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Information Report

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Textbook used by cbse schools

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Contents
Forewordiii Prefacev
Chapter 1
Rational Numbers1
Chapter 2
Linear Equations in One Variable21
Chapter 3
Understanding Quadrilaterals37
Chapter 4
Practical Geometry57
Chapter 5
Data Handling69
Chapter 6
Squares and Square Roots89
Chapter 7
Cubes and Cube Roots109
Chapter 8
Comparing Quantities117
Chapter 9
Algebraic Expressions and Identities137
Chapter 10
Visualising Solid Shapes153
Chapter 11
Mensuration169
Chapter 12
Exponents and Powers193
Chapter 13
Direct and Inverse Proportions201
Chapter 14
Factorisation217
Chapter 15
Introduction to Graphs231
Chapter 16
Playing with Numbers249
Answers
261
Just for Fun
275
R
ATIONAL
N
UMBERS
1
1.1 Introduction
In Mathematics, we frequently come across simple equations to be solved. For example,the equation
x
+ 2 =13(1)is solved when
x
= 11, because this value of
x
satisfies the given equation. The solution11 is a
natural number
. On the other hand, for the equation
x
+ 5 =5(2)the solution gives the
whole number
0 (zero). If we consider only natural numbers,equation (2) cannot be solved. To solve equations like (2), we added the number zero tothe collection of natural numbers and obtained the whole numbers. Even whole numberswill not be sufficient to solve equations of type
x
+ 18 =5(3)Do you see ‘why’? We require the number –13 which is not a whole number. Thisled us to think of
integers, (positive and negative)
. Note that the positive integerscorrespond to natural numbers. One may think that we have enough numbers to solve allsimple equations with the available list of integers. Consider the equations2
x
=3(4)5
x
+ 7 =0(5)for which we cannot find a solution from the integers. (Check this)We need the numbers
32
to solve equation (4) and
75
−
to solveequation (5). This leads us to the collection of
rational numbers
.We have already seen basic operations on rationalnumbers. We now try to explore some properties of operationson the different types of numbers seen so far.
Rational Numbers
CHAPTER
1
2
M
ATHEMATICS
1.2 Properties of Rational Numbers
1.2.1 Closure
(i) Whole numbers
Let us revisit the closure property for all the operations on whole numbers in brief.
Operation Numbers Remarks
Addition0 + 5 = 5, a whole numberWhole numbers are closed4 + 7 = ... . Is it a whole number?under addition.In general,
a
+
b
is a wholenumber for any two wholenumbers
a
and
b
.Subtraction5 – 7 = – 2, which is not aWhole numbers are
not
closedwhole number.under subtraction.Multiplication0 × 3 = 0, a whole numberWhole numbers are closed3 × 7 = ... . Is it a whole number?under multiplication.In general, if
a
and
b
are any twowhole numbers, their product
ab
is a whole number.Division5
÷
8 =
58
, which is not awhole number.Check for closure property under all the four operations for natural numbers.
(ii) Integers
Let us now recall the operations under which integers are closed.
Operation Numbers Remarks
Addition– 6 + 5 = – 1, an integerIntegers are closed underIs – 7 + (–5) an integer?addition.Is 8 + 5 an integer?In general,
a
+
b
is an integerfor any two integers
a
and
b
.Subtraction7 – 5 = 2, an integerIntegers are closed underIs 5 – 7 an integer?subtraction.– 6 – 8 = – 14, an integerWhole numbers are
not
closedunder division.

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