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  1. 1. ADRIEL G. ROMAN MYRICHEL ALVAREZ AUTHORS NOEL A. CASTRO MODULE CONSULTANT FOR-IAN V. SANDOVAL MODULE ADVISER Next
  2. 2. VISION A premier university in CALABARZON, offering academic programs and related services designed to respond to the .requirements of the Philippines and the global economy, particularly, Asian countries Contents Back Next
  3. 3. MISSION AND MAIN THRUST The University shall primarily provide advanced education, professional, technological and vocational instruction in agriculture, fisheries, forestry, science, engineering, ind ustrial technologies, teacher education, medicine, law, arts and sciences, information technology and other related fields. It shall also undertake research and extension services, and provide a progressive leadership in its areas of specialization. Back Next
  4. 4. GOALS In pursuit of the college vision/mission the College of Education is committed to develop the full potentials of the individuals and equip them with knowledge, skills and attitudes in Teacher Education allied fields to effectively respond to the increasing demands, challenges and opportunities of changing time for global competitiveness. Back Next
  5. 5. OBJECTIVES OF BACHELOR OF SECONDARY EDUCATION (BSEd) Produce graduates who can demonstrate and practice the professional and ethical requirements for the Bachelor of Secondary Education such as: 1. To serve as positive and powerful role models in the pursuit of learning thereby maintaining high regards to professional growth. 2. Focus on the significance of providing wholesome and desirable learning environment. 3. Facilitate learning process in diverse types of learners. 4. Use varied learning approaches and activities, instructional materials and learning resources. 5. Use assessment data, plan and revise teaching-learning plans. 6. Direct and strengthen the links between school and community activities. 7. Conduct research and development in Teacher Education and other related activities. Back Next
  6. 6. This teacher’s guide Visual Presentation Hand-out entitled: “MASTERING FUNDAMENTAL OPERATIONS AND INTEGERS (MODULAR WORKBOOK FOR 1st YEAR HIGH SCHOOL)” is part of the requirements in educational technology 2 under the revised Education curriculum based on CHEd Memorandum Order (CMO)- 30, series of 2004. Educational technology 2 is a three (3) unit course designed to introduce both traditional and innovative technologies to facilitate and foster meaningful and effective learning where students are expected to demonstrate a sound understanding of the nature, application and production of the various types of educational technologies. Contents Back Next
  7. 7. The students are provided with guidance and assistance of selected faculty members of the college through the selection, production and utilization of appropriate technology tools in developing technology based teacher support materials. Through the role and functions of computers especially the internet, the student researchers and the advisers are able to design and develop various types of alternative delivery systems. These kinds of activities offer a remarkable learning experience for the education students as future mentors especially in the preparation of instructional materials. Back Next
  8. 8. The output of the group’s effort may serve as an educational research of the institution in providing effective and quality education. The lessons and evaluations presented in this module may also function as a supplementary reference for secondary teachers and students. FOR-IAN V. SANDOVAL Computer Instructor/ Adviser/Dean CAS NOEL A. CASTRO Engineer/Mathematics Instructor Back Next
  9. 9. PREFACE This modular workbook entitled “Mastering Fundamental Operations and Integers (modular workbook for First Year High School)” aims you to become fluent in solving any mathematical expressions and problems. This instructional material will serve as your first step in entering to the world of high school mathematics. This modular workbook is divided into two units; the unit I consist of four chapters which pertains to the four basic operations in mathematics dealing with whole numbers and the unit II which pertains to the use of four fundamental operations in integers. In mastering the four fundamental operations, you will study the different parts of the four basic operations (addition, subtraction, division and multiplication), and their uses and the different shortcuts in using them. In this part, you will also learn on how to check one’s operation using their inverse operation. Contents Back Next
  10. 10. In the unit II, you may apply here all the knowledge that you have gained from the unit I. in this part, you may encounter several expressions where you need to use all the knowledge that you have gained from the unit I. you will also learn the nature of Integers, and also the Positive, Zero and Negative Integers. This instructional material was designed for you to have a further understanding about the four fundamental operations dealing with Whole Numbers and Integers. It was also designed for you to have a deep interest in exploring Mathematics. The authors feel that after finishing this lesson, you should be able to feel that EXPLORING MATHEMATICS IS INTERESTING AND FUN!!! THE AUTHORS Back Next
  11. 11. ACKNOWLEDGEMENT The authors would like to give appreciation to the following: To Mr. For- Ian V. Sandoval, for his kind consideration and for his advice to make this instructional material more knowledgeable. To Mrs. Corazon San Agustin, for her guidance to finish this instructional modular workbook. To Prof. Lydia R. Chavez for her wonderful advice to make this instructional material becomes more knowledgeable. To Mrs. Evangeline Cruz for her kind consideration in allowing us to borrow books from the library. Contents Back Next
  12. 12. To Mr. Noel Castro for giving his advice to make this instructional material become knowledgeable. To BSED Section 2 who gave the authors strength to finish this instructional material. To our Parents who support us morally and financially while making this instructional material. And to ALMIGHTY GOD who gave us knowledge, strength and power to make and finish this modular workbook. THE AUTHORS Back Next
  13. 13. Table of Contents VMGOs Foreword Preface Acknowledgement Table of Contents UNIT I- MASTERING BASIC FUNDAMENTAL OPERATIONS CHAPTER 1- ADDITION OF WHOLE NUMBERS Lesson 1- What is Addition? Lesson 2- Properties of Addition Lesson 3- Mastering Skills in Adding Whole Numbers Lesson 4- Different Methods in Adding Whole Numbers Lesson 5- How to solve a word problem? Lesson 6- Application of addition of whole numbers: WORD PROBLEM CHAPTER 2- SUBTRACTION OF WHOLE NUMBERS Lesson 7- What is Subtraction? Lesson 8- Mastering Skills in Subtraction Lesson 9- Problem Solving Involving Subtraction of whole numbers Back Next
  14. 14. CHAPTER 3- MULTIPLICATION OF WHOLE NUMBERS Lesson 10- What is Multiplication? Lesson 11- Properties of Multiplication Lesson 12- Mastering Skills in Multiplying Whole Numbers Lesson 13- “The 99 Multiplier” Shortcut in multiplying whole numbers Lesson 14- “Power of Ten Multiplication” Shortcut In Multiplying Whole Numbers Lesson 15- Problem solving involving Multiplication of Whole Numbers CHAPTER 4- DIVISION OF WHOLE NUMBERS Lesson 16- What is Division? Lesson 17- Mastering Skills in Division of Whole Numbers Lesson 18- “Cancellation of Insignificant Zeros” Easy ways in Dividing Whole Numbers Lesson 19- Problem Solving Involving Division of Whole Numbers Back Next
  15. 15. UNIT II- INTEGERS CHAPTER 5- WORKING WITH INTEGERS Lesson 20- What is Integer? Lesson 21- Addition of Integers Lesson 22- Subtraction of Integers Lesson 23- Multiplication of Integer Lesson 24- Division of Integers Lesson 25- Punctuation and Precedence of Operation MATH AND TECHNOLOGY REFERENCES About the Authors Back Next
  16. 16. Overview In this unit, you will understand the concept of the basic fundamental operations dealing with whole numbers. This workbook will help you to master and to become skilled in the fundamental operations. This modular workbook provides information about four operations and how to perform such kind of operation in solving word problem. It also provides exercises and activities that will help you become skilled and for you to master the fundamental operations. Objectives: After studying this unit, you are expected to: •discuss the four fundamental operations; •perform the operations well; •check the answers in addition and multiplication using their inverse operation. Contents Back Next
  17. 17. Introduction In this chapter, you will learn deeply the addition operation, the different parts of it, the different properties and the use of this operation in solving a word problem. This chapter will serve as your first step in mastering the basic fundamental operations for this chapter will discuss how to solve a word problem using systematic ways. All the information you need to MASTER THE FUNDAMENTAL OPERATIONS DEALING WITH WHOLE NUMBERS is provided in this chapter. Contents Back Next
  18. 18. Lesson 1 WHAT IS ADDITION? Objectives: After this lesson, the students are expected to: • define what addition is; • identify the different properties of addition; • perform the operation (addition) correctly. How well do you remember your basic addition facts? In addition sentence, 326 + 258 = 584 Sum 326 + 258 = 584, which are the addends and which is the sum? Addition is a mathematical method on putting things together. Adding whole numbers together is a method that requires placing the numbers in column to get the answer. Addition is represented by the plus sign (+). Addends The addends and the sum are the two parts of addition. The sum is the total and the addends are the numbers needed to add. Examples: 1.27 +31=58 the addends are 27 and 31 and the sum is 58. 2.11+21=32 the sum is 32 and the addends are 11 and 21. Contents Back Next
  19. 19. WORKSHEET NO. 1 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ •Define the following terms •ADDITION- _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _______________________________________________________________. •ADDENDS- _________________________________________________________________ _________________________________________________________________ _________________________________________________________________ _______________________________________________________________. •SUM- ________________________________________________________________ ________________________________________________________________ ________________________________________________________________ _______________________________________________________________. Back Next
  20. 20. ADD THE FOLLOWING SOLUTION 1. 31481+369=__________________ 2. 23634+12438=________________ 3. 3497+6826=__________________ 4. 81650+3897601=______________ 5. 7333+62766=_________________ 6. 6. 178654321+236754=___________ 7. 6585+8793=__________________ 8. 4333+9586=__________________ 9. 423381+46537=_______________ 10. 546263+9520=________________ Back Next
  21. 21. Lesson 2 PROPERTIES OF ADDITION Objectives: After this lesson, the students are expected to: •define the properties of addition; •use the different properties of addition in solving; •perform an operation using the properties of addition. The 0 Property in Addition This property states that any number added to 0 is the number itself, that is, if “a” is any number, a + 0 = a. Examples: 8 + 0 = 8 27 + 0 = 27 10 + 0 = 10 31 + 0 = 31 The Commutative Property of Addition This property states that changing the order of the addends does not change the sum. This means you need to remember only half of the basic facts. In symbols, the property says that a + b = b + a, for any numbers a and b.: Contents Back Next
  22. 22. Examples: 6 + 8 = 14 8 + 6 = 14 11 + 27 = 38 27 + 11 = 3 Associative Property of Addition This property states that changing the grouping of the addends does not affect or change the sum, that is, if a, b and c are any numbers, (a + b) = c = a + (b + c). Examples: (4 + 3) + 8 = 4 + (3 = 8) = 15 9 + (8 + 6) = (9 + 8) + 6 = 23 Remember to work in the parenthesis first. Summary: The 0 Property in Addition If “a” is any number, a + 0 = a. The Commutative Property of Addition If a + b = b + a, for any numbers a and b. The Associative Property of Addition If a, b and c are any numbers, (a + b) = c = a + (b + c). Back Next
  23. 23. WORKSHEET NO. 2 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ Identify the properties of the following 1. 265 + 547 = 547 + 265___________________________ 2. 85 + 78 = 78 + 85_______________________________ 3. 15 + 0 = 15____________________________________ 4. 3 + (5 + 9) = (3 + 5) + 9 =17______________________ 5. 31+ (21+15) = (31+21) +15 = 67___________________ 6. 59 + 0 = 59____________________________________ 7. 100 + 0 = 100__________________________________ 8. 65 + 498 = 498 + 65_____________________________ 9. 9 + 5 = 5 + 9___________________________________ 10. (10+10) + 10 = 10+ (10+10) =30___________________ Back Next
  24. 24. Lesson 3 MASTERING SKILLS IN ADDING WHOLE NUMBERS USING ADDITION TABLE Objectives After this lesson, the students are expected to: •use the addition in table properly; •mastering skills in addition using tables; •discuss the use of addition table. Addition Table The Addition Table can help you to master the addition operation + 0 1 2 3 4 5 6 7 8 9 10 11 12 0 0 1 2 3 4 5 6 7 8 9 10 11 12 1 1 2 3 4 5 6 7 8 9 10 11 12 13 2 2 3 4 5 6 7 8 9 10 11 12 13 14 3 3 4 5 6 7 8 9 10 11 12 13 14 15 4 4 5 6 7 8 9 10 11 12 13 14 15 16 5 5 6 7 8 9 10 11 12 13 14 15 16 17 6 6 7 8 9 10 11 12 13 14 15 16 17 18 7 7 8 9 10 11 12 13 14 15 16 17 18 19 8 8 9 10 11 12 13 14 15 16 17 18 19 20 9 9 10 11 12 13 14 15 16 17 18 19 20 21 10 10 11 12 13 14 15 16 17 18 19 20 21 22 Contents Back Next
  25. 25. How to use Example: 3 + 5 + 1 2 3 4 5 6 7 Go down to the "3" row 1 2 3 4 5 6 7 8 then along to the "5" column, and there is your answer! "8" 2 3 4 5 6 7 8 9 3 4 5 6 7 8 9 10 4 5 6 7 8 9 10 11 5 6 7 8 9 10 11 12 You could also go down to "5" + 1 2 3 4 5 6 7 and along to "3", 1 2 3 4 5 6 7 8 or along to "3" and 2 3 4 5 6 7 8 9 down to "5" 3 4 5 6 7 8 9 10 4 5 6 7 8 9 10 11 to get your answer. 5 6 7 8 9 10 11 12 Back Next
  26. 26. WORKSHEET NO. 3 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ •MOTHER OF ALL SCIENCE!!! FOLLOW THE INSTRUCTION 1. Have your own addition table 2. With your addition table, add the following 1+4, 0+1, 3+4, 5+0, 5+4 6+4, 7+2, 8+0, 9+2, 10+4 1+6, 3+6, 5+6, 3+10 6+6, 10+6, 6+8, 10+10 3. After adding, try to put dots in every sum. Try to connect the dots by a line in every number to find what the mother of all science is. Back Next
  27. 27. Add the following numbers correctly. SOLUTION 1. 593423+4467=_____________________ 2. 359+4843=________________________ 3. 1297+4548=_______________________ 4. 696493+266=______________________ 5. 1898976+219876=__________________ 6. 78589+66533=_____________________ 7. 6485092+1764243=___________________ 8. 828637+86464=______________________ 9. 12379+2873=________________________ 10. 53746+783579=_____________________ 11. 642578+325646=_____________________ 12. 12398+6327355=_____________________ 13. 563745+654689=_____________________ 14. 57684+8765358=_____________________ 15. 425778+87654=______________________ Back Next
  28. 28. Lesson 4 DIFFERENT METHODS IN ADDING WHOLE NUMBERS Objectives After this lesson, the students are expected to: solve addition using other methods; discuss the different methods in adding whole numbers; solve mathematical problems using the other method. There are some easy ways in adding whole numbers. Adding the column separately. Let 326+258 use as our illustrative example. Adding in reverse order 326 300+20+6 +258 200+50+8 •Add the numbers in the hundreds 500 place. •Add the numbers in the tens place. 300+20+6 •Add the numbers in the ones place. 200+50+8 •Then add their sum to get the total 500+70+14 sum. 500+70+14=584 Contents Back Next
  29. 29. •Adding in column separately EXAMPLE: + 526 278 14 1.Arrange the numbers vertically. 2.Add the numbers in the ones place. + 9 3.Then add the tens place and place the sum under the tens place. 7 4.Then add the numbers in column. 804 To check; •Add it upward. •Subtract the sum to one of the addends. •Add the numbers in the addends and in the sum if your answer in the •sum is the same as in the addends, then your answer is correct. Back Next
  30. 30. WORKSHEET NO. 4 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ •Using any of the given ways, add the following and write the answer in the space provided. Show all your solutions. 1. 39, 28_________________ 6. 343, 86________________ 2. 43, 29_________________ 7. 987, 652_______________ 3. 69, 51_________________ 8. 6232, 7434_____________ 4. 70, 623________________ 9. 853 234, 578____________ 5. 890, 431_______________ 10.6 754 236, 643 123_______ SOLUTION: Back Next
  31. 31. B. Perform the operation using the procedure discussed. Check your answer by using the short method. WRITE YOUR SOLUTION 1. 642 890+57 829=______________________ 2. 564 872 389+54 738=___________________ 3. 12 345+42 321=________________________ 4. 3255+6472865=________________________ 5. 6437286+56387=_______________________ 6. 54390+529=___________________________ 7. 6348901+65890=_______________________ 8. 7395+7598043=________________________ 9. 225+264=____________________________ 10. 367+201=____________________________ 11. 9 632+2 330=_________________________ 12. 1 423+54 673=________________________ 13. 543 265+65 223=______________________ 14. 673 895 462+54 289=___________________ 15. 629 075+57823=_______________________ Back Next
  32. 32. Lesson 5 SOLVING WORD PROBLEM Objectives After this lesson, the students are expected to: •discuss how to solve a word problem; •solve any given problems systematically; •use problem solving plan in solving any given word problem. This problem solving plan should be used every time we solve word problems. Careful reading is an important step in solving the problem. This lesson serves as an introduction to the next chapter. Throughout this lesson, we will be solving problems that deal with real numbers. In solving word problems, the following plan is suggested: Contents Back Next
  33. 33. PROBLEM SOLVING PLAN 1. Understand the problem. 2. Devise a plan. 3. Carry out the plan. One harvest season, a farmer 4. Check the answer. harvested 531 sacks of rice. This was 87 more than his previous harvest. How many sacks did he harvest during the previous season? Example: PROBLEM SOLVING PLAN 1. UNDERSTAND THE PROBLEM Understand the problem and get the general idea. Read the problem •What is the problem about? one or more times. Each time you read ask: •What information is given? Represent what is asked with a symbol. {The problem is about the •What is being asked? number of sacks harvested. Let S be the number of sacks during the previous harvest.} 2. DEVISE A PLAN This is a key part in the 4 step plan for solving problems. Different “87 more” suggests addition and we can problem solving strategies have to be applied. A figure, diagram, chart write a formula: might help or a basic formula might be needed. It is also likely that a related 87+S=531. problem can be solved and can be used to solve the given problem. Another devise is to use the “trial and learn from your errors” process. There is a lot of problem solving strategies and every problem solver has own special technique. Back Next
  34. 34. 3. CARRY OUT THE PLAN If step two of the problem solving plan has been successfully completed in detail, it would be easy to carry out the plan. It will involve organizing and doing the necessary computations. Remember that confidence in the plan creates a better working atmosphere in carrying it out . Solve the equations: 87+S=531 S=531-87 S=444 sack 4. CHECK THE ANSWER This is an important but most often neglected part of problem solving. There are several questions to consider in this phase. One is to ask if we use another plan or solution to the problem do we arrive at the same answer. . It is reasonable that the farmer harvested 444 sacks during the previous harvest. His harvest now which is 531 is more than the last harvest Back Next
  35. 35. WORKSHEET NO. 5 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ A. Discuss the different problem solving plan briefly. 1. Understand the problem _____________________________________________________________________ _____________________________________________________________________ _____________________________________________________________________ ____________________________________________________________. 2. Devise a plan- ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ _________________________________________________________. 3. Carry out the plan ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ _________________________________________________________. • Check the answer ______________________________________________________________________ ______________________________________________________________________ ______________________________________________________________________ _________________________________________________________. Back Next
  36. 36. Lesson 6 APPLYING ADDITION OF WHOLE NUMBERS IN WORD PROBLEM Objectives After this lesson, the students are expected to: •analyze the given problem; •to develop the skills and knowledge in solving word problems; •identify the different steps in word problems involving addition. LOOK AT THE EXAMPLE A farmer gathered 875 eggs from one poultry house and 648 from another. How many eggs did he gather? We want the answer to 875 + 648 =? Add the ones: 5 + 8 = 13 ones = 1 ten + 3 ones. • Write 3 in the ones column and bring the 1 ten to 11 the tens column. • Add the tens: 1 +7 +2 = 12 tens = 1 hundred + 2 875 tens. • Write 2 under the tens column and bring the 1 +648 hundred to the hundreds column. • 1 523 Add the hundreds: 1 + 8 + 6 = 15 hundreds = 1 thousand + h hundreds. Write 15 to the left of 2. The farmer gathered 1 523 eggs. Contents Back Next
  37. 37. Here is another example: Add: 5 326 + 1 456 =? •6 + 6 = 12 =10 + 2 •1 ten + 2 tens + 5 tens = 8 tens Add: 5 986 + 3 759 =? •3 hundred + 4 hundreds=7 hundreds •6 + 9 = 15 =10 + 5 5 thousand +1 thousands= 6 thousands. 1 11 •1 ten + 8 tens + 5 tens = 14 tens = 1 hundred + 4 tens. Thus, 5 326 + 1 456 =6782 •1 hundred + 9 hundreds +7 hundreds = 17 hundreds = 1 5 986 thousand + 7 hundreds. +3 759 1 thousand +5 thousands + 3 thousands = 9 thousands. 1 9 745 Thus, 5 986 + 3 759 = 9 745 5 326 + 1 456 6782 Back Next
  38. 38. WORKSHEET NO. 6 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ Answer the following problem solving 1. Mr. Parma spent Php.260 for a shirt and Php.750for a pair of shoes. How much did he pay in all? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ______________________________________________________________. 2. Miss Callanta drove her car 15 287 kilometers and 15 896 kilometers the next year. How many kilometers did she drive her car in two years? ____________________________________________________________________________________ ____________________________________________________________________________________ ____________________________________________________________________________________ ______________________________________________________________. Back Next
  39. 39. 3. Four performances of a play had attendance figures of 235, 368, 234, and 295. How many people saw the play during the period? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _____________________________________________________________________________. 4. The monthly production of cars as follows: January-4,356, February- 4,252, and March- 4425, June-4456, July-4287, August-4223, September-4265, October-4365, November-4109, and December- 4270. How many cars were produced in the whole year? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ _____________________________________________________________________________. 5. If a sheetrock mechanic has 3 jobs that require 120 4x8 sheets, 115 4x8 sheets, and 130 4x8 sheets of sheetrock respectively. How many 4x8 sheets of sheetrock are needed to complete the 3 jobs? _______________________________________________________________________________ _______________________________________________________________________________ _______________________________________________________________________________ __________________________________________________________________________ Back Next
  40. 40. Introduction In this chapter, you will learn the subtraction operation, the different parts of it and the use of this operation in solving word problem. You will also learn the different ways on how to solve and check the answer or the difference which you can use in your everyday life. This chapter provides the information that will help you master the subtraction as one of the fundamental operation in Mathematics. Contents Back Next
  41. 41. Lesson 7 WHAT IS SUBTRACTION? Objectives After this lesson, the students are expected to: define what is subtraction; identify the parts in subtraction; differentiate the subtraction from addition. What is Subtraction? After learning and describing addition as a process of combining two or more groups of objects, we can now consider its opposite operation --- Subtraction. If addition is combining of group of object, subtraction is the process of taking away or of removing something. The symbol used for subtraction is the minus sign (-). Contents Back Next
  42. 42. When we write 12 – 6, we wish to subtract 6 from 12 or to take away 6 from 12. To find the difference between two numbers, we have to look for a number which when added to the subtrahend, will give the minuend. The table shows the relation between addition and subtraction. One undoes the work of the other. Let us consider the notation below. + 6 addend 12 addend 18 sum Minuend 18 Subtrahend -6 Difference 12 Difficulties may arise in subtraction when a digit of the subtrahend is larger than the corresponding digit in the minuend. The process of doing a subtraction of this type is called barrowing or regrouping Back Next
  43. 43. WORKSHEET NO. 7 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ A. Give the meaning of the following words. 1. Subtraction-________________________________________________ 2. Minuend-__________________________________________________ 3. Subtrahend-________________________________________________ 4. Difference-_________________________________________________ B. Name the following parts of the mathematical expression given below. 12638 _____ - 3630 _____ 9008 _____ Back Next
  44. 44. D. Solve the following to get the difference WRITE YOUR SOLUTION HERE: 1. 349 2. 1243 3. 5428 4. 10,000 -265 -360 -2001 -6,543 1. 5637584-43675=________________ 2. 5389-782=_____________________ 3. 43674-768=____________________ 4. 376598-5281=__________________ 5. 67396-683=____________________ 6. 57290-7849=___________________ 7. 56284-6847=___________________ 8. 683963-68363=_________________ 9. 6254-978=_____________________ 10. 654-87=______________________ Back Next
  45. 45. Lesson 8 MASTERING SKILLS IN SUBTRACTING WHOLE NUMBERS Objectives After this lesson, the students are expected to: •enhance the knowledge in terms of subtracting whole numbers; •develop the speed in solving subtraction; •perform the steps in subtracting whole numbers. Cain kiblah type his report in physics at the computer shop for about 5 hours and 17 minutes while Lane Margaret types her report for only 3 hours and 28 minutes. How fast does Lane Margaret type her report than Cain kiblah? To make the subtraction convenient, we borrow 1 minute so we have: 5 hrs + 17 mins 5 hrs + 17 mins - 3 hrs + 28 mins 77mins 1 hr + 49mins - 3 hrs + 28 mins Contents Back Next
  46. 46. WORKSHEET NO. 8 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ Solve and get the difference Simplify the following numbers 1.10327-1685=____________ •Subtract 381 from 1895 2.74577-7658=____________ •Subtract 852 from 1682 3.9443-99195=____________ •Subtract 665 from 694 4.14652-9195=____________ Subtract 443 from 1084 5.19919-8881=____________ •Subtract 154 from 1284 6.8322-4909=____________ •Subtract 46 from 850 7.8851-8453=____________ •Subtract 132 from 957 8.7609-6957=____________ •Subtract670 from 2064 9.8858-182=_____________ •Subtract 739 from 1591 10. 8905-18=___________ •Subtract 754 from 772 Back Next
  47. 47. Lesson 9 PROBLEM SOLVING INVOLVING SUBTRACTION Objectives After this lesson, the students are expected to: follow the steps correctly in problem solving involving subtraction; discuss the different steps in problem solving; develop the knowledge in problem solving. To master the application of subtraction in problem solving, here are some examples: Pedro had marbles. He gave away two of his marbles to Juan. If Pedro had twelve marbles, how many marbles left to Pedro after he gave two to Juan? We can use the problem solving plan: 1. Know what the problem is. a. What is asked? How many marbles left to Pedro? b. What are given? 12 marbles of Pedro and 2 to Juan c. What operation to be used? Subtraction Contents Back Next
  48. 48. 12 – 2 = n 12 – 2 = 10 N = 10 marbles left to Pedro. Checking: 2 + 10 = n 2 + 10 = 12 Another example: Mt. Everest, is 29 028 ft. high, while the Mt. McKinley is 20 320 ft. high. How much is Mt. Everest higher than Mt. McKinley? 1. What is asked? How much Mt. Everest higher than Mt. McKinley? 2. What are given? Mt. Everest, is 29 028 ft. high and Mt. McKinley is 20 320 ft. high. 3. What operation to be used? Subtraction 29 028 – 20 320 = n 29 028 – 20 320 = 8 708 ft. Checking: 8 708 + 20 320 = n 8 708 + 20 320 = 29 028 Back Next
  49. 49. WORKSHEET NO. 9 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ A. Get one whole sheet of paper and solve the following problem. 1. In 1992, William Clinton got 44 908 254 votes as the president of USA while George Bush got 39 10 343 votes and Foss Perot got 19 741 65 votes. How many more votes did Clinton have than Bush? Bush than Foss? ____________________________________________________________________________________________ ____________________________________________________________________________________________ ___________________________________________________________________________________________. 2. In May of 1994, there were 42 518 000 beneficiaries in the social security program while there were 41 784 000 beneficiaries on May 1993. How much was the increase of beneficiaries from 1993 to 1994? ____________________________________________________________________________________________ ____________________________________________________________________________________________ ___________________________________________________________________________________________. Back Next
  50. 50. 3. In 1998, a school had an enrollment of 5908 pupils while there are 6519 pupils enrolled in 1999. How much more pupils enrolled in 1999 than in 1998? _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ ________________________________. 4. Martial law was declared in 1972. Now, it is 2009, how many years ago it was? _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ ________________________________. 5. If Clark was born on December 31 2009, how old is he now? ________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ _________________________________. 6. What number will make 2 816 to become 5229? _________________________________________________________________________________ _________________________________________________________________________________ _________________________________________________________________________________ ____________________________. 7. A philanthropist donated P850 765 to an orphanage. The amount was used for some repairs and the purchase of some equipment worth P519 800. How much money was left for other projects? Back Next
  51. 51. ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ _________________. 8. If you born on 1953, how old are you now? ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ _________________. 9. Mr. Fabre exported to other Asian countries P2 759 000 worth of furniture while Mr. Co exported P5 016 298 worth. How much more where Mr. Co’s exports than those of Mr. Fabre? ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ________________. 10. The total number of eggs produced in the United States in 1993 was 71, 391, 000,000. The total number of eggs produced in 1992 was 70,541,000,000. How many more eggs were produced in the United States in 1993 than in 1992? ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ _________________. Back Next
  52. 52. Introduction In this chapter, you will learn about the multiplication operation, its different parts and ways in solving it and the use of this operation in word problem. This chapter provides lessons and exercises that will help you to master the multiplication of whole numbers. Contents Back Next
  53. 53. Lesson 10 WHAT IS MULTIPLICATION? Objectives After this lesson, the students are expected to; •define what multiplication is. •identify the part of multiplication. •perform the multiplication operation properly. Multiplication is a repeated addition. It can be thought of as addition repeated a given number of times. For example, 3 x 5 = 15 can be solving as 5 + 5 + 5 =15. 3 mean that the 5 is to be used three times. The same problem can also be thought of as 5x 3, or 3 + 3 +3 + 3 + 3 =15. Written this way, the three is used as a total of five times in either case is 15. The number in the upper part is called the multiplicand and in the lower position is called the 3 multiplicand multiplier. The answer in the multiplication is called product. 5 multiplier 15 product Contents Back Next
  54. 54. WORKSHEET NO. 10 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ A. Identify the following. 7 __________ 2 __________ 14 ___________ B. Get the product of the following. 1.32 x 25= 6. 14 x 193= 2. 10 x10 = 7. 66 x 15= 3.25 x 68= 8. 157 x 11= 4.31 x1545= 9. 655 x 8= 5.27 x 17781= 10. 856 x 18= Back Next
  55. 55. Lesson 11 PROPERTIES OF MULTIPLICATION Objectives After this lesson, the students are expected to: oreview the different properties of multiplication; odevelop the knowledge in the properties of multiplication; oapply the properties of multiplication in solving problem. 1. IDENTITY PROPERTY The product of the 1 and any number a is a, that is, 1 x a = a for any number. Example: 21 x a = 21 27 x a =27 31 x a = 31 11 x a = 11 5xa=5 13 x a = 13 2. ZERO PROPERTY The product of 0 and any number a is 0, that is a x 0 = 0 for any number a. Example: 0 x 87 = 0 0 x 98 = 0 15 x 0 = 0 45 x 0 = 0 14 x 0 = 0 58 x 0 = 0 Contents Back Next
  56. 56. 3. COMMUTATIVE PROPERTY Changing the order of the factors does not change the product, that is, a x b = b x a for any number of a and b. Example: 7 x 4 = 28 = 4 x 7 5 x 12 = 60 = 12 x 5 5 x 6 = 30 = 6 x 5 4 x 11 = 44 = 11 x 4 4. ASSOCIATIVE PROPERTY Changing the grouping of the factors does not affect the product, that is, a x (b x c) = (a x b) x c for any number of a, b, and c. Example: (7 x 4) x 5 = 140 = 7 x (4 x 5) (4 x 6) x 8 = 192 = 4 x (6 x 8) 5. DISTRIBUTIVE PROPERTY If one factor is a sum of two numbers, multiply the addends to the multiplier before adding will not change the answer, that is a x (b + c) = (a x b) + (a x c). Example: 5 x (6 + 7) = 30 + 35 = 65 6 x (7 + 9) = 42 + 54 = 9 Back Next
  57. 57. WORKSHEET NO. 11 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ AFill on the blank and identify the property of each. 1. (8 x 4) + (8 x 6) = 8 x (__ + 6) = ______ 2. (7 x 5) x 2 = 7 x (__ x __) = ______ 3. (9 x 5) = 25 x__ = _______ 4.8 x 0 = ______ 5. (12 x 3) + (12 x 7) = _____ B. Fill the missing number. Use the property of multiplication to get product 1. 6 x 7 = __ x 6 6. (7 x __) + (__ x 6) = 7 x (3 +6) 2. 5 x 0 = __ 7. 27 x __ = 27 3. 8 x 1 __ 8. 8 x __ = 0 4. (4 x 5) x 7 = 4 x (__ x 7) 9. 6 x (3 x 4) = (6 x __) x 4 5. 8 x (2 + __) = (8 x 2) + (8 x __) 10. 4 x 9 =__ x 4 Back Next
  58. 58. Lesson 12 MASTERING SKILLS IN MULTIPLYING WHOLE NUMBERS Objectives After this lesson, the students are expected to: multiply whole numbers in easy way; develop the speed in multiplying whole numbers; perform multiplication correctly. Since multiplication is a shortcut for 1 1 Carries repeated addition, we can get the product of a 2 4 two factors without the use of a two factors without the use of repeated addition. Take a look 3 5 8 Multiplicand at the example: x 2 5 Multiplier 1 7 9 0 1st partial product +7 1 6 2nd partial product 8 9 5 0 Product Contents Back Next
  59. 59. In mastering the multiplication operation, knowing how to multiply using multiplication table helps you to become fluent in multiplying numbers. How to use multiplication table? Back Next
  60. 60. Multiplication Table X 0 1 2 3 4 5 6 7 8 9 10 11 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 1 2 3 4 5 6 7 8 9 10 11 12 2 0 2 4 6 8 10 12 14 16 18 20 22 24 3 0 3 6 9 12 15 18 21 24 27 30 33 36 4 0 4 8 12 16 20 24 28 32 36 40 44 48 5 0 5 10 15 20 25 30 35 40 45 50 55 60 6 0 6 12 18 24 30 36 42 48 54 60 66 72 7 0 7 14 21 28 35 42 49 56 63 70 77 84 8 0 8 16 24 32 40 48 56 64 72 80 88 96 9 0 9 18 27 36 45 54 63 72 81 90 99 108 10 0 10 20 30 40 50 60 70 80 90 100 110 120 11 0 11 22 33 44 55 66 77 88 99 110 121 132 12 0 12 24 36 48 60 72 84 96 108 120 132 144 Example: Remembering 9's What's 9 x 7? Use the 9-method! Hold out all 10 fingers, and lower the 7th finger. There are 6 fingers to the left and 3 fingers on the right. The answer is 6. Back Next
  61. 61. WORKSHEET NO. 12 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ • Find the product of the following. (You may use a multiplication table if you want). WRITE YOUR SOLUTION HERE: 1. 59x 8 =________________ 2. 48 x 3 =_______________ 3. 31 x 6 =_______________ 4. 27 x 21 =______________ 5. 11 x 15 =_______________ 6. 21 x 27 =_______________ 7. 14 x 17 =_______________ 8. 8 x 32 = ________________ 9. 78 x 45 =_______________ 10. 11 x 23 =_____________ Back Next
  62. 62. Lesson 13 “THE 99 MULTIPLIER” SHORTCUT IN MULTIPLYING WHOLE NUMBER Objectives After this lesson, the students are expected to: multiply whole numbers mentally; appreciate exploring the world of multiplication; appreciate the multiplication operation. This lesson is concern in one of the easy ways in getting the product in multiplication. If the digits in the multiplier (or even multiplicand) are all 9 such as 9, 99, 999…, annex to the multiplicand as many zeros as there are 9’s in the multiplier and from it, subtract the multiplicand. Here some examples: 999 364= 364 000-364= 369 636 Why? 2834 99= 283 400-2834= 280566 Why? 31×999= 31 000-31= 30 969 Why? Contents Back Next
  63. 63. WORKSHEET NO. 13 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ •Multiply the following using the “99 multiplier” method. •99×99=________________________ •33×99=________________________ •47x99=________________________ •65x9=_________________________ •21x99=________________________ •81x99=________________________ •72x999=_______________________ •56x9999=______________________ •34x9=_________________________ •8x9=__________________________ B. Solve the following •Find the product of 873 and 9999=________________________ •Find the product of 132 and 999=_________________________ •Find the product of 665 and 99=__________________________ •Find the product of 670 and 9=___________________________ •Find the product of 154 and 9999=________________________ •Find the product of 1063 and 999=________________________ •Find the product of 948 and 9999=________________________ •Find the product of 323 and 99=__________________________ •Find the product of 493 and 999=_________________________ •Find the product of 490 and 99=__________________________ Back Next
  64. 64. Lesson 14 “THE POWER OF TEN” MULTIPLICATION Objectives After this lesson, the students are expected to: specializing skills in multiplication; perform multiplication easily; develop the speed in multiplying numbers. When the factors are in the power of ten such as 10, 100, 1000, 10 000, 100 000 and so on and so fort, just multiply the digit that is form 1 to 9 and add the number of zeros. Example: 31 x 100 = 3 100 270 x 10 = 2 700 15 000 x 100 = 1 500 000 When the factors are end in both zero, multiply the significant number and used the number of zeros in both factors to the product. Example: 2 380 x 40 = 95 200 2 380 x 400 = 952 000 Contents Back Next
  65. 65. WORSHEET NO. 14 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ A. Based to the power of ten, multiply the following. 1. 100 x 320 =_________ 6. 75 x 100 =_________ 2. 10 x 27 = __________ 7. 56 x 10 = __________ 3. 100 x 414 = ________ 8. 38 x 100 =__________ 4. 176 x 100 = ________ 9. 68 x 10 000 =________ 5. 39 x 1 000 = ________ 10. 59 x 1 000 =________ B. Find the product of the following. 1. 2 080 x 30 =____________ 6. 720 x 40 =____________ 2. 3 150 x 60 =____________ 7. 7 230 x 50 =___________ 3. 1 470 x 20 =____________ 8. 2 030 x 60=___________ 4. 30 x 90 =____________ 9. 456 x 70=____________ 5. 30 x 80 =____________ 10. 86 x 690=____________ Back Next
  66. 66. Lesson 15 PROBLEM SOLVING INVOLVING MULTIPLICATION Objectives After this lesson, the students are expected to: •describe how to use the multiplication in problem solving; •follow the steps correctly in multiplication of word problem; •discuss the use of multiplication in problem solving. A screw machine can produce 95 screws in one minute. How many screws it can produce in one hour? 1. What is asked? How many screws a screw machine can produce in one hour? 2. What are given? Screw machine can produce 95 screws in a minute. 3. What operation to be used? Multiplication Contents Back Next
  67. 67. Solution: 60 minutes = 1 hour 95 crews x 60 minutes = n Therefore, the screw machine can produce 5 700 crews in one hour. N = 5 700 screws. Here is another example, A department store bought 32 crates of portable radios. Each crate contains 50 radios. How many portable radios does the store have? 1. What is asked? How many portable radios does the store have? 2. What are given? 50 portable radios in 1 crate and 32 crates 3. What operation to be used? Multiplication Solution: 1 crate = 50 radios 32 crates x 50 radios = n N = 1 600 portable radios Therefore, there are 1 600 portable radios does the store have. Back Back Next Next
  68. 68. WORKSHEET NO. 15 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ Answer the following word problem. 1. Victoria and her brother, Daniel, deliver Sunday papers together. She delivers 58 papers and he delivers 49 papers. Each earns 75 cents for each paper delivered. How much more does Victoria earn than Daniel each Sunday? ________________________________________________________________________________________ ________________________________________________________________________________________ _______________________________________________________________________________________. 2. In one basketball stadium, a section contains 32 rows and each row contains 25 seats. If the stadium has 4 sections, how many seats it has? ________________________________________________________________________________________ ________________________________________________________________________________________ _______________________________________________________________________________________. 3. Season tickets for 45 home games cost P789. Single tickets cost P15 each. How much more does a season ticket cost than individual tickets bought of each game? ________________________________________________________________________________________ ________________________________________________________________________________________ _______________________________________________________________________________________. Back Next
  69. 69. 4. A store has 124 boxes of pencils with 144 pencils in each box. How many pencils they have? _________________________________________________________________________________________ _________________________________________________________________________________________ _____________________________________________________________________________________. 5. An eagle flies 70 miles per hour. How far can an eagle fly in 15 hours? _________________________________________________________________________________________ _________________________________________________________________________________________ _____________________________________________________________________________________. 6. Mandy can laid 65 bricks in 30 minutes. How many bricks can Mandy lay in 5 hours? _________________________________________________________________________________________ _________________________________________________________________________________________ _____________________________________________________________________________________. 7. Sound waves travels approximately 1 100 ft. per sec. in air. How far will the sound waves travel in 3 hours? _________________________________________________________________________________________ _________________________________________________________________________________________ _____________________________________________________________________________________. Back Next
  70. 70. 8. One cassette seller sold 650 cassettes. The cassettes cost her P15.00 each and sold them for P29.00 each. What was her total profit? ____________________________________________________________________________________________ ____________________________________________________________________________________________ _______________________________________________________________________________. 9. If a worker can make 357 bolts in one hour, how many bolts he can make in eight hours? ____________________________________________________________________________________________ ____________________________________________________________________________________________ _______________________________________________________________________________. 10. If 1cubic yard of concrete costs P55.00, how much would 13cubic yards cost? ____________________________________________________________________________________________ ____________________________________________________________________________________________ _______________________________________________________________________________. SOLUTION: Back Next
  71. 71. Introduction In this chapter, you will learn about the division operation its different parts and uses in solving word problem. This chapter provides you the information you need to master one of the fundamental operations in mathematics which is division. Contents Back Next
  72. 72. Lesson 16 WHAT IS DIVISION? Objectives After this lesson, the students are expected to:  define division;  identify the parts of division;  discuss the division operation. In mathematics, especially in elementary arithmetic, division ( ) is the arithmetic operation that is the inverse of multiplication. Division can be described as repeated subtraction whereas multiplication is repeated addition. Division is defined as this reverse of multiplication. In high school, the process is also the same. 64 8=8 since since 8 X 8=64 Contents Back Next
  73. 73. In the above expression, a is called the dividend, b the divisor and c the quotient. Example: Suppose that we have twelve students in the class and we want to divide the class into three equal groups. How many should be in each group? Solution: We can ask the alternative question, "Three times what number equals twelve?" The answer to this question is four. We write 4 3 12 or 12 3=4 we call the number 12 the dividend, the number 3 the divisor, and the number 4 the quotient. quotient divisor dividend or dividend divisor = quotient Back Next
  74. 74. Example •Division by Oneself Suppose that you had $100 and had to distribute all the money to 100 people so that each person received the same amount of money. How much would each person get? Solution If you gave each person $1 you would achieve your goal. This comes directly from the identity property of one. Since the questions asks what number times 100 equals 100. In general we conclude, Any number divided by itself equals 1 Example 100 100 = 1 38 38 = 1 15 15 = 1 B. Division by 1 Example Now let’s suppose that you have twelve pieces of paper and need to give them to exactly one person. How many pieces of paper does that person receive? Back Next
  75. 75. Solution Since the only person to collect the paper is the receiver, that person gets all twelve pieces. This also comes directly from the identity property of one, since one times twelve equals one. In general we conclude, Examples 12 1 = 12 42 1 = 42 33 1 = 33 When Zero is the Dividend Any number divided by 1 equals itself Example Now lets suppose that you have zero pieces of pizza and need to distribute your pizza to four friends so that each person receives the same number of pieces. How many pieces of pizza does that person receive? Solution Since you have no pizza to give, you give zero slices of pizza to each person. This comes directly from the multiplicative property of zero, since zero times four equals zero. In general we conclude, Back Next
  76. 76. Zero divided by any nonzero number equals zero Examples 0 4=0 0 1 = 0 0 24 = 0 The Problem with Dividing by Zero Example Finally lets suppose that you have five bags of garbage and you have to get rid of all the garbage, but have no places to put the garbage. How can you distribute your garbage to no places and still get rid of it all? Solution You can't! This is an impossible problem. There is no way to divide by zero. In general we conclude, Dividing by zero is impossible Examples 5 0 = undefined 0 0 = undefined 1 0 = undefined Back Next
  77. 77. WORKSHEET NO. 16 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ A. Give the name of the following unknown parts of division. ___________ 56 8=7 _________ _______________ B. As far as you remember, try to divide the following. 1.56 7= 2.54 6= 3.900 100= 4.64 16= 5.56 8= 6.122 11= 7.144 12= 8.256 16= 9.180 9= 10.360 4= Back Next
  78. 78. Lesson 17 MASTERING SKILLS IN DIVISION OF WHOLE NUMBERS Objectives After this lesson, the students are expected to: •develop knowledge in dividing whole numbers; •follow the steps in dividing whole numbers; •master the division of whole numbers. In mastering the division operation, you should need to know all the things in this operation. When dividing numbers, it has not always given an exact quotient. This process is what we called division with remainder. Division with Remainder Often when we work out a division problem, the answer is not a whole number. We can then write the answer as a whole number plus a remainder that is less than the divisor. Example 34 5 Solution Since there is no whole number when multiplied by five produces 34, we find the nearest number without going over. Notice that 5 x 6 = 30 and 5 x 7 = 35 Hence 6 is the nearest number without going over. Now notice that 30 is 4 short of 34. We write 34 5 = 6 R 4 "6 with a remainder of 4“0 Contents Back Next
  79. 79. Example 4321 6 Solution 720 6 | 4321 42 6 x 7 = 42 12 43 - 42 = 1 and drop down the 2 12 6 x 2 = 12 01 12 - 12 = 0 and drop down the 1 0 6x0 = 0 We can conclude that 4321 6 = 720 R1 1 1-0 = 1 In general we write (Divisor x quotient) + Remainder = dividend Example 511 37 18932 185 37 x 5 = 185 43 189 - 185 = 4 and drop down the 3 37 37 x 1 = 37 62 43 - 37 = 6 and drop down the 2 37 37 x 1 = 37 25 62 - 37 = 25 We can conclude that 18932 37 = 511 R25 Take note: the remainder may also be expressed in decimals. Back Next
  80. 80. (SPECIAL TOPIC) Mental Division of Whole Numbers The process of division is just multiplication in reverse. This means that if 4 3 = 12 then 12 3 = 4 and 12 4=3 If you know your multiplication tables well, you should find it reasonably easy to do simple divisions in your head . For example: you want to work out 42 7, and you remember that 6 7 = 42, • Brackets first so the answer is 6. • O • Divide When there is more than one operation in a question, you need to remember the order in • Multiply which operations are carried out. This can be summarized by BODMAS: • Add • Subtract If you see two of the same operation you just do them in the order they appear (left to right). Below are three examples of BODMAS used in a question. (a) 3 + 4 5 = 3 + 20 = 23 (Multiply before Add) (b) 10 ( 2 + 3 ) = 10 5=2 (Brackets before Division) (c) 20 2 2 = 10 2=5 (do operations left to right) Back Next
  81. 81. WORKSHEET NO. 17 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ Work out the answers to the questions below and fill in the boxes. Question 1 (a) 16 4 _________ (b) 12 6 _________ (c) 15 5 _________ (d) 20 4 _________ (e) 18 9 _________ (f) 40 8 _________ Use mental arithmetic to answer these questions (g) 36 9 _________ (do not use a calculator). Then check. (h) 15 3 _________ (i) 64 8 _________ (j) 42 7 _________ (k) 24 6 _________ (l) 32 8 _________ Back Next
  82. 82. Use BODMAS to work out whether these statements are TRUE or FALSE. (a) 10 2=2 10 __________ (b) 12 + 8 2 = 10 __________ (c) 3 + 12 4=6 __________ (d) 6 2+3=6 __________ Work out the answers to the following questions (without a calculator). (a) 3 + 4 8 __________ (b) 8 + 3 6 __________ (c) 8 6-4 __________ (d) 12 2+5 __________ (e) 5 - 12 3 __________ (f) 14 2+8 __________ (g) 3 2+8 4 __________ Back Next
  83. 83. Lesson 18 “CANCELLATION OF INSIGNIFICANT ZEROS “EASY WAYS IN DIVIDING WHOLE NUMBERS Objectives After this lesson, the students are expected to: divide whole numbers using other method; perform division of whole numbers mentally; define “ cancellation of insignificant zeros.” The cancellation of Insignificant Zeros is one of the easy ways in performing division of whole numbers. It is done by cancelling the insignificant zeros in both the divisor and the dividend. Contents Back Next
  84. 84. 101 50 5050 505 5=101 ( both dividend and divisor) 50 050 050 0 210 2. 5 1050 105 5=21(10) =210 (the insignificant zero in -10 dividend was cancelled) -50 To check multiply the quotient to the divisor then 50 multiply also the place value of the removed zeros 0 Remember that in cancelling both the dividend and divisor, the insignificant zeros are Examples needed to be the same. If you cancelled 3 zeros in the dividend, you need 300÷10=30 also to cancel 3 zeros 50÷50=1 from the divisor. 1000÷10=100 Back Next
  85. 85. WORKSHEET NO. 18 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ •Divide the following using the Cancellation of Insignificant Method. 1. 640 80=___________________ 2. 140 20=___________________ 3. 36000 600=________________ 4. 700 350=__________________ 5. 3500 70=__________________ 6. 350 100=__________________ 7. 5600 800=_________________ 8. 600 30=___________________ 9. 100 50=____________________ 10. 800 40=___________________ Back Next
  86. 86. 11. 1000 100=_________________ WRITE YOUR SOLUTION HERE: 12. 140 70=___________________ 13. 420 20=____________________ 14. 14000 70=_________________ 15. 36000 180=_________________ 16. 4800 240=_________________ 17. 99000 330=________________ 18. 860 20=___________________ 19. 770 770=__________________ 20. 630 30=___________________ Draw a 2 dimensional clock. Then draw a line across the clock so that the sum of the numbers in each group is the same. B. CHALLENGE!!! • Copy the figure. Show how to divide it into 2 equal parts. Each part must have the same size and shape. • Copy the figure again. Show how to divide it in 3 equal parts. • Copy the figure again. Show how to divide it in 4 equal parts. Back Next
  87. 87. Lesson 19 PROBLEM SOLVING INVOLVING DIVISION OF WHOLE NUMBERS Objectives After this lesson, the students are expected to: • solve the given problem critically; • follow the steps in problem solving ; • apply the division of whole numbers in solving mathematical problem. Like the first three operations, the division operation is very usable to our daily lives. We use also this operation to solve some problems. Take a look and study the examples given below Example You are the manager of a ski resort and noticed that during the month of January you sold a total of 111,359 day ski tickets. What was the average number of tickets that were sold that month? Contents Back Next
  88. 88. Solution Since there are 31 days in January, we need to divide the total number of tickets by 31 3589 31 | 111259 93 31 x 3 = 93 182 111 - 93 = 18 and drop down the 2 Answer: The ski resort 155 31 x 5 = 155 averaged 3,589 ticket sales 275 182 - 155 = 27 and drop down the 5 per day in the month of 248 31 x 8 = 248 January. 279 275 - 248 = 27 279 31 x 9 = 279 0 Another example Courtney is hanging glow in the dark stars in each room of his house. If there are 160 stars in the box and she wants 16 in each room, how many rooms can she hang stars? Solution Since there are 160 stars in the box and she wants 16 in each room. And the problem is asking for how many stars in each room will be? 10 16 160 16x1=16 Answer: Courtney can hang 16 16-16=0 her 160 stars in 10 rooms 00 16x0=0 00 0 Back Next
  89. 89. WORKSHEET NO. 19 NAME: ___________________________________ DATE: _____________ YEAR & SECTION: ________________________ RATING: ___________ A. Analyze and solve the following problems. 1. Jacinta has 5 pennies in a jar. If she divides it into 2 stacks of 50, how many stacks does she have now? ____________________________________________________________________________________________ ____________________________________________________________________________________________ ____________________________________________________________________________________________ ____________________________________________________________________________________________ ________________. 2. Harry has 300 pieces of chalk with the same amount in each box. There are 20 boxes how many pieces of chalk in EACH box? ____________________________________________________________________________________________ ____________________________________________________________________________________________ ____________________________________________________________________________________________ ____________________________________________________________________________________________ ____________________. Back Next
  90. 90. 3. The surface area of a floor is 150 square feet. How many 10 ft. square tiles will be needed (inside of 150 feet) to cover the floor? (How many 10's are inside of 150?) ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ ______________________________________________________________________________________ _____________________________________________. 4. Billy was offered a job at the nearby golf course. The owner offered him $500.00 per seven day week or $50. the first day and agreed to double it for each following day. How could Billy make the most amount of money? Which deal should he accept and why? _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _________________________________________. 5. Sally is having a birthday party with 10 people. When everyone gets there she asks everyone to introduce themselves and shake everyone's hand. How many handshakes will there be? How do you know? _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _______________________________________________________________________________________ _________________________________________. Back Next
  91. 91. Overview In UNIT II, you will expect the concept of the basic fundamental operations dealing with the integers the concept, the nature and the difference between them. Likewise, the lessons provided in this unit will enable you to perform skillfully the four fundamental operations with integers. You will think much critically to perform the activities and to solve the exercises that will be given to you in this unit. This unit also contains precedence of operations which you can use in Algebra II. Objectives: After studying this unit, you are expected to: 1. discuss the integers; 2. use the fundamental operations in solving integers; 3. appreciate the integers as a part of your discussion; 4. gain more knowledge about integers that will guide you in the world of algebra; 5. discuss the order of operation. Contents Back Next
  92. 92. Introduction You have finished Unit 1 of this modular workbook. You now already reviewed what you have taken in your Elementary level . Now, you are ready to proceed to the next chapter of this modular workbook, the INTEGERS. This chapter will give you a deep understanding about integers, the different kinds of integers, the uses of integers in Mathematics and the functions of integers in our real world. In studying high school math, integers are always present. It seems that you have already mastered the fundamental operations in whole numbers you may now proceed to the next chapter which is the application of the four fundamental operations that you have mastered. Contents Back Next

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