7 th std maths CBSE chapter 1 solution in c w note copy please send for my sister​

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7 th std maths CBSE chapter 1 solution in c w note copy please send for my sister​

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    2021-10-04T16:33:19+00:00

    Answer:

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    2021-10-04T16:34:04+00:00

    Introduction to Integers

    Introduction to Numbers

    Natural Numbers : The collection of all the counting numbers is called set of natural numbers. It is denoted by N = {1,2,3,4….}

    Whole Numbers: The collection of natural numbers along with zero is called a set of whole numbers. It is denoted by W = { 0, 1, 2, 3, 4, 5, … }

    Properties of Addition and Subtraction of Integers

    Closure under Addition and subtraction

    For every integer a and b,  a+b and a–b are integers.

    Commutativity Property for addition

    for every integer a and b,  a+b=b+a

    Associativity Property for addition

    for every integer a,b and c, (a+b)+c=a+(b+c)

    Additive Identity & Additive Inverse

    Additive Identity

    For every integer a, a+0=0+a=a here 0 is Additive Identity, since adding 0 to a number leaves it unchanged.

    Example : For an integer 2, 2+0 = 0+2 = 2.

    Additive inverse

    For every integer a, a+(−a)=0 Here, −a is additive inverse of a and a is the additive inverse of-a.

    Example : For an integer 2, (– 2) is additive inverse  and for (– 2), additive inverse is 2. [Since + 2 – 2 = 0]

    Properties of Multiplication of Integers

    Properties of Multiplication of Integers

    Closure under Multiplication

    For every integer a and b, a×b=Integer

    Commutative Property of Multiplication

    For every integer a and b, a×b=b×a

    Multiplication by Zero

    For every integer a, a×0=0×a=0

    Multiplicative Identity

    For every integer a, a×1=1×a=a. Here 1 is the multiplicative identity for integers.

    Associative property of Multiplication

    For every integer a, b  and c,  (a×b)×c=a×(b×c)

    Distributive Property of Integers

    Under addition and multiplication,  integers show the distributive property.

    i.e., For every integer a, b  and c,  a×(b+c)=a×b+a×c

    These properties make calculations easier.

    Division of Integers

    Division of Integers

    When a positive integer is divided by a positive integer, the quotient obtained is a positive integer.

    Example: (+6) ÷ (+3) = +2

    When a negative integer is divided by a negative integer, the quotient obtained is a positive integer.

    Example: (-6) ÷ (-3) = +2

    When a positive integer is divided by a negative integer or negative integer is divided by a positive integer, the quotient obtained is a negative integer.

    Example: (-6) ÷ (+3) =−2 and Example: (+6) ÷ (-3) = −2

    The Number Line

    Number Line

    Representation of integers on a number line

    On a number line when we

    (i) add a positive integer for a given integer, we move to the right.

    Example : When we add +2 to +3, move 2 places from +3 towards right to get +5

    (ii) add a negative integer for a given integer, we move to the left.

    Example : When we add -2 to +3, move 2 places from +3 towards left to get +1

    (iii) subtract a positive integer from a given integer, we move to the left.

    Example: When we subtract +2 from -3, move 2 places from -3 towards left to get -5

    (iv) subtract a negative integer from a given integer, we move to the right

    Example: When we subtract -2 from -3, move 2 places from -3 towards right to get 1

    Addition and Subtraction of Integers

    The absolute value of +7 (a positive integer) is 7

    The absolute value of -7 (negative integer) is 7 (its corresponding positive integer)

    Addition of two positive integers gives a positive integer.

    Example : (+3)+(+4) = +7

    Addition of two negative integers gives a negative integer.

    Example : (−3)+(−4) = −3−4=−7

    When one positive and one negative integers are added, we take their difference and place the sign of the bigger integer.

    Example : (−7)+(2) = −5

    For subtraction, we add the additive inverse of the integer that is being subtracted, to the other integer.

    Example : 56–(–73) = 56+73 = 129

    Introduction to Zero

    Integers

    Integers are the collection of numbers which is formed by whole numbers and their negatives. 

    The set of Integers is denoted by Z or I. I =  { …, -4, -3, -2, -1, 0, 1, 2, 3, 4,… }

    Properties of Division of Integers

    Properties of Division of Integers

    For every integer a,

    (a) a÷0 is not defined

    (b) a÷1 = a

    Note:  Integers are not closed under division

    Example: (– 9) ÷ (– 3) = 2. Result is an integer.

    and (−3)÷(−9)= 1/3. Result is not an integer.

    Multiplication of Integers

    Multiplication of Integers

    Product of two positive integers is a positive integer.

    Example : (+2)×(+3) = +6

    Product of two negative integers is a positive integer.

    Example :(−2)×(−3) = +6

    Product of a positive and a negative integer is a negative integer.

    Example :(+2)×(−3) = −6 and (−2)×(+3) = −6

    Product of even number of negative integers is positive and product of odd number of negative integers is negative.

    These properties make calculations easier.

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