths must be added to thousandths, hundredths must be added to hundredths, tenths to tenths, and ones to ones, it is important to “have the decimal points in line.” Line up the decimals. Add: 0.845 + 0.750 = 1.595 meters Always place the decimal point in the answer exactly below the decimal points of the addends. The total length of the tussle & ribbon is 1.595 meters. 19. Arrange the following in column then add. 1. 45.0246 + 0. 2323 = 2. 0. 2935 + 1. 3799 = 3. 23.5675 + 0.53= 4. 327.599 + 45.3333= 5. 95.678 + 89.5021 = Arrange in column then add. 1) 0.12 + 0.132 + 0.3231 = 2) 0.1323 + 0.05 + 0.5010 = 3) 0.650 + 0.1219 +.03 = 4) 0.0522 + 7.106 + 9.14 = 5) 0.0231 + 5.23 + 23.108 = What I Have Learned In adding decimal numbers follow these steps: Align the decimal points Add like adding whole numbers. Regroup if necessary. Place the decimal point exactly below the decimal points of the addends. Assessment Directions: Arrange the following in column then add. 1. 3.512 + 4.436 = 2. 45.333 + 5.52= 3. 415.56 + 21.144= 4. 299.765 + 233.349= 5. Increase 0.750 by 0.250= 20  Multiplying Decimals and Mixed Decimals Lesson 5 Solving routine and non-routine problems involving multiplication of decimals and mixed decimals including money What I Need to Know At the end of this lesson, you are expected to: multiplies decimals and mixed decimals with factors up to 2 decimal places. writes the decimal point correctly in the product writes solutions to multiplication equations involving decimals up to the hundredths place. What I Know I. Choose the letter of the correct answer and write your answer in your Activity Notebook. 1. What is 0.24 x 3.12? A. 0.7488 C. 3.0036 B. 2.88 D. 7.488 2. What is the product of 0.31 and 1.4? A. 1.74 C. 0.434 B. 0.444 D. 0.234 3. What is the value of N in 0.94 x 2.14 = N? A. 1.2 C. 3.08 B. 2.0116 D. 4.03 4. If 201 x 61 = 12 261, what is 2.01 x 6.1 equal to? A. 1 226.1 C. 12.261 B. 122.61 D. 1.2261 5. If a meter of cloth cost ₱88.50, how much would 5.5 m cost? A. ₱575.25 C. ₱398.25 B. ₱486.75 D. ₱309.75 II. Solve each problem and write the answer in your Activity Notebook. 1. Betty bought 0.75 m of ribbon for her project. If a meter cost ₱12.80, how much will she pay? 2. If 2.03 x 7.3 = 20.3 x N, what is the value of N? 3. Alvin and Bernice went to the market to buy some vegetables. Alvin bought 2.4 kg of eggplant at ₱25.50 a kilogram while Bernice bought 1.6 kg of carrots at ₱40.50 a kilogram. Who spent less and by how much? 21  What’s In In the last module, you were able to add and subtract decimals. You even solve 1 or more step problems involving addition and/or subtraction of decimals and mixed decimals. This week, you are going to perform the repeated addition which is multiplication. For make you ready for this lesson, let’s have the activity Trail with me. Trail with me! Help Nikki pass through the trail by answering the problems written on the trail. Write your answers in your Activity Notebook. There are _____ decimal places in 8.706 has ___ 34.02 decimal places 83 x 84 52 x 21 367.7 has ___ 92 decimal x 24 places 745 There are x3 ___ decimal places in 1.6 24 0.654 x 13 has _____ 123 decima x5 l places 22  What’s New Activity 1. Solve with me! Read and help the girls know how much each will pay. Beth and Carla went to a grocery store. Beth bought 12 boxes of ube jam at ₱850.00 each while Carla bought 1.2 grams of sprinkles at ₱8.50 a gram. How much did each of the girls pay? 1) What is being asked? ____________ 2) What are given? _________________ 3) What operation is needed to solve the problem? ______ 4) What is the equation or number sentence for each? ________ Let us solve how much did each of the girls pay. Beth Carla 12 x ₱850 = N 1.2 x ₱8.50 = N 850 8.50 x 12 x 1.2 1700 1700 8500 8500 10200 10.200 Beth pays ₱10,200.00 Carla pays ₱10.20 What is It Let us study the two given sets, Beth and Carla. How are the multiplication sentences similar? _________ How are they different? ___________ How does multiplication in whole numbers compare to multiplication of decimal numbers? ___________ Is there any difference in multiplying whole numbers and decimal numbers? ________ 23 Look at the solution for the amount Carla will pay. 1.2 x 8.50 = 10.200 How many decimal places are in the first factor? _____________ How many decimal places are in the second factor? _____________ How many decimal places are in the product? _____________ What can you say about the combined number of decimal places in the factors and the number of decimal places in the product? __________ Let’s try more examples. 4.12 x 8.3 0.54 x 0.19 4.12 0.54 three decimal four decimal places x 8.3 places x 0.19 1236 486 32960 540 34.196 three decimal 0.1026 four decimal places places 6.8 x 0.7 0.28 x 0.08 6.8 0.28 two decimal places four decimal places x 0.7 x 0.08 4.76 two decimal places 0.0224 four decimal places What’s More Activity 2.Cross Number Puzzle Multiply the decimals below and place the product into the puzzle. The decimal point has its own space. Example, the product 2.345 will take 5 spaces in the puzzle. a g j Across b b. 4.6 x 3.7 c. 102.5 x 0.16 e. 270.12 x 0.27 c d h i f. 2.32 x 6.25 g. 1.25 x 1.25 h. 0.48 x 0.4 Down e a. 12.3 x 0.12 d. 91.05 x 0.48 f g. 40.7 x 0.03 i. 7.1 x 0.9 j. 4.16 x 1.25 24 Activity 3 Match it up! Match the problems in Column A to the correct answers in Column B. Write the letter of the correct answer in your Activity Notebook. COLUMN A COLUMN B 1. 2.45 X 3.7 a. 2.925 2. What is the value of N in 0.39 x 7.5 = N? b. 13.035 3. If 237 x 55 = 13 035, what is 2.37 x 5.5? c. 205.9375 km 4. A car travels 75.25 km per hour. How far can d. ₱61.48 it travel in 2.75 hours? e. 9.065 5. Shane bought 4.24 kg of watermelon at f. 130.35 ₱14.50 a kilogram. How much did she pay? g. 206.9375 km h. ₱64.18 What I Have Learned Activity 3. Fill me! In multiplying decimals and mixed decimals: 1. Multiply the _________ like _________. 2. Then, count the _________ in the factors. 3. Lastly, put the ______ as many places in the _____ as there are in the ______. What I Can Do Activity 4. I can do this! Let us apply what you have learned in this lesson. Answer the following problems and write your answer in your Activity Notebook. 1. 2.45 x 9.32 2. If 625 x 625 = 390 625, what is 62.5 x 6.25 equal to? 3. If 3.65 x 2.25 = 36.5 x N, what is the value of N? 25  Assessment To measure your knowledge of the concepts you have learned in this lesson, answer the following questions. I. Choose the letter of the correct answer and write your answers in your Activity Notebook. 1. What is 12.25 x 0.23? A. 2.8635 C. 2.5875 B. 2.8175 D. 1.5925 2. Find the product of 8.23 and 0.38. A. 2.3044 C. 3.0894 B. 2.7474 D. 3.1274 3. What is the value of N in 4.23 x 2.09 = N? A. 4.6107 C. 8.8407 B. 8.6317 D. 9.2637 4. If 425 x 57 = 24 225, What is 42.5 x 5.7? A. 2 422.5 C. 24.225 B. 242.25 D. 2.4225 5. If a meter of cloth cost ₱85.25, how much would 6.4 m cost? A. ₱460.35 C. ₱545.60 B. ₱539.20 D. ₱630.85 II. Solve each problem and write the answer in your activity notebook. 1. Cathy bought 2.25 m of lace for her project. If a meter of lace cost ₱35.60, how much will she pay? _____________ 2. If 9.24 x 0.95 = 0.924 x N, what is the value of N? _____________ 3. Danny and Dianne went to the market and bought some fruits. Danny bought 4.6 kg of banana at ₱50.50 a kilogram while Dianne bought 3.4 kg of mango at ₱75.50 a kilogram. Who spent less and by how much? 26  Solving Multi-step Problems involving Lesson 6 Multiplication and Addition or Subtraction of Decimals, Mixed Decimals and whole numbers including money What I Need to Know After going through this module, you are expected to: 1. analyze multi-step problems involving multiplication and addition or subtraction of decimals, mixed decimals and whole numbers including money using appropriate problem solving strategies and tools; and 2. solves multi-step problems involving multiplication and addition or subtraction of decimals, mixed decimals and whole numbers including money using appropriate problem solving strategies and tools. What I Know Solve each problem carefully. Write your final answer on the blank. 1. Jill practices her piano lesson for 3.2 hours in the morning and 2.75 hours in the afternoon. How many hours does she spend practicing in 6 days? 2. A farm lot is 45.5 m long and 25 m wide. How much will Mr. Yarra pay for the entire lot if one square meter costs P330.50? 3. Mae bought 3 dozen of eggs at Php48.50 per dozen and a kilogram of meat for Php130.00. How much did she pay for the eggs and meat? What’s In Read the problems below, analyze and solve each problem item then, identify your score by writing the description. 5 - excellent; 4 – very good; 3 and below- good job but need to study further 1. Cindy runs 4.8 km every morning. How many kilometres does she run in a week? 2. What is the area of a rectangle with a length of 9.5 cm and a width 6.45 cm? 3. If gasoline costs P49.70, how much does 10.5 litres cost? 27  What’s New The word problems below involves multi-step in solving problems involving multiplication and addition or subtraction of decimals, mixed decimals and whole numbers including money. Problem 1. Sally bought a blouse, 2 undershirts, and 3 pairs of socks for P494.25. The cost of an undershirt and 1 pair of socks was P106.00. How much did she pay for the blouse and 1 pair of socks? Step 1. Understand the problem: (Know what are given and what is/are asked.) Given: 1 blouse, 2 undershirts, and 3 pairs of socks cost P494.25 1 undershirt and 1 pair of socks cost P106.00 What to find: cost of 1 blouse and 1 pair of socks Hidden questions: How much does 1 blouse, 1 undershirt, and 2 pairs pf socks cost Step 2. Devise a plan: (Think of a strategy to solve the problem.) Draw a diagram to solve the problem. ---------------------------------------------P494.00-------------------------------------------- blouse undershirt ------------P106.00--------- pair of socks Step 3. Carry out the plan. (Solve the problem by using the chosen strategy.) Write the related number sentences. 1 blouse + 2 undershirts + 3 pairs of socks = Php494.25 1 undershirt + 1 pair of socks = P106.00 1 blouse + 1 undershirt + 2 pairs of socks = P388.25 1 blouse + 1 pair of socks = P282.25 ---------------------------------------------P494.00-------------------------------------------- P282.25 ------------P106.00--------- P106.00 Step 4. Look Back. (Read the problem again and check if the answer makes sense.) Will P282.25 + Php106.00 + 106.00 = P494.25? YES Therefore, the answer makes sense. 28 Problem 2: Benito has a bamboo stick that is 70 cm long. He cuts it into 3 pieces. The first is half the length of the second piece, which is the longest. If the longest piece is 28.4 cm, how long is each of the other two pieces? Strategy: Draw 3 pieces of rectangles to represent the sticks. ------------------------------------------70 cm----------------------------------------------- 14.2 cm 28.4 cm 27.4 cm First piece Longest piece Third piece The first and third pieces are 14.2 cm and 27.4 cm long, respectively. What is It To solve multi-step problems involving multiplication and addition or subtraction of decimals, mixed decimals and whole numbers including money using appropriate problem solving strategies and tools, you need to remember these four steps namely: Understand (What is asked in the problem? What are the given facts) Plan (What operation/s are we going to use? What is the mathematical sentence or equation?) Solve (Perform the equation.) Check (Look back if your answer is correct or not.) There are many problem-solving strategies and some of these are as follows: a. Draw a picture b. Guess and check c. Make a list d. Make a table e. Act it out f. Work backwards g. Write a number sentence h. Use objects 29  What’s More What strategy will you use to solve each of these? Solve the problem. 1. Nelson earns P20.25 for selling newspaper and P8.00 for fetching water. If he earns this amount everyday, how much would he earn in 5 days? 2. Dan and Orlan helped their father prepare their rice field for planting. Each day, Dan worked 3.6 hours while Orlan worked 3.2 hours. Find the total number of hours the two boys worked in 6 days. 3. Lory brought to the market 35 heads of chicken from her poultry yard. She sold 5 heads at P60.00 each, 15 heads at P65.00 each and the rest for P75.00 each. How much did she receive? What I Have Learned What are the steps in solving multi-step problems involving multiplication and addition or subtraction of decimals, mixed decimals and whole numbers including money? What are some strategies that you can use to solve multi-step problems involving multiplication and addition or subtraction of decimals, mixed decimals and whole numbers including money? What I Can Do Solve the problem below. Phoebe has P280.50 in her wallet. Her mother gives her P240.50 and her aunt gives her P125.25 to buy a dress. a. How much money does she have in all? b. The dress that Phoebe wants cost P750.40. How much more money does she need before she can buy the dress? c. Will she able to buy the dress if her father gave her an additional amount of P195.40? 30  Assessment Solve each problem carefully. Write your final answer on the blank. 1. Jill practices her piano lesson for 3.2 hours in the morning and 2.75 hours in the afternoon. How many hours does she spend practicing in 6 days? 2. A farm lot is 45.5 m long and 25 m wide. How much will Mr. Yarra pay for the entire lot if one square meter costs P330.50? 3. Mae bought 3 dozen of eggs at Php48.50 per dozen and a kilogram of meat for Php130.00. How much did she pay for the eggs and meat? 4. Mother gives ₱50.00 to Christy every day. Christy spends 35.50 for food each day. She saves the rest of her money. How much will Christy save in 12 days? 5. Dina asked Carlo to buy 5 ice cream cones worth ₱22.50 each. How much will be his change if Dina gives him a ₱200.00 peso bill? 31  Lesson 7 Dividing Decimals What I Need to Know After going through this module, you are expected to: 1. Divides whole numbers by decimals up to 2 decimal places and vice versa. 2. Dividesdecimalsup to 4 decimal places by 0.1, 0.01, and 0.001 3. Divides decimals up to 2 decimal places by 10, 100, and 1 000 mentally. 4. Solves situational problems involving decimals. What I Know Solve for the quotient of the following equations. 1. 1 3 6 ÷ 4 = 2. 345 ÷ 5 = 3. 238 ÷ 7 = What’s In Write the letter of the correct answer. 1. 8⟌16.20 a. 2.025 b. 2025 c. 20.25 d. 0.2025 2. 40 ⟌56.74 a. 141.85 b. 1.4185 c. 14.185 d. 0.14185 3. 15 ⟌165.60 a. 0.1104 b. 110.4 c. 11.04 d. 1.104 4. 175 ⟌3.5 a. 0.0002 b. 2.0 c. 0.002 d. 0.02 5. 125 ⟌8.65 a. 0.0692 b. 6.92 c. 69.2 d. 0.00692 What’s New Read and analyze the problem. Maria buys 8.75 meters of cloth to make pillow cases. If she wants to make 7 pillowcases, how many meters of cloth must she use for each pillow cases? 32  What’s It Ask the following questions: a) What is asked in the problem? b) What are the given facts? c) What should be done to solve the problem? d) Translate the problem into an equatio What’s More Dividing Decimals by a Whole Number Step 1 : Divide the whole number part and align 5 ____ the decimal point in the quotient with that of the dividend 6 ⟌31.50 _____ - 30 15 Continue dividing as in whole numbers. Step 2 : 5.25 6 ⟌31.50 - 30 _____ -30 15 30 - 120 Multiply quotient by the divisor. To check : 5.25 quotient x 6 divisor 31.50 dividend Dividing Decimals by Another Decimal 33 Step 1. Move the decimal point of the divisor and dividend two places to the right to make the divisor a whole number. 1.8 ⟌4.6 8 Step 2. Divide as in dividing whole numbers. 2.6 18⟌46.8 _____ -36 108 0 - 108 Dividing Decimals 10, 100, and 1,000 When a decimal is to be divided by 10, move the decimal point 1 place to the left to get the quotient. Examples : 145.34 ÷ 10 = 14.534 76.812 ÷ 10 = 7.6812 To divide a decimal 100, move the decimal point 2 places to the left to get the quotient. Examples : 567.91 ÷ 100 = 5.6791 34.157 ÷ 100 = 0.34157 When a decimal is to be divided by 1,000, move the decimal point 3 places to the left to get the quotient. Examples : 782.59 ÷ 1,000 = 0.78259 4,314.14 ÷ 1,000 = 4.31414 Dividing Decimals 0.1, 0.01, and 0.001 When a decimal is to be divided by 0.1, move the decimal point 1 place to the right to get the quotient. Examples : 235.46 ÷ 0.1 = 2354.6 0.158 ÷ 0.1 = 1.58 When a decimal is to be divided by 0.01, move the decimal point 2 places to the right to get the quotient. 34 Examples : 46.157 ÷ 0.01 = 4615.7 324.479 ÷ 0.01 = 3,2447.9 When a decimal is to be divided by 0.001, move the decimal point 3 places to the right to get the quotient. Examples : 11.4087 ÷ 0.001 = 11,408.7 82.74519 ÷ 0.001 = 82,745.19 What I Have Learned In dividing decimals by whole numbers, align the decimal point in the quotient. Divide as if dividing whole numbers. In dividing a decimal or mixed decimal by a decimal, move the decimal point of the dividend and divisor as many places to the right to make the divisor a whole number. Then divide decimals the same way you would- divide whole numbers. In dividing a decimal by: o 10, move the decimal point one place to the left to get the quotient. o 100, move the decimal point two places to the left to get the quotient. o 1000, move the decimal point three places to the left to get the quotient. In dividing a decimal by: o 0.1, move the decimal point one place to the right of the divided to get the quotient. o 0.01, move the decimal point two places to the right of the divided to get the quotient. o 0.001, move the decimal point three places to the right of the divided to get the quotient. Always annex zeroes to the needed place value. What I Can Do 35 Divide the following: 1. 6.324 ÷ 100 = _______ 6. 0.3487 ÷ 0.001 = _______ 2. 236.38 ÷ 0.1 = _______ 7. 402.30 ÷ 100 = _______ 3. 85.14 ÷ 10 = _______ 8. 53.82 ÷ 0.01 = _______ 4. 0.763 ÷ 1,000 = _______ 9. 94.36 ÷ 10 = _______ 5. 49.61 ÷ 0.01 = _______ 10. 125.39 ÷ 0.1 = _______ Assessment A.Divide, then compare. Put >,