Lowest Common Multiple and Highest Common Factor


 Asher O’Neal’
 2 years ago
 Views:
Transcription
1 Lowest Common Multiple and Highest Common Factor Multiple: The multiples of a number are its times table If you want to find out if a number is a multiple of another number you just need to divide the first one by the second number, if the result is a round figure then the first number is a multiple of the second. Any number can have an infinity of multiples Example: 9 is a multiple of 3 because 9:3=3 144 is a multiple of 12 because 144:9= is a multiple of 5 because 225:5=45 In order to verify if a number is a multiple of another one here are some secret rules: The number is divisible by: 2 if the last digit is 0, 2, 4, 6, or 8 (example: 12346); 3 if the sum of digits in the number are divisible by 3 (example: 1236, because = 12 = 3 x 4); 4 if the last 2 digits are divisible by 4 (example: , because 44 = 4 x 11); 5 if the last digit is 0 or 5 (example: or 40980); 6 if it is divisible by 2 and 3; 7 sorry, no rule (you have to divide); 8 if the last 3 digits are divisible by 8 (example: , because 080 = 8 x 10; 1
2 9 if the sum of digits is divisible by 9 (example: , because = 18 = 9 x 2); 10 if the last digit is 0 (example: ); 100 if the last 2 digits are 0 (example ); Lowest Common Multiple (LCM) Definition: The Lowest Common Multiple of two numbers is the smallest number that can be divided by both numbers. Multiples of 10: 10, 20, 30, 40, 50, 60, 70, 80, Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 2. The LCM of 14, 56 and 28 is: Multiples of 56: 56, 112, 168, 224 Multiples of 28: 28, 56, 84, 112 Multiples of 14: 14, 28, 42, 56 Observation: Another way to find the LCM of two or three prime numbers you just need find the biggest power of each factor from the numbers and multiply these together If you need to find the LCM of any numbers start by listing their multiples. Find the common one. Example: 1. The LCM of 10 and 12 is: Example: The LCM of 50 and 20 is 50 = 2 * 5 * 5 20 = 2 * 2 * 5 LCM = 2* 2* 5* 5 =100 2
3 Highest Common Factor (HCF) The highest common factor of two or more whole numbers is the largest whole number that divides evenly into each of the numbers. There are two ways to find the highest common factor. The first method is to list all of the factors of each number, then list the common factors and choose the largest one. Example: Find the HCF of 36 and 54. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. The common factors of 36 and 54 are 1, 2, 3, 6, 9, 18 Although the numbers in bold are all common factors of both 36 and 54, 18 is the highest common factor. The second method for finding the greatest common factor is to list the prime factors, then multiply the common prime factors. Example: Let's use the same numbers, 36 and 54 again to find their greatest common multiple. The prime factorization of 36 is 2 x 2 x 3 x 3 The prime factorization of 54 is 2 x 3 x 3 x 3 Notice that the prime factorizations of 36 and 54 both have one 2 andtwo 3s in common. So, we 3
4 simply multiply these common prime factors to find the greatest common factor. Like this... 2 x 3 x 3 = 1 Other examples: The HCF of 50 and 20 is 50 = 2 * 5 * 5 20 = 2 * 2 * 5 HCF = 2* 5 = 10 The HCF of 70 and 120 is 70 = 2*5* = 2*5* 3* 2 HCF = 2*5 = 10 See, both methods for finding the greatest common factor work! 4
5 Let s Practice: 1. Write this numbers as the product of their prime factors a) 42 b) 64 c) 75 d) 125 e) 144 f) 269 g) Find the lowest common multiple of the following. a) 2, 3 b) 2, 3, 5 c) 7, 11 d) 11, 13 e) 3, 7, 2 3. Find the LCM of: a) 12 and 24 b) 25 and 75 c) 13 and 39 d) 27 and 9 e) 60 and Match the numbers with their LCM 9 and and and and What is the LCM for the given numbers? a) 5, 7, 8 b) 8, 16, 32 c) 4, 12, 16 5
6 d) 24, 36, 42 The HCF of 30 and 50 is : 6. Find the first ten multiples of this numbers: a) 10 a) 12 b) 150 b) 9 c) 100 c) 15 d) 25 e) Find the LCM of the next pairs of numbers a) 14 and 24 The HCF of 60 and 85 is: a) 5 b) 15 c) 13 b) 80 and 25 c) 64 and Find the right answer The LCM of 13, 26 and 169 a) 169 b) 13 The LCM of 45 and 20 is: c) 69 a) Let s solve the table b) 5 c) and 18 is 10 and 40 is 30 and 10 is 6 and 4 is 9 and 21 is 6
7 9 and 6 is 4 and 18 is 9 and 18 is 40 and 10 is 30 and 15 is 45 and 35 is 12 and 18 is 18 and 24 is 24 and 27 is 16 and 18 is 10.Let s solve the table 45 and 25 is 16 and 14 is 15 and 20 is 24 and 21 is 12 and 6 is 18 and 15 is 6 and 15 is 15 and 10 is 24 and 18 is 8 and 10 is 12 and 14 is 27 and 15 is 14 and 10 is 21 and 18 is 15 and 6 is 40 and 10 is 15 and 18 is 12 and 9 is 21 and 9 is 12 and 24 is 24 and 6 is 18 and 27 is 35 and 25 is 15 and 27 is 18 and 15 is 20 and 15 is 25 and 45 is 8 and 14 is 9 and 6 is 10 and 18 is 16 and 10 is 15 and 27 is 40 and 35 is 12 and 27 is 40 and 20 is The Lowest Common Multiple (L.C.M.) of: 10 and 30 is 4 and 10 is 10 and 12 is 9 and 30 is 6 and 36 is 6 and 30 is 9 and 12 is 25 and 30 is 10 and 20 6 and 20 is 15 and 30 9 and 12 is is is 15 and 30 6 and 12 is 4 and 16 is 4 and 12 is is 4 and 24 is 6 and 18 is 25 and 18 9 and 8 is is 10 and 8 is 10 and and 12 4 and 30 is is is 10 and 20 is 10 and 12 is 10 and 20 is 15 and 12 is 15 and 12 is 6 and 30 is 7
8 6 and 8 is 9 and 12 is 4 and 10 is 10 and 9 is 10 and 30 is 18 and 6 is 10 and and and 20 6 and 20 is is is is 10 and 4 is 15 and and and 12 6 and 4 is is is is 25 and 4 is 25 and and and and 12 is is is is 8
Adding and Subtracting Fractions. 1. The denominator of a fraction names the fraction. It tells you how many equal parts something is divided into.
Tallahassee Community College Adding and Subtracting Fractions Important Ideas:. The denominator of a fraction names the fraction. It tells you how many equal parts something is divided into.. The numerator
More informationTips, tricks and formulae on H.C.F and L.C.M. Follow the steps below to find H.C.F of given numbers by prime factorization method.
Highest Common Factor (H.C.F) Tips, tricks and formulae on H.C.F and L.C.M H.C.F is the highest common factor or also known as greatest common divisor, the greatest number which exactly divides all the
More information18. [Multiples / Factors / Primes]
18. [Multiples / Factors / Primes] Skill 18.1 Finding the multiples of a number. Count by the number i.e. add the number to itself continuously. OR Multiply the number by 1, then 2,,, 5, etc. to get the
More informationNAME TEST DATE FRACTION STUDY GUIDE/EXTRA PRACTICE PART 1: PRIME OR COMPOSITE?
NAME TEST DATE FRACTION STUDY GUIDE/EXTRA PRACTICE PART 1: PRIME OR COMPOSITE? A prime number is a number that has exactly 2 factors, one and itself. Examples: 2, 3, 5, 11, 31 2 is the only even number
More informationPrime Factorization, Greatest Common Factor (GCF), and Least Common Multiple (LCM)
Prime Factorization, Greatest Common Factor (GCF), and Least Common Multiple (LCM) Definition of a Prime Number A prime number is a whole number greater than 1 AND can only be divided evenly by 1 and itself.
More informationClass VI Chapter 3 Playing with Numbers Maths
Exercise 3. Question : Write all the factors of the following numbers: (a) 24 (b) 5 (c) 2 (d) 27 (e) 2 (f) 20 (g) 8 (h) 23 (i) 36 (a) 24 24 = 24 24 = 2 2 24 = 3 8 24 = 4 6 24 = 6 4 Factors of 24 are, 2,
More informationCalculate Highest Common Factors(HCFs) & Least Common Multiples(LCMs) NA1
Calculate Highest Common Factors(HCFs) & Least Common Multiples(LCMs) NA1 What are the multiples of 5? The multiples are in the five times table What are the factors of 90? Each of these is a pair of factors.
More informationGreatest Common Factor and Least Common Multiple
Greatest Common Factor and Least Common Multiple Intro In order to understand the concepts of Greatest Common Factor (GCF) and Least Common Multiple (LCM), we need to define two key terms: Multiple: Multiples
More informationPrime Time: Homework Examples from ACE
Prime Time: Homework Examples from ACE Investigation 1: Building on Factors and Multiples, ACE #8, 28 Investigation 2: Common Multiples and Common Factors, ACE #11, 16, 17, 28 Investigation 3: Factorizations:
More information3 PLAYING WITH NUMBERS
3 PLAYING WITH NUMBERS Exercise 3.1 Q.1. Write all the factors of the following numbers : (a) 24 (b) 15 (c) 21 (d) 27 (e) 12 (f) 20 (g) 18 (h) 23 (i) 36 Ans. (a) 24 = 1 24 = 2 12 = 3 8 = 4 6 Hence, factors
More informationMEP Y8 Practice Book A
2 Factors MEP Y8 Practice Book A 2.1 Factors and Prime Numbers A factor divides exactly into a number, leaving no remainder. For example, 13 is a factor of 26 because 26 13 = 2 leaving no remainder. A
More informationFACTORS, PRIME NUMBERS, H.C.F. AND L.C.M.
Mathematics Revision Guides Factors, Prime Numbers, H.C.F. and L.C.M. Page 1 of 10 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Foundation Tier FACTORS, PRIME NUMBERS, H.C.F. AND L.C.M. Version:
More informationNumber. ch?v=mquhqkknldk (maths is confusing funny)
Number http://www.youtube.com/watch?v =52CzD31SqaM&feature=related (maths is confusing II funny) http://www.youtube.com/wat ch?v=mquhqkknldk (maths is confusing funny) SLO To find multiples of a number
More informationNumber boards for mini mental sessions
Number boards for mini mental sessions Feel free to edit the document as you wish and customise boards and questions to suit your learners levels Print and laminate for extra sturdiness. Ideal for working
More informationFACTORS, PRIME NUMBERS, H.C.F. AND L.C.M.
Mathematics Revision Guides Factors, Prime Numbers, H.C.F. and L.C.M. Page 1 of 16 M.K. HOME TUITION Mathematics Revision Guides Level: GCSE Higher Tier FACTORS, PRIME NUMBERS, H.C.F. AND L.C.M. Version:
More informationChapter 4 Fractions and Mixed Numbers
Chapter 4 Fractions and Mixed Numbers 4.1 Introduction to Fractions and Mixed Numbers Parts of a Fraction Whole numbers are used to count whole things. To refer to a part of a whole, fractions are used.
More informationGrade 6 Math Circles March 10/11, 2015 Prime Time Solutions
Faculty of Mathematics Waterloo, Ontario N2L 3G1 Centre for Education in Mathematics and Computing Lights, Camera, Primes! Grade 6 Math Circles March 10/11, 2015 Prime Time Solutions Today, we re going
More information1.5 Greatest Common Factor and Least Common Multiple
1.5 Greatest Common Factor and Least Common Multiple This chapter will conclude with two topics which will be used when working with fractions. Recall that factors of a number are numbers that divide into
More informationnorth seattle community college
INTRODUCTION TO FRACTIONS If we divide a whole number into equal parts we get a fraction: For example, this circle is divided into quarters. Three quarters, or, of the circle is shaded. DEFINITIONS: The
More informationSect 3.2  Least Common Multiple
Let's start with an example: Sect 3.2  Least Common Multiple Ex. 1 Suppose a family has two different pies. If they have 2 3 of one type of pie and 3 of another pie, is it possible to combine the pies
More informationOperations with Radicals
3.4 Operations with Radicals GOAL Simplify and perform operations on mixed and entire radicals. INVESTIGATE the Math The distance, s(t), in millimetres of a particle from a certain point at any time, t,
More informationFACTORS AND MULTIPLES Answer Key
I. Find prime factors by factor tree method FACTORS AND MULTIPLES Answer Key a. 768 2 384 2 192 2 96 2 48 2 24 2 12 2 6 2 3 768 = 2*2*2*2*2*2*2*2 *3 b. 1608 3 536 2 268 2 134 2 67 1608 = 3*2*2*2*67 c.
More informationExponents, Factors, and Fractions. Chapter 3
Exponents, Factors, and Fractions Chapter 3 Exponents and Order of Operations Lesson 31 Terms An exponent tells you how many times a number is used as a factor A base is the number that is multiplied
More informationCommon Multiples. List the multiples of 3. The multiples of 3 are 3 1, 3 2, 3 3, 3 4,...
.2 Common Multiples.2 OBJECTIVES 1. Find the least common multiple (LCM) of two numbers 2. Find the least common multiple (LCM) of a group of numbers. Compare the size of two fractions In this chapter,
More informationGrade 7 & 8 Math Circles October 19, 2011 Prime Numbers
1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 7 & 8 Math Circles October 19, 2011 Prime Numbers Factors Definition: A factor of a number is a whole
More informationFun Number Theory Meeting (Computation, Factors, Exponent Patterns, Factorials, Perfect Squares and Cubes)
Fun Number Theory Meeting (Computation, Factors, Exponent Patterns, Factorials, Perfect Squares and Cubes) Topic This meeting s topics fall in the category of number theory. Students will apply their knowledge
More informationSCHOOL OF ENGINEERING & BUILT ENVIRONMENT. Mathematics. Numbers
SCHOOL OF ENGINEERING & BUILT ENVIRONMENT Mathematics Numbers. Factors 2. Multiples 3. Prime and Composite Numbers 4. Modular Arithmetic 5. Boolean Algebra 6. Modulo 2 Matrix Arithmetic 7. Number Systems
More informationPreAlgebra Homework 2 Factors: Solutions
PreAlgebra Homework 2 Factors: Solutions 1. Find all of the primes between 70 and 100. : First, reject the obvious nonprime numbers. None of the even numbers can be a prime because they can be divided
More informationGCSE Revision Notes Mathematics Number s and Algebra
GCSE Revision Notes Mathematics Number s and Algebra irevise.com 2014. All revision notes have been produced by mockness ltd for irevise.com. Email: info@irevise.com Copyrighted material. All rights reserved;
More informationSession 6 Number Theory
Key Terms in This Session Session 6 Number Theory Previously Introduced counting numbers factor factor tree prime number New in This Session composite number greatest common factor least common multiple
More informationIntroduction to Fractions
Introduction to Fractions Fractions represent parts of a whole. The top part of a fraction is called the numerator, while the bottom part of a fraction is called the denominator. The denominator states
More informationCONTENTS. Please note:
CONTENTS Introduction...iv. Number Systems... 2. Algebraic Expressions.... Factorising...24 4. Solving Linear Equations...8. Solving Quadratic Equations...0 6. Simultaneous Equations.... Long Division
More informationFactoring Whole Numbers
2.2 Factoring Whole Numbers 2.2 OBJECTIVES 1. Find the factors of a whole number 2. Find the prime factorization for any number 3. Find the greatest common factor (GCF) of two numbers 4. Find the GCF for
More information6.1 The Greatest Common Factor; Factoring by Grouping
386 CHAPTER 6 Factoring and Applications 6.1 The Greatest Common Factor; Factoring by Grouping OBJECTIVES 1 Find the greatest common factor of a list of terms. 2 Factor out the greatest common factor.
More informationThe GMAT Guru. Prime Factorization: Theory and Practice
. Prime Factorization: Theory and Practice The following is an ecerpt from The GMAT Guru Guide, available eclusively to clients of The GMAT Guru. If you would like more information about GMAT Guru services,
More informationDay One: Least Common Multiple
Grade Level/Course: 5 th /6 th Grade Math Lesson/Unit Plan Name: Using Prime Factors to find LCM and GCF. Rationale/Lesson Abstract: The objective of this two part lesson is to give students a clear understanding
More informationObjectives: In this fractions unit, we will
Objectives: In this fractions unit, we will subtract and add fractions with unlike denominators (pp. 101 102) multiply fractions(pp.109 110) Divide fractions (pp. 113 114) Review: Which is greater, 1/3
More informationMultiples and factors quiz
Level A 1. 18, 27 and 36 are all multiples of nine. 2. 500 is a multiple of 200. 3. Which list is made up of multiples of 12? A) 1, 12, 48 B) 12, 24, 36 C) 12, 22, 32 4. The digit sums (the one digit answer
More informationHOW TO COMPARE FRACTIONS
HOW TO COMPARE FRACTIONS Introducing: common denominator least common denominator like fractions unlike fractions. Compare Fractions 1 The fractions 3 / 4 and 2 / 4 have the same denominator. Fractions
More informationPowers and roots 5.1. Previous learning. Objectives based on NC levels and (mainly level ) Lessons 1 Working with integer powers of numbers
N 5.1 Powers and roots Previous learning Before they start, pupils should be able to: recognise and use multiples, factors (divisors), common factor, highest common factor, lowest common multiple and primes
More informationInternational Indian School, Riyadh SA1 Worksheet 20152016 Class: VI Mathematics
International Indian School, Riyadh SA1 Worksheet 20152016 Class: VI Mathematics CH KNOWING OUR NUMBERS I Fill In the blanks 1. 1km = mm 2. 1 gram = milligrams 3. The roman numeral M stands for the number
More informationFractions and Linear Equations
Fractions and Linear Equations Fraction Operations While you can perform operations on fractions using the calculator, for this worksheet you must perform the operations by hand. You must show all steps
More informationUnit 1 Number Sense. In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions.
Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L34) is a summary BLM for the material
More informationGrade 7/8 Math Circles Fall 2012 Factors and Primes
1 University of Waterloo Faculty of Mathematics Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Fall 2012 Factors and Primes Factors Definition: A factor of a number is a whole
More informationWhole Numbers. Solve.
1 CHAPTER PROBLEM SOLVING Thinking Skills Solve. 1. A bag contains a yellow ball and a red ball. a. Daisy picked the yellow ball with a 4digit number written on it. When she rounded the number to the
More informationMath 201: Homework 7 Solutions
Math 201: Homework 7 Solutions 1. ( 5.2 #4) (a) The factors of 72 are 1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, and 72. (b) The factors of 81 are 1, 3, 9, 27, and 81. (c) The factors of 62 are 1, 2, 31, and
More informationGreatest Common Factors and Least Common Multiples with Venn Diagrams
Greatest Common Factors and Least Common Multiples with Venn Diagrams Stephanie Kolitsch and Louis Kolitsch The University of Tennessee at Martin Martin, TN 38238 Abstract: In this article the authors
More informationAddition with Unlike Denominators
Lesson. Addition with Unlike Denominators Karen is stringing a necklace with beads. She puts green beads on _ of the string and purple beads on of the string. How much of the string does Karen cover with
More informationRound decimals to the nearest whole number
Round decimals to the nearest whole number Learning Objective Simplifying Fractions Simplified Fractions To simplify a fraction, we find an equivalent fraction which uses the smallest numbers possible.
More information47 Numerator Denominator
JH WEEKLIES ISSUE #22 20122013 Mathematics Fractions Mathematicians often have to deal with numbers that are not whole numbers (1, 2, 3 etc.). The preferred way to represent these partial numbers (rational
More information2.6 Adding and Subtracting Fractions and Mixed Numbers with Unlike Denominators
2.6 Adding and Subtracting Fractions and Mixed Numbers with Unlike Denominators Learning Objective(s) 1 Find the least common multiple (LCM) of two or more numbers. 2 Find the Least Common Denominator
More informationThe Next Step. Mathematics Applications for Adults. Book Fractions
The Next Step Mathematics Applications for Adults Book 101  Fractions OUTLINE Mathematics  Book 101 Fractions Understanding and Comparing Fractions explain proper and improper fractions provide equivalent
More informationMean, Median, Mode, Range and Outlier
Mean, Median, Mode, Range and Outlier For Learning to Happen: Take out a calculator. 1 Sum the answer to an addition problem. Addend the numbers you added together to get the sum. Or how many total numbers
More information1. When the least common multiple of 8 and 20 is multiplied by the greatest common factor of 8 and 20, what is the result?
Black Equivalent Fractions and LCM 1. When the least common multiple of 8 and 20 is multiplied by the greatest common factor of 8 and 20, what is the result? 2. The sum of three consecutive integers is
More informationMathematics Scheme of Work: Form
Textbook: Formula One Maths B2 Hodder and Stoughton Chapter No. First Term Revising Time Topic and Subtopic October  December Handout Notes 2 Numbers 2.1 Basic conversions: Changing from large units to
More informationFRACTION REVIEW. 3 and. Any fraction can be changed into an equivalent fraction by multiplying both the numerator and denominator by the same number
FRACTION REVIEW A. INTRODUCTION. What is a fraction? A fraction consists of a numerator (part) on top of a denominator (total) separated by a horizontal line. For example, the fraction of the circle which
More informationCOMPASS Numerical Skills/PreAlgebra Preparation Guide. Introduction Operations with Integers Absolute Value of Numbers 13
COMPASS Numerical Skills/PreAlgebra Preparation Guide Please note that the guide is for reference only and that it does not represent an exact match with the assessment content. The Assessment Centre
More informationCourse notes on Number Theory
Course notes on Number Theory In Number Theory, we make the decision to work entirely with whole numbers. There are many reasons for this besides just mathematical interest, not the least of which is that
More informationFractions. If the top and bottom numbers of a fraction are the same then you have a whole one.
What do fractions mean? Fractions Academic Skills Advice Look at the bottom of the fraction first this tells you how many pieces the shape (or number) has been cut into. Then look at the top of the fraction
More informationChapter 1: Number and Numeration
2 TH Easy Maths 5 Chapter : Number and Numeration Exercise. Refer answers at the end of book. Exercise.2 3. Greatest 6 digit number = 999999 Greatest 5 digit number = 99999 Total 6 digit numbers = Greatest
More informationREVIEW SHEETS BASIC MATHEMATICS MATH 010
REVIEW SHEETS BASIC MATHEMATICS MATH 010 A Summary of Concepts Needed to be Successful in Mathematics The following sheets list the key concepts that are taught in the specified math course. The sheets
More informationCategory 3 Number Theory Meet #1, October, 2000
Category 3 Meet #1, October, 2000 1. For how many positive integral values of n will 168 n be a whole number? 2. What is the greatest integer that will always divide the product of four consecutive integers?
More informationFraction Competency Packet
Fraction Competency Packet Developed by: Nancy Tufo Revised 00: Sharyn Sweeney Student Support Center North Shore Community College To use this booklet, review the glossary, study the examples, then work
More informationSection R.2. Fractions
Section R.2 Fractions Learning objectives Fraction properties of 0 and 1 Writing equivalent fractions Writing fractions in simplest form Multiplying and dividing fractions Adding and subtracting fractions
More information17 Greatest Common Factors and Least Common Multiples
17 Greatest Common Factors and Least Common Multiples Consider the following concrete problem: An architect is designing an elegant display room for art museum. One wall is to be covered with large square
More informationAlgebra for Digital Communication
EPFL  Section de Mathématiques Algebra for Digital Communication Fall semester 2008 Solutions for exercise sheet 1 Exercise 1. i) We will do a proof by contradiction. Suppose 2 a 2 but 2 a. We will obtain
More information1 Number System. Introduction. Face Value and Place Value of a Digit. Categories of Numbers
RMAT Success Master 3 1 Number System Introduction In the decimal number system, numbers are expressed by means of symbols 0, 1,, 3, 4, 5, 6, 7, 8, 9, called digits. Here, 0 is called an insignificant
More informationFactors and Products
CHAPTER 3 Factors and Products What You ll Learn use different strategies to find factors and multiples of whole numbers identify prime factors and write the prime factorization of a number find square
More informationSection 6.1 Factoring Expressions
Section 6.1 Factoring Expressions The first method we will discuss, in solving polynomial equations, is the method of FACTORING. Before we jump into this process, you need to have some concept of what
More informationMultiplying and Dividing Fractions
Multiplying and Dividing Fractions 1 Overview Fractions and Mixed Numbers Factors and Prime Factorization Simplest Form of a Fraction Multiplying Fractions and Mixed Numbers Dividing Fractions and Mixed
More informationBasic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704.
Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. The purpose of this Basic Math Refresher is to review basic math concepts so that students enrolled in PUBP704:
More informationSequential Skills. Strands and Major Topics
Sequential Skills This set of charts lists, by strand, the skills that are assessed, taught, and practiced in the Skills Tutorial program. Each Strand ends with a Mastery Test. You can enter correlating
More informationReal Numbers. Learning Outcomes. chapter. In this chapter you will learn:
chapter Learning Outcomes In this chapter you will learn: ÂÂ ÂÂ ÂÂ ÂÂ ÂÂ ÂÂ ÂÂ ÂÂ How to define the real numbers About factors, multiples and prime factors How to write a whole number as a product of prime
More informationGRE MATH REVIEW #2. Fractions
GRE MATH REVIEW #2 Fractions A fraction is just a shorthand way of expressing a division problem. In other words, 5/2 = 5 2. The Numerator is the top number in a fraction and the Denominator is the bottom
More informationPrime Numbers A prime number is a whole number, greater than 1, that has only 1 an itself as factors.
Prime Numbers A prime number is a whole number, greater than 1, that has only 1 an itself as factors. Composite Numbers A composite number is a whole number, greater than 1, that are not prime. Prime Factorization
More informationTransition To College Mathematics
Transition To College Mathematics In Support of Kentucky s College and Career Readiness Program Northern Kentucky University Kentucky Online Testing (KYOTE) Group Steve Newman Mike Waters Janis Broering
More informationMath Workshop October 2010 Fractions and Repeating Decimals
Math Workshop October 2010 Fractions and Repeating Decimals This evening we will investigate the patterns that arise when converting fractions to decimals. As an example of what we will be looking at,
More informationMiniPosters. LES 1 Shopping at the Coop
MiniPosters LES 1 Shopping at the Coop Application Situation 1 p. 1 Application Situation 2 p. 48 Application Situation 3 p. 53 Application Situation 4 p. 54 Table of Contents APPLICATION SITUATION 1
More informationTopics Included. (1) Q. No. 1 to 50 are based on basic. Calculation questions related to Addition,
Organized by Global Maths Science Education In Association with Math Vision Pte.Ltd., Singapore. www.mathsshow.com Total Marks : 200 Time : 90 min Total No of questions: 100 Topics Included. (1) Q. No.
More informationSquares and Square Roots
SQUARES AND SQUARE ROOTS 89 Squares and Square Roots CHAPTER 6 6.1 Introduction You know that the area of a square = side side (where side means the length of a side ). Study the following table. Side
More informationExpanding brackets and factorising
Chapter 7 Expanding brackets and factorising This chapter will show you how to expand and simplify expressions with brackets solve equations and inequalities involving brackets factorise by removing a
More informationChapter R.4 Factoring Polynomials
Chapter R.4 Factoring Polynomials Introduction to Factoring To factor an expression means to write the expression as a product of two or more factors. Sample Problem: Factor each expression. a. 15 b. x
More informationUnit: Polynomials and Factoring
Name Unit: Polynomials: Multiplying and Factoring Specific Outcome 10I.A.1 Demonstrate an understanding of factors of whole numbers by determining: Prime factors Greatest common factor Least common multiple
More informationNumbers and Computation
hot topics Numbers and Computation 1 1 1 2 1 3 1 4 1 5 Place Value of Whole Numbers 70 Properties 74 Order of Operations 78 Factors and Multiples 80 Integer Operations 88 What do you already know? You
More information3 cups ¾ ½ ¼ 2 cups ¾ ½ ¼. 1 cup ¾ ½ ¼. 1 cup. 1 cup ¾ ½ ¼ ¾ ½ ¼. 1 cup. 1 cup ¾ ½ ¼ ¾ ½ ¼
cups cups cup Fractions are a form of division. When I ask what is / I am asking How big will each part be if I break into equal parts? The answer is. This a fraction. A fraction is part of a whole. The
More informationSome sequences have a fixed length and have a last term, while others go on forever.
Sequences and series Sequences A sequence is a list of numbers (actually, they don t have to be numbers). Here is a sequence: 1, 4, 9, 16 The order makes a difference, so 16, 9, 4, 1 is a different sequence.
More informationWorking with whole numbers
1 CHAPTER 1 Working with whole numbers In this chapter you will revise earlier work on: addition and subtraction without a calculator multiplication and division without a calculator using positive and
More informationChapter 5. Rational Expressions
5.. Simplify Rational Expressions KYOTE Standards: CR ; CA 7 Chapter 5. Rational Expressions Definition. A rational expression is the quotient P Q of two polynomials P and Q in one or more variables, where
More informationAn Introduction to Number Theory Prime Numbers and Their Applications.
East Tennessee State University Digital Commons @ East Tennessee State University Electronic Theses and Dissertations 82006 An Introduction to Number Theory Prime Numbers and Their Applications. Crystal
More informationPreviously, you learned the names of the parts of a multiplication problem. 1. a. 6 2 = 12 6 and 2 are the. b. 12 is the
Tallahassee Community College 13 PRIME NUMBERS AND FACTORING (Use your math book with this lab) I. Divisors and Factors of a Number Previously, you learned the names of the parts of a multiplication problem.
More informationPREPARATION FOR MATH TESTING at CityLab Academy
PREPARATION FOR MATH TESTING at CityLab Academy compiled by Gloria Vachino, M.S. Refresh your math skills with a MATH REVIEW and find out if you are ready for the math entrance test by taking a PRETEST
More informationNCERT. not to be republished NUMBER SYSTEM UNIT 1 MATHEMATICS. (A) Main Concepts and Results
MATHEMATICS UNIT 1 NUMBER SYSTEM (A) Main Concepts and Results (i) Knowing our Numbers Large numbers upto one crore Reading and writing of large numbers Comparing large numbers Indian System of Numeration
More informationModule 2: Working with Fractions and Mixed Numbers. 2.1 Review of Fractions. 1. Understand Fractions on a Number Line
Module : Working with Fractions and Mixed Numbers.1 Review of Fractions 1. Understand Fractions on a Number Line Fractions are used to represent quantities between the whole numbers on a number line. A
More informationMTH 231 Practice Test SKILLS Problems (Sections 3.3, 3.4, 4.1, 4.2, 5.1, 5.2) Provide an appropriate response.
MTH 231 Practice Test SKILLS Problems (Sections 3.3, 3.4, 4.1, 4.2, 5.1, 5.2) Calculate / demonstrate using the expanded algorithm. Then do the same problem using the standard algorithm. 1) 72 + 806 A)
More informationPrime Numbers and Divisibility Section 2.1 Prime Number Any whole number that has exactly two factors, 1 and itself. numbers.
2 Summary DEFINITION/PROCEDURE EXAMPLE REFERENCE Prime Numbers and Divisibility Section 2. Prime Number Any whole number that has exactly two factors, and itself. 7, 3, 29, and 73 are prime numbers. p.
More informationCard Games. ***All card games require the teacher to take out the face cards except aces. The aces have a value of one.
Card Games ***All card games require the teacher to take out the face cards except aces. The aces have a value of one. Salute: (Multiplication or Addition) Three students are needed to play this game.
More informationCHAPTER 7: FACTORING POLYNOMIALS
CHAPTER 7: FACTORING POLYNOMIALS FACTOR (noun) An of two or more quantities which form a product when multiplied together. 1 can be rewritten as 3*, where 3 and are FACTORS of 1. FACTOR (verb)  To factor
More informationUnit 1 Review Part 1 3 combined Handout KEY.notebook. September 26, 2013
Math 10c Unit 1 Factors, Powers and Radicals Key Concepts 1.1 Determine the prime factors of a whole number. 650 3910 1.2 Explain why the numbers 0 and 1 have no prime factors. 0 and 1 have no prime factors
More informationMath Games with a Deck of Cards. Math Games with a Deck of Cards
Math Games with a Deck of Cards Math Games with a Deck of Cards Place Value Battle Materials: one shuffled deck of cards with the tens and face cards removed Shuffle the cards. One player deals the cards
More information3.1. RATIONAL EXPRESSIONS
3.1. RATIONAL EXPRESSIONS RATIONAL NUMBERS In previous courses you have learned how to operate (do addition, subtraction, multiplication, and division) on rational numbers (fractions). Rational numbers
More information