SUBJECTABLE MATHMATICS

Size: px
Start display at page:

Download "SUBJECTABLE MATHMATICS"

Transcription

1

2 SUBJECTABLE MATHMATICS

3 PREFACE (A NOTE TO THE READER) This book, A COMPLETE BOOK ON SUBJECTIVE (CONVEN- TIONAL) ARITHMETIC has been specially prepared for candidates appearing for competitive entrance examination held by Staff Selection Commission (S.S.C.). Syllabus of ARITHMETIC Questions are designed to test the ability of arithmetical computations of whole numbers, decimals and fractions. The questions are based on arithmetical concepts of various topics and the candidates have to give a detailed explanation in order to arrive at the final result of the problem. Every topic of arithmetic in this book starts with the introduction which is followed by plenty of solved examples with complete explanation that can help the candidates to secure full marks. At the end of every chapter, an excercise containing different types of questions is given for your practice. All questions are fully solved with proper explanation. I am confident that this book will be very useful to the candidates. Best of Luck. S.L. Gulati

4 CONTENTS Preface v 1. Numbers and Simplifications 1 2. H.C.F and L.C.M Ratio and Proportion Percentage Average Profit and Loss Interest Time and Work Time and Distance Mensuration Data Interpretation Partnership Alligation 302

5 1 NUMBERS AND SIMPLIFICATIONS 1. ARITHMETIC is a science that deals with numbers, and of the methods of computing by means of numbers. 2. Integers: Numbers like 3, 2, 1, 0, 1, 2, 3 etc. are called integers. 3. Rational numbers: All numbers of the type p/q where q ¹ 0 and p is an integer are called rational numbers; e.g. 2, 7 3, 4 9, 0, 2, 7 13 etc. are all rational numbers. 4. Irrational numbers: Numbers like 2, 3, 5 etc. are called irrational numbers. 5. Real numbers: All rational numbers, irrational numbers and a combination of rational and irrational numbers are called real numbers; e.g. 5, 7/3, 2, + 3 etc. real numbers. 6. Natural numbers: The numbers 1, 2, 3, 4, are called natural numbers. (i) Sum of the first n natural numbers, i.e n = n ( n + 1) 2 (ii) Sum of the first n square numbers, i.e n 2 = n ( n + 1) ( 2n + 1) 6

6 2 Subjective Arithmetic (iii) Sum of the first n cube numbers i.e n 3 = L NM n( n+ 1) Þ n 3 = ( n) Multiplication Table. 8. Division is the method of finding how often one given number, called the Divisor is contained in another given number, called the Dividend. The number expressing the times the divisor is contained in the dividend is called the Quotient. 9. Long Division: When the divisor is greater than 20, the process is called Long Division. The least number consisting of figures from the left of the dividend in which the divisor 536 is contained in 870 is called the first partial dividend. The next figure in the dividend 3344 is called the second partial dividend and 1282 is the third partial dividend. The last figure, which should be less than the divisor, is called the Remainder. This is clear that = Dividend = Divisor Quotient + Remainder. 11. Division by factors (successive division); complete remainder. Let us divide by 210, using factors and explain the rule to find the remainder. 2 O QP Divisor Dividend Quotient , Remainder 2 Now 210 = If we take 5, 6, 7 as d 1, d 2, d 3 and 3, 2, 2, as r 1, r 2, r 3. Remainder = = Quotient = 274 \ = , 7, 6, 1, 2, 6 1, 1, 5, 2, 2, 3 7 1, 9, 2, 0, 2 2, 7, 4, 2

7 Numbers and Simplifications 3 The remainder obtained by the Division by factors method is called the complete remainder or true remainder. Þ Complete remainder = r 1 + d 1 r 2 + d 1 d 2 r Metric System: The Government of India has introduced the metric system of weights and measures throughout the country. This system derives its name from the word "Metre" which is the standard unit of length in this system. The advantage of the metric system is the great simplification of calculation in different spheres of work. In this system, the various units of length, area (surface) volume, capacity and weight (mass) always bear a strictly decimal relation to each other. The international names of the five main units in the metric system of weights and measures are: Length measure unit is a Metre. Area measure unit is a square metre. Volume measure unit is a cubic metre. weight measure unit is a Gram. Capacity measure unit is a Litre. An are contains 100 sq. metres and A Hectare contains 100 areas or 10,000 sq. metres. A cubic metre of volume contains 1000 litres or 1 kilo litre. 13. Vulgar Fractions: A fraction is represented by two numbers written one above the other and sperated by a horizontal line. Thus the fraction two-fifths is written as 2/5. The upper number is called the numerator where as the lower number is called the denominator. The numerator and the denominator of a fraction are its terms. A fraction is zero when its numerator is zero alone. The denominator of a fraction is always non-zero. Fractions such as 3/5, 8 11, 7 25 etc. are called common or vulgar fractions. The value of the vulgar fraction is not altered by multiplying or dividing by the numerator and the denominator by the same number. 14. If the numerator and the denominator are large numbers, or if their common factors cannot easily be guessed, we may find their H.C.F.

8 4 Subjective Arithmetic 15. A fraction is said to be a proper fraction if its numerator is less than its denominator. Thus 5/7, 9 13, 19 are all proper fractions. An 23 improper fraction is the one whose numerator is equal to N greater than its denominator. Thus 7 7, 7 3, 15 are improper fractions. A 11 mixed fraction is one which consists of a whole number and a fraction. Thus 2 1 7, 15 2 are mixed fractions. 3 Complex Fraction is the one in which the numerator or denominator or both are fractions Thus 4 7/ 9, / 3, 4 7 are complex fractions Continued Fractions: or are called continued fractions. To simplify such fractions, begin at the bottom and work upwards. 17. Decimal Fractions: A decimal fraction or a decimal is a fraction which has 10 or any power of 10 for its denominator and is expressed in the decimal system of notation. A decimal fraction is not altered by annexing ciphers to the right of the last figure. Thus and are equal. 18. Addition of decimals: Write down the number under one another, placing units under units etc. then add as in the case of integers, and place the decimal point under the points in the given numbers. e.g. Add together 5.406, 0.8, and Ans.

9 Numbers and Simplifications SIMPLIFICATION: of vulgar fractions. (BODMAS). In questions on fractions, signs,, +,, of (means multiplication) and brackets are often involved. In simplifying these questions the following order B O D M A S i.e. (i) Remove the brackets (if any). (ii) Then numbers or fractions which are connected by of should be simplified. (iii) Then the division and multiplication in order must be carried out and (iv) Lastly the operations of addition (plus) or subtraction (minus) should be performed. 20. SIMPLIFICATION: by Algebric formulae. Remember the following. 1. x - y x - y = x + y and x - y x + y = (x y). 2. (x + y) 2 (x y) 2 = 4xy 3. ( x + y) + ( x - y) = 2. ( x + y ) x y x - xy + y x y x - xy + y = (x + y) = (x y) 6. (x + y) 3 = x 3 + y 3 + 3xy (x + y) 7. (x y) 3 = x 3 y 3 3xy (x y). 8. x 2 + y 2 + z 2 xy yz zx = 1 2 [(x y)2 + (y z) 2 + (z x) 2 ] x + y + z - 3xyz 2 ( x + y + z zx yx - yz) = (x + y + z) 10. If x + y + z = 0, then (i) x 3 + y 3 + z 3 = 3xyz (ii) x + y + z 3xyz = 1.

10 6 Subjective Arithmetic SOLVED EXAMPLES Example 1. In a division sum, the quotient is 195, the divisor is equal to the sum of the quotient and the remainder. Find the dividend. Solution: We know that Dividend = Divisior Quotient + Remainder Remainder = 195 Quotient = 105 Divisor = = 300 \ Dividend = = = Ans. Example 2. A number when divided by 899 gives a remainder 63. What will be the remainder, when the same number be divided by 29? Solution: A number when divided by 899 gives a quotient say Q. The remainder is given to be 63 Þ Such a number = 899 Q + 63 (i) Expressing this as multiple of 29, we have The number = 29 (31Q) + (2 29) + 5 \ The remainder obtained by dividing this number by 29 is 5. Ans. 5. Example 3. A certain number x is divided by 385 by dividing by three prime factors. The quotient is 102, the first remainder is 4, the second remainder is 6 and the third is 10. Solution: 385 = Let x be the required number. Y and Z be the respective quotients. X = 5Y + 4 Y = 7Z + 6 Z = = = Y = 7z + 6 = 7 (1132) + 6 = = 7930 (i) (ii) (iii) 5 X 7 Y 4 11 Z

11 Subjective Arithmetic : For All Competitive Exams 30% OFF Publisher : Cosmos Bookhive ISBN : Author : S L Gulati Type the URL : Get this ebook

Accuplacer Arithmetic Study Guide

Accuplacer Arithmetic Study Guide Testing Center Student Success Center Accuplacer Arithmetic Study Guide I. Terms Numerator: which tells how many parts you have (the number on top) Denominator: which tells how many parts in the whole

More information

Session 29 Scientific Notation and Laws of Exponents. If you have ever taken a Chemistry class, you may have encountered the following numbers:

Session 29 Scientific Notation and Laws of Exponents. If you have ever taken a Chemistry class, you may have encountered the following numbers: Session 9 Scientific Notation and Laws of Exponents If you have ever taken a Chemistry class, you may have encountered the following numbers: There are approximately 60,4,79,00,000,000,000,000 molecules

More information

PREPARATION FOR MATH TESTING at CityLab Academy

PREPARATION 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 PRE-TEST

More information

Exponents, Radicals, and Scientific Notation

Exponents, Radicals, and Scientific Notation General Exponent Rules: Exponents, Radicals, and Scientific Notation x m x n = x m+n Example 1: x 5 x = x 5+ = x 7 (x m ) n = x mn Example : (x 5 ) = x 5 = x 10 (x m y n ) p = x mp y np Example : (x) =

More information

Quick Reference ebook

Quick Reference ebook This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed

More information

MATH-0910 Review Concepts (Haugen)

MATH-0910 Review Concepts (Haugen) Unit 1 Whole Numbers and Fractions MATH-0910 Review Concepts (Haugen) Exam 1 Sections 1.5, 1.6, 1.7, 1.8, 2.1, 2.2, 2.3, 2.4, and 2.5 Dividing Whole Numbers Equivalent ways of expressing division: a b,

More information

Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any.

Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any. Algebra 2 - Chapter Prerequisites Vocabulary Copy in your notebook: Add an example of each term with the symbols used in algebra 2 if there are any. P1 p. 1 1. counting(natural) numbers - {1,2,3,4,...}

More information

How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.

How do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left. The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics

More information

Recall the process used for adding decimal numbers. 1. Place the numbers to be added in vertical format, aligning the decimal points.

Recall the process used for adding decimal numbers. 1. Place the numbers to be added in vertical format, aligning the decimal points. 2 MODULE 4. DECIMALS 4a Decimal Arithmetic Adding Decimals Recall the process used for adding decimal numbers. Adding Decimals. To add decimal numbers, proceed as follows: 1. Place the numbers to be added

More information

Negative Integer Exponents

Negative Integer Exponents 7.7 Negative Integer Exponents 7.7 OBJECTIVES. Define the zero exponent 2. Use the definition of a negative exponent to simplify an expression 3. Use the properties of exponents to simplify expressions

More information

Number Sense and Operations

Number Sense and Operations Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents

More information

Math Released Set 2015. Algebra 1 PBA Item #13 Two Real Numbers Defined M44105

Math Released Set 2015. Algebra 1 PBA Item #13 Two Real Numbers Defined M44105 Math Released Set 2015 Algebra 1 PBA Item #13 Two Real Numbers Defined M44105 Prompt Rubric Task is worth a total of 3 points. M44105 Rubric Score Description 3 Student response includes the following

More information

Number: Multiplication and Division

Number: Multiplication and Division MULTIPLICATION & DIVISION FACTS count in steps of 2, 3, and 5 count from 0 in multiples of 4, 8, 50 count in multiples of 6, count forwards or backwards from 0, and in tens from any and 100 7, 9, 25 and

More information

Integer Operations. Overview. Grade 7 Mathematics, Quarter 1, Unit 1.1. Number of Instructional Days: 15 (1 day = 45 minutes) Essential Questions

Integer Operations. Overview. Grade 7 Mathematics, Quarter 1, Unit 1.1. Number of Instructional Days: 15 (1 day = 45 minutes) Essential Questions Grade 7 Mathematics, Quarter 1, Unit 1.1 Integer Operations Overview Number of Instructional Days: 15 (1 day = 45 minutes) Content to Be Learned Describe situations in which opposites combine to make zero.

More information

FRACTIONS MODULE Part I

FRACTIONS MODULE Part I FRACTIONS MODULE Part I I. Basics of Fractions II. Rewriting Fractions in the Lowest Terms III. Change an Improper Fraction into a Mixed Number IV. Change a Mixed Number into an Improper Fraction BMR.Fractions

More information

3 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

3 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 information

Decimals Adding and Subtracting

Decimals Adding and Subtracting 1 Decimals Adding and Subtracting Decimals are a group of digits, which express numbers or measurements in units, tens, and multiples of 10. The digits for units and multiples of 10 are followed by a decimal

More information

100 Math Facts 6 th Grade

100 Math Facts 6 th Grade 100 Math Facts 6 th Grade Name 1. SUM: What is the answer to an addition problem called? (N. 2.1) 2. DIFFERENCE: What is the answer to a subtraction problem called? (N. 2.1) 3. PRODUCT: What is the answer

More information

This is a square root. The number under the radical is 9. (An asterisk * means multiply.)

This is a square root. The number under the radical is 9. (An asterisk * means multiply.) Page of Review of Radical Expressions and Equations Skills involving radicals can be divided into the following groups: Evaluate square roots or higher order roots. Simplify radical expressions. Rationalize

More information

SIMPLIFYING SQUARE ROOTS

SIMPLIFYING SQUARE ROOTS 40 (8-8) Chapter 8 Powers and Roots 8. SIMPLIFYING SQUARE ROOTS In this section Using the Product Rule Rationalizing the Denominator Simplified Form of a Square Root In Section 8. you learned to simplify

More information

Math Workshop October 2010 Fractions and Repeating Decimals

Math 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 information

Chapter 1: Order of Operations, Fractions & Percents

Chapter 1: Order of Operations, Fractions & Percents HOSP 1107 (Business Math) Learning Centre Chapter 1: Order of Operations, Fractions & Percents ORDER OF OPERATIONS When finding the value of an expression, the operations must be carried out in a certain

More information

47 Numerator Denominator

47 Numerator Denominator JH WEEKLIES ISSUE #22 2012-2013 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 information

Why Vedic Mathematics?

Why Vedic Mathematics? Why Vedic Mathematics? Many Indian Secondary School students consider Mathematics a very difficult subject. Some students encounter difficulty with basic arithmetical operations. Some students feel it

More information

Florida Math 0018. Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower

Florida Math 0018. Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower Florida Math 0018 Correlation of the ALEKS course Florida Math 0018 to the Florida Mathematics Competencies - Lower Whole Numbers MDECL1: Perform operations on whole numbers (with applications, including

More information

Connect Four Math Games

Connect Four Math Games Connect Four Math Games Connect Four Addition Game (A) place two paper clips on two numbers on the Addend Strip whose sum is that desired square. Once they have chosen the two numbers, they can capture

More information

Simplifying Square-Root Radicals Containing Perfect Square Factors

Simplifying Square-Root Radicals Containing Perfect Square Factors DETAILED SOLUTIONS AND CONCEPTS - OPERATIONS ON IRRATIONAL NUMBERS Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you!

More information

FACTORS AND MULTIPLES Answer Key

FACTORS 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 information

3.1. RATIONAL EXPRESSIONS

3.1. 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

Tips, 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.

Tips, 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 information

MyMathLab ecourse for Developmental Mathematics

MyMathLab ecourse for Developmental Mathematics MyMathLab ecourse for Developmental Mathematics, North Shore Community College, University of New Orleans, Orange Coast College, Normandale Community College Table of Contents Module 1: Whole Numbers and

More information

EVALUATING ACADEMIC READINESS FOR APPRENTICESHIP TRAINING Revised For ACCESS TO APPRENTICESHIP

EVALUATING ACADEMIC READINESS FOR APPRENTICESHIP TRAINING Revised For ACCESS TO APPRENTICESHIP EVALUATING ACADEMIC READINESS FOR APPRENTICESHIP TRAINING For ACCESS TO APPRENTICESHIP MATHEMATICS SKILL OPERATIONS WITH INTEGERS AN ACADEMIC SKILLS MANUAL for The Precision Machining And Tooling Trades

More information

The Euclidean Algorithm

The Euclidean Algorithm The Euclidean Algorithm A METHOD FOR FINDING THE GREATEST COMMON DIVISOR FOR TWO LARGE NUMBERS To be successful using this method you have got to know how to divide. If this is something that you have

More information

Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers.

Math 0980 Chapter Objectives. Chapter 1: Introduction to Algebra: The Integers. Math 0980 Chapter Objectives Chapter 1: Introduction to Algebra: The Integers. 1. Identify the place value of a digit. 2. Write a number in words or digits. 3. Write positive and negative numbers used

More information

2 is the BASE 5 is the EXPONENT. Power Repeated Standard Multiplication. To evaluate a power means to find the answer in standard form.

2 is the BASE 5 is the EXPONENT. Power Repeated Standard Multiplication. To evaluate a power means to find the answer in standard form. Grade 9 Mathematics Unit : Powers and Exponent Rules Sec.1 What is a Power 5 is the BASE 5 is the EXPONENT The entire 5 is called a POWER. 5 = written as repeated multiplication. 5 = 3 written in standard

More information

Paramedic Program Pre-Admission Mathematics Test Study Guide

Paramedic Program Pre-Admission Mathematics Test Study Guide Paramedic Program Pre-Admission Mathematics Test Study Guide 05/13 1 Table of Contents Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7 Page 8 Page 9 Page 10 Page 11 Page 12 Page 13 Page 14 Page 15 Page

More information

Radicals - Multiply and Divide Radicals

Radicals - Multiply and Divide Radicals 8. Radicals - Multiply and Divide Radicals Objective: Multiply and divide radicals using the product and quotient rules of radicals. Multiplying radicals is very simple if the index on all the radicals

More information

Lesson Plan. N.RN.3: Use properties of rational and irrational numbers.

Lesson Plan. N.RN.3: Use properties of rational and irrational numbers. N.RN.3: Use properties of rational irrational numbers. N.RN.3: Use Properties of Rational Irrational Numbers Use properties of rational irrational numbers. 3. Explain why the sum or product of two rational

More information

TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers

TYPES OF NUMBERS. Example 2. Example 1. Problems. Answers TYPES OF NUMBERS When two or more integers are multiplied together, each number is a factor of the product. Nonnegative integers that have exactly two factors, namely, one and itself, are called prime

More information

A.4 Polynomial Division; Synthetic Division

A.4 Polynomial Division; Synthetic Division SECTION A.4 Polynomial Division; Synthetic Division 977 A.4 Polynomial Division; Synthetic Division OBJECTIVES 1 Divide Polynomials Using Long Division 2 Divide Polynomials Using Synthetic Division 1 Divide

More information

Rational Exponents. Squaring both sides of the equation yields. and to be consistent, we must have

Rational Exponents. Squaring both sides of the equation yields. and to be consistent, we must have 8.6 Rational Exponents 8.6 OBJECTIVES 1. Define rational exponents 2. Simplify expressions containing rational exponents 3. Use a calculator to estimate the value of an expression containing rational exponents

More information

Math Review. for the Quantitative Reasoning Measure of the GRE revised General Test

Math Review. for the Quantitative Reasoning Measure of the GRE revised General Test Math Review for the Quantitative Reasoning Measure of the GRE revised General Test www.ets.org Overview This Math Review will familiarize you with the mathematical skills and concepts that are important

More information

Section 4.1 Rules of Exponents

Section 4.1 Rules of Exponents Section 4.1 Rules of Exponents THE MEANING OF THE EXPONENT The exponent is an abbreviation for repeated multiplication. The repeated number is called a factor. x n means n factors of x. The exponent tells

More information

HFCC Math Lab Arithmetic - 4. Addition, Subtraction, Multiplication and Division of Mixed Numbers

HFCC Math Lab Arithmetic - 4. Addition, Subtraction, Multiplication and Division of Mixed Numbers HFCC Math Lab Arithmetic - Addition, Subtraction, Multiplication and Division of Mixed Numbers Part I: Addition and Subtraction of Mixed Numbers There are two ways of adding and subtracting mixed numbers.

More information

Activity 1: Using base ten blocks to model operations on decimals

Activity 1: Using base ten blocks to model operations on decimals Rational Numbers 9: Decimal Form of Rational Numbers Objectives To use base ten blocks to model operations on decimal numbers To review the algorithms for addition, subtraction, multiplication and division

More information

P.E.R.T. Math Study Guide

P.E.R.T. Math Study Guide A guide to help you prepare for the Math subtest of Florida s Postsecondary Education Readiness Test or P.E.R.T. P.E.R.T. Math Study Guide www.perttest.com PERT - A Math Study Guide 1. Linear Equations

More information

Vocabulary Words and Definitions for Algebra

Vocabulary Words and Definitions for Algebra Name: Period: Vocabulary Words and s for Algebra Absolute Value Additive Inverse Algebraic Expression Ascending Order Associative Property Axis of Symmetry Base Binomial Coefficient Combine Like Terms

More information

Numeracy Preparation Guide. for the. VETASSESS Test for Certificate IV in Nursing (Enrolled / Division 2 Nursing) course

Numeracy Preparation Guide. for the. VETASSESS Test for Certificate IV in Nursing (Enrolled / Division 2 Nursing) course Numeracy Preparation Guide for the VETASSESS Test for Certificate IV in Nursing (Enrolled / Division Nursing) course Introduction The Nursing course selection (or entrance) test used by various Registered

More information

Working with whole numbers

Working 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 information

Simplifying Algebraic Fractions

Simplifying Algebraic Fractions 5. Simplifying Algebraic Fractions 5. OBJECTIVES. Find the GCF for two monomials and simplify a fraction 2. Find the GCF for two polynomials and simplify a fraction Much of our work with algebraic fractions

More information

Factoring Polynomials

Factoring Polynomials UNIT 11 Factoring Polynomials You can use polynomials to describe framing for art. 396 Unit 11 factoring polynomials A polynomial is an expression that has variables that represent numbers. A number can

More information

Multiplying and Dividing Signed Numbers. Finding the Product of Two Signed Numbers. (a) (3)( 4) ( 4) ( 4) ( 4) 12 (b) (4)( 5) ( 5) ( 5) ( 5) ( 5) 20

Multiplying and Dividing Signed Numbers. Finding the Product of Two Signed Numbers. (a) (3)( 4) ( 4) ( 4) ( 4) 12 (b) (4)( 5) ( 5) ( 5) ( 5) ( 5) 20 SECTION.4 Multiplying and Dividing Signed Numbers.4 OBJECTIVES 1. Multiply signed numbers 2. Use the commutative property of multiplication 3. Use the associative property of multiplication 4. Divide signed

More information

Higher Education Math Placement

Higher Education Math Placement Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication

More information

Sequential Skills. Strands and Major Topics

Sequential 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 information

COLLEGE ALGEBRA. Paul Dawkins

COLLEGE ALGEBRA. Paul Dawkins COLLEGE ALGEBRA Paul Dawkins Table of Contents Preface... iii Outline... iv Preliminaries... Introduction... Integer Exponents... Rational Exponents... 9 Real Exponents...5 Radicals...6 Polynomials...5

More information

FRACTIONS OPERATIONS

FRACTIONS OPERATIONS FRACTIONS OPERATIONS Summary 1. Elements of a fraction... 1. Equivalent fractions... 1. Simplification of a fraction... 4. Rules for adding and subtracting fractions... 5. Multiplication rule for two fractions...

More information

CONTENTS. Please note:

CONTENTS. 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 information

Zeros of a Polynomial Function

Zeros of a Polynomial Function Zeros of a Polynomial Function An important consequence of the Factor Theorem is that finding the zeros of a polynomial is really the same thing as factoring it into linear factors. In this section we

More information

Indices and Surds. The Laws on Indices. 1. Multiplication: Mgr. ubomíra Tomková

Indices and Surds. The Laws on Indices. 1. Multiplication: Mgr. ubomíra Tomková Indices and Surds The term indices refers to the power to which a number is raised. Thus x is a number with an index of. People prefer the phrase "x to the power of ". Term surds is not often used, instead

More information

Chapter 7 - Roots, Radicals, and Complex Numbers

Chapter 7 - Roots, Radicals, and Complex Numbers Math 233 - Spring 2009 Chapter 7 - Roots, Radicals, and Complex Numbers 7.1 Roots and Radicals 7.1.1 Notation and Terminology In the expression x the is called the radical sign. The expression under the

More information

Cancelling Fractions: Rules

Cancelling Fractions: Rules Cancelling Fractions: Rules The process of cancelling involves taking fractions with large numerators and denominators (top and bottom numbers) and rewriting them with smaller numerators and denominators

More information

Square Roots. Learning Objectives. Pre-Activity

Square Roots. Learning Objectives. Pre-Activity Section 1. Pre-Activity Preparation Square Roots Our number system has two important sets of numbers: rational and irrational. The most common irrational numbers result from taking the square root of non-perfect

More information

MATH 10034 Fundamental Mathematics IV

MATH 10034 Fundamental Mathematics IV MATH 0034 Fundamental Mathematics IV http://www.math.kent.edu/ebooks/0034/funmath4.pdf Department of Mathematical Sciences Kent State University January 2, 2009 ii Contents To the Instructor v Polynomials.

More information

Unit 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. Unit 1 Number Sense In this unit, students will study repeating decimals, percents, fractions, decimals, and proportions. BLM Three Types of Percent Problems (p L-34) is a summary BLM for the material

More information

MATHCOUNTS TOOLBOX Facts, Formulas and Tricks

MATHCOUNTS TOOLBOX Facts, Formulas and Tricks MATHCOUNTS TOOLBOX Facts, Formulas and Tricks MATHCOUNTS Coaching Kit 40 I. PRIME NUMBERS from 1 through 100 (1 is not prime!) 2 3 5 7 11 13 17 19 23 29 31 37 41 43 47 53 59 61 67 71 73 79 83 89 97 II.

More information

Number: Multiplication and Division with Reasoning

Number: Multiplication and Division with Reasoning count in multiples of twos, fives and tens (copied from Number and Number: Multiplication and Division with Reasoning MULTIPLICATION & DIVISION FACTS Year 1 Year 2 Year 3 Year 4 Year 5 Year 6 count in

More information

1.6 The Order of Operations

1.6 The Order of Operations 1.6 The Order of Operations Contents: Operations Grouping Symbols The Order of Operations Exponents and Negative Numbers Negative Square Roots Square Root of a Negative Number Order of Operations and Negative

More information

SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS

SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS (Section 0.6: Polynomial, Rational, and Algebraic Expressions) 0.6.1 SECTION 0.6: POLYNOMIAL, RATIONAL, AND ALGEBRAIC EXPRESSIONS LEARNING OBJECTIVES Be able to identify polynomial, rational, and algebraic

More information

MATHS LEVEL DESCRIPTORS

MATHS LEVEL DESCRIPTORS MATHS LEVEL DESCRIPTORS Number Level 3 Understand the place value of numbers up to thousands. Order numbers up to 9999. Round numbers to the nearest 10 or 100. Understand the number line below zero, and

More information

Decimals and other fractions

Decimals and other fractions Chapter 2 Decimals and other fractions How to deal with the bits and pieces When drugs come from the manufacturer they are in doses to suit most adult patients. However, many of your patients will be very

More information

POLYNOMIAL FUNCTIONS

POLYNOMIAL FUNCTIONS POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a

More information

EXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS

EXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS To the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requires

More information

Expression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds

Expression. Variable Equation Polynomial Monomial Add. Area. Volume Surface Space Length Width. Probability. Chance Random Likely Possibility Odds Isosceles Triangle Congruent Leg Side Expression Equation Polynomial Monomial Radical Square Root Check Times Itself Function Relation One Domain Range Area Volume Surface Space Length Width Quantitative

More information

0.8 Rational Expressions and Equations

0.8 Rational Expressions and Equations 96 Prerequisites 0.8 Rational Expressions and Equations We now turn our attention to rational expressions - that is, algebraic fractions - and equations which contain them. The reader is encouraged to

More information

Chapter 5. Rational Expressions

Chapter 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 information

INTRODUCTION TO FRACTIONS

INTRODUCTION TO FRACTIONS Tallahassee Community College 16 INTRODUCTION TO FRACTIONS Figure A (Use for 1 5) 1. How many parts are there in this circle?. How many parts of the circle are shaded?. What fractional part of the circle

More information

A Short Guide to Significant Figures

A Short Guide to Significant Figures A Short Guide to Significant Figures Quick Reference Section Here are the basic rules for significant figures - read the full text of this guide to gain a complete understanding of what these rules really

More information

Rules of Exponents. Math at Work: Motorcycle Customization OUTLINE CHAPTER

Rules of Exponents. Math at Work: Motorcycle Customization OUTLINE CHAPTER Rules of Exponents CHAPTER 5 Math at Work: Motorcycle Customization OUTLINE Study Strategies: Taking Math Tests 5. Basic Rules of Exponents Part A: The Product Rule and Power Rules Part B: Combining the

More information

Mathematics. Steps to Success. and. Top Tips. Year 5

Mathematics. Steps to Success. and. Top Tips. Year 5 Pownall Green Primary School Mathematics and Year 5 1 Contents Page 1. Multiplication and Division 3 2. Positive and Negative Numbers 4 3. Decimal Notation 4. Reading Decimals 5 5. Fractions Linked to

More information

Accuplacer Arithmetic Study Guide

Accuplacer Arithmetic Study Guide Accuplacer Arithmetic Study Guide Section One: Terms Numerator: The number on top of a fraction which tells how many parts you have. Denominator: The number on the bottom of a fraction which tells how

More information

Simplification of Radical Expressions

Simplification of Radical Expressions 8. Simplification of Radical Expressions 8. OBJECTIVES 1. Simplify a radical expression by using the product property. Simplify a radical expression by using the quotient property NOTE A precise set of

More information

Solution Guide Chapter 14 Mixing Fractions, Decimals, and Percents Together

Solution Guide Chapter 14 Mixing Fractions, Decimals, and Percents Together Solution Guide Chapter 4 Mixing Fractions, Decimals, and Percents Together Doing the Math from p. 80 2. 0.72 9 =? 0.08 To change it to decimal, we can tip it over and divide: 9 0.72 To make 0.72 into a

More information

YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR!

YOU MUST BE ABLE TO DO THE FOLLOWING PROBLEMS WITHOUT A CALCULATOR! DETAILED SOLUTIONS AND CONCEPTS - DECIMALS AND WHOLE NUMBERS Prepared by Ingrid Stewart, Ph.D., College of Southern Nevada Please Send Questions and Comments to ingrid.stewart@csn.edu. Thank you! YOU MUST

More information

Cancelling a Fraction: Rules

Cancelling a Fraction: Rules Cancelling a Fraction: Rules The process of canceling involves taking fractions with larger numbers on top and bottom and re-writing those fractions with smaller numbers ensuring the value of the fraction

More information

ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers Basic Math 1.2 - The Number Line Basic Math 1.3 - Addition of Whole Numbers, Part I

ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers Basic Math 1.2 - The Number Line Basic Math 1.3 - Addition of Whole Numbers, Part I ModuMath Basic Math Basic Math 1.1 - Naming Whole Numbers 1) Read whole numbers. 2) Write whole numbers in words. 3) Change whole numbers stated in words into decimal numeral form. 4) Write numerals in

More information

6.4 Special Factoring Rules

6.4 Special Factoring Rules 6.4 Special Factoring Rules OBJECTIVES 1 Factor a difference of squares. 2 Factor a perfect square trinomial. 3 Factor a difference of cubes. 4 Factor a sum of cubes. By reversing the rules for multiplication

More information

of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433

of surface, 569-571, 576-577, 578-581 of triangle, 548 Associative Property of addition, 12, 331 of multiplication, 18, 433 Absolute Value and arithmetic, 730-733 defined, 730 Acute angle, 477 Acute triangle, 497 Addend, 12 Addition associative property of, (see Commutative Property) carrying in, 11, 92 commutative property

More information

Multiplying and Dividing Algebraic Fractions

Multiplying and Dividing Algebraic Fractions . Multiplying and Dividing Algebraic Fractions. OBJECTIVES. Write the product of two algebraic fractions in simplest form. Write the quotient of two algebraic fractions in simplest form. Simplify a comple

More information

We could also take square roots of certain decimals nicely. For example, 0.36=0.6 or 0.09=0.3. However, we will limit ourselves to integers for now.

We could also take square roots of certain decimals nicely. For example, 0.36=0.6 or 0.09=0.3. However, we will limit ourselves to integers for now. 7.3 Evaluation of Roots Previously we used the square root to help us approximate irrational numbers. Now we will expand beyond just square roots and talk about cube roots as well. For both we will be

More information

All the examples in this worksheet and all the answers to questions are available as answer sheets or videos.

All the examples in this worksheet and all the answers to questions are available as answer sheets or videos. BIRKBECK MATHS SUPPORT www.mathsupport.wordpress.com Numbers 3 In this section we will look at - improper fractions and mixed fractions - multiplying and dividing fractions - what decimals mean and exponents

More information

Free Pre-Algebra Lesson 55! page 1

Free Pre-Algebra Lesson 55! page 1 Free Pre-Algebra Lesson 55! page 1 Lesson 55 Perimeter Problems with Related Variables Take your skill at word problems to a new level in this section. All the problems are the same type, so that you can

More information

FACTORISATION YEARS. A guide for teachers - Years 9 10 June 2011. The Improving Mathematics Education in Schools (TIMES) Project

FACTORISATION YEARS. A guide for teachers - Years 9 10 June 2011. The Improving Mathematics Education in Schools (TIMES) Project 9 10 YEARS The Improving Mathematics Education in Schools (TIMES) Project FACTORISATION NUMBER AND ALGEBRA Module 33 A guide for teachers - Years 9 10 June 2011 Factorisation (Number and Algebra : Module

More information

Math 0306 Final Exam Review

Math 0306 Final Exam Review Math 006 Final Exam Review Problem Section Answers Whole Numbers 1. According to the 1990 census, the population of Nebraska is 1,8,8, the population of Nevada is 1,01,8, the population of New Hampshire

More information

Facebook. GMAT Club CAT Tests. GMAT Toolkit ipad App. gmatclub.com/iphone. gmatclub.com/tests. The Verbal Initiative. gmatclub.

Facebook. GMAT Club CAT Tests. GMAT Toolkit ipad App. gmatclub.com/iphone. gmatclub.com/tests. The Verbal Initiative. gmatclub. For the latest version of the GMAT ok, please visit: http://gmatclub.com/ GMAT Club s Other Resources: GMAT Club CAT Tests gmatclub.com/tests GMAT Toolkit ipad App gmatclub.com/iphone The Verbal Initiative

More information

This assignment will help you to prepare for Algebra 1 by reviewing some of the things you learned in Middle School. If you cannot remember how to complete a specific problem, there is an example at the

More information

Previously, 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

Previously, 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 information

Florida Math 0028. Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper

Florida Math 0028. Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper Florida Math 0028 Correlation of the ALEKS course Florida Math 0028 to the Florida Mathematics Competencies - Upper Exponents & Polynomials MDECU1: Applies the order of operations to evaluate algebraic

More information

5.1 Radical Notation and Rational Exponents

5.1 Radical Notation and Rational Exponents Section 5.1 Radical Notation and Rational Exponents 1 5.1 Radical Notation and Rational Exponents We now review how exponents can be used to describe not only powers (such as 5 2 and 2 3 ), but also roots

More information

FACTORING POLYNOMIALS

FACTORING POLYNOMIALS 296 (5-40) Chapter 5 Exponents and Polynomials where a 2 is the area of the square base, b 2 is the area of the square top, and H is the distance from the base to the top. Find the volume of a truncated

More information

MBA Jump Start Program

MBA Jump Start Program MBA Jump Start Program Module 2: Mathematics Thomas Gilbert Mathematics Module Online Appendix: Basic Mathematical Concepts 2 1 The Number Spectrum Generally we depict numbers increasing from left to right

More information