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Title Pages.Pmd © Government of Tamilnadu First Edition-2003 Reprint - 2005 Chairperson Dr. K. SRINIVASAN Reader in Mathematics Presidency College (Autonomous) Chennai - 600 005. Reviewers Prof. (Mrs.) SHIELA BOSE Thiru M.K. SUBRAMANIAN Head Department of Mathematics, Deputy Director, Lady Willingdon Institute of Directorate of Teacher Education, Advanced Study in Education, Research and Training, Chennai - 600 005. Chennai - 600 006. Authors Thiru G. GNANASUNDARAM Thiru M. PALANIVASAN P.G. Teacher, P.G. Teacher, S.S.V. Higher Secondary School, I.C.F. Higher Secondary School, Park Town, Chennai - 600 003. Chennai - 600 038. Thiru P. NAGARAJAN Thiru T. KATHIRVEL B.T. Assistant, Assistant Headmaster, B.R. Govt. High School, Govt. Higher Secondary School, Puzhal-600 066. Arumbakkam, Tiruvallur Dt. Chennai - 600 106. Price : Rs. 33-00 This book has been prepared by The Directorate of School Education on behalf of the Government of Tamilnadu This book has been printed on 60 G.S.M. Paper Printed by Offset at : CONTENTS Page No. 1. NUMBER WORK 1 1.1 Numbers – Revision 1 1.1.1 Natural Numbers and Whole Numbers 1.1.2 Face value and Place value 1.1.3 Expanded form 1.2 Four fundamental operations on Whole numbers 5 1.2.1 Addition 1.2.2 Subtraction 1.2.3 Multipliction 1.2.4 Division 1.3 Number patterns 13 1.3.1 Divisors, Factors and Multiples 1.3.2 Even and Odd numbers 1.3.3 Prime and Composite numbers 1.4 Large numbers in Exponential form 17 1.5 Tests of divisibility – Revision 20 1.6 Greatest common divisor and Least common multiple 23 1.7 Integers 28 1.7.1 Directed numbers 1.7.2 Integers and order in number line 1.7.3 Addition and Subtraction of integers 1.7.4 Multiplication of integers 1.7.5 Division of integers 1.8 Fractions 41 1.8.1 Fractions – Revision 1.8.2 Addition and Subtraction on Fractions 1.8.3 Multiplication and Division on Fractions 1.9 Decimal numbers 53 1.9.1 Decimal form of fractions 1.9.2 Four fundamental operations on decimals 2. EVERYDAY ARITHMETIC 65 2.1 Ratio and Proportion 65 2.1.1 Ratio formation 2.1.2 Comparison of ratios 2.1.3 Proportion formation 2.1.4 Proportion – Applications 2.1.5 Direct variation 2.2 Percentage 77 2.2.1 Percentages, Fractions and Decimals – Relationship 2.2.2 Profit and Loss 2.2.3 Profit and Loss percentage 2.3 Shopping 84 2.3.1 Verification of bill amount 2.3.2 Preparation of a bill 2.4 Finance 90 2.4.1 Simple Interest (Unitary Method) 2.4.2 Formula for Simple Interest 3. MEASUREMENTS 95 3.1 Metric measures 95 3.1.1 Linear measures (measures of length) 3.1.2 Measures of weight 3.1.3 Measures of capacity 3.1.4 Addition and Subtraction in metric measures 3.1.5 Multiplication and Division in metric measures 3.1.6 Measures of area 3.1.7 Measures of volume 3.2 Measures of Time 111 3.2.1 Ordinary time and Railway time; Ordinary year and Leap year 3.2.2 Calculating number of days. 3.2.3 Finding the day of the week 3.3 Area and Perimeter 121 3.3.1 Area and perimeter of a square 3.3.2 Area and perimeter of a rectangle 3.3.3 Area and perimeter of a right angled triangle 3.3.4 Area of Four walls 4. ALGEBRA 137 4.1 Introduction 137 4.2 Mathematical statements 137 4.3 Place holders 138 4.4 Literals 140 4.5 Constants and Variables 141 4.6 Power (or Exponent or Index) of a variable 143 4.7 Coefficients 144 4.8 Terms 145 4.9 Addition and Subtraction of terms 147 5. GEOMETRY 151 5.1 Basic geometrical concepts 151 5.1.1 Point 5.1.2 Line 5.1.3 Ray 5.1.4 Line segment 5.1.5 Plane 5.2 Relationship between points and lines 155 5.2.1 Concurrent lines 5.2.2 Collinear points 5.2.3 Intersecting and Parallel lines 5.3 Angles 159 5.3.1 Angle and measure of an angle 5.3.2 Types of angles 5.3.3 Complementary and Supplementary angles 5.3.4 Bisector of an angle 5.4 Triangles 164 5.4.1 Parts of a triangle 5.4.2 Types of triangles 5.4.3 Important properties of triangles 5.5 Special quadrilaterals 169 5.5.1 Quadrilateral and its parts 5.5.2 Special type of quadrilaterals 6. PRACTICAL GEOMETRY 173 6.1 Geometrical instruments box 173 6.2 Line segment 176 6.3 Constructing a line segment of a given measurement 177 6.4 Measuring the length of a given line segment 178 6.5 Constructing a line perpendicular to a given line at a given point on it 179 6.6 Constructing the perpendicular bisector of a given line segment 181 6.7 Measuring angles 185 6.8 Constructing angles of given measures 188 6.8.1 Constructing 90° and 45° using paper folding method 6.8.2 Drawing angles with the help of a protractor 6.9 Constructing the angle bisector of a given angle 189 6.9.1 Paper folding method 6.9.2 Using protractor and compass 7. HANDLING DATA 191 7.1 Meaning of an average (mean) 191 7.2 Median 194 7.3 Mode 195 7.4 Pictograph 197 7.5 Bar Graph 201 ANSWERS 207 1. NUMBER WORK “Numbers are my friends” says Ramanujan, the well known Indian Mathematician. He loved numbers and his contribution to Mathematics is great. We are familiar with some fundamental mathematical calculations with numbers in the previous classes. Now we briefly revise the number system which we have studied. Any number is a concept. ‘one’ is a number name and we use the numeral or symbol ‘1’ to denote it. ‘Five’ is a number name and we use the numeral ‘5’ to denote it. In olden days, different symbols were used in different parts of the world to denote the numerals. The present system is based on ten numerals 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. It was developed by Indians. Arabs made these numerals known to western countries. Hence these numerals are called Indo-Arabic numerals. This system is universally accepted. 1.1 Numbers – Revision 1.2 Four fundamental operations on Whole numbers 1.3 Number patterns 1.4 Large numbers in Exponential form 1.5 Tests of divisibility – Revision 1.6 Greatest common divisor and Least common multiple 1.7 Integers 1.8 Fractions 1.9 Decimal numbers. 1.1 Numbers – Revision 1.1.1 Natural Numbers and Whole Numbers 1.1.2 Face value and Place value 1.1.3 Expanded form 1.1.1. (a) Natural Numbers : The counting numbers 1, 2, 3, ……… are called natural numbers. Natural numbers are beginning with 1 and increasing one by one. The set of natural numbers is denoted by the symbol N. In the set of natural numbers, 2 is called the successor of 1. 1 is called the predecessor of 2 and 3 is called successor of 2 and 2 is called predecessor of 3. Can you give the last natural number? Thus N = {1, 2, 3, ……… } (b) Whole Numbers : If we include the number 0 to the set of natural numbers, we get 0, 1, 2, 3, ……… . This is called the set of whole numbers and is denoted by the symbol W. Thus W = {0, 1, 2, 3, ……… } 1 1.1.2 Face Value and Place Value The numerals 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are called digits. It is by using these ten digits, we are generating all the numbers in the set of whole numbers. For example, to write the numeral for two thousand four hundred and eighty seven, we write 2487. Here we use the digits together with place value. Every digit in a number has a face value and a place value. For example in 2487, the digits we have used are 2, 4, 8 and 7. The face value of these digits are respectively 2, 4, 8 and 7 only. However depending upon the place they occupy in the number, each digit has a distinct value. In 2487, the place value of 2 is 2000; the place value of 4 is 400 ; the place value of 8 is 80 ; the place value of 7 is 7 ; Using the ten digits and the concept of place value, we can write any number. The place value increases in powers of 10, starting from units. The digits in numbers from right to left have the place values of 1, 10, 100, 1000, 10000 etc. Thus the place value of each digit in 894063217 is as follows : The place value of 7 is 7 ones 7 The place value of 1 is 1 ten 10 The place value of 2 is 2 hundreds 200 The place value of 3 is 3 thousands 3000 The place value of 6 is 6 ten thousands 60000 The place value of 0 is 0 lakh 0 The place value of 4 is 4 ten lakhs 4000000 The place value of 9 is 9 crores 90000000 The place value of 8 is 8 ten crores 800000000 Now this number can be read as eightynine crore, forty lakh, sixtythree thousand two hundred and seventeen and is written as 89,40,63,217. Another method of expressing the numbers is known as international notation.
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