Integers

Integers are the set of whole numbers and their negatives. It is represented by Z. Z = {…-3, -2, -1, 1, 2, 3, …}. The direction of an integer is indicated by its sign (+ or –), that it is right of 0 or left of 0 on the number line.

Properties of addition and subtraction of integers: a) Integers are closed under addition and subtraction. If a and b are two integers, then (a + b) and (a – b) are also integers.

b) Integers are commutative under addition. {a + b = b + a} c) Integers are associative under addition. {(a + b) + c = a + (b + c)} d) The integer 0 is the additive identity. {a + 0 = a = 0 + a} e) For any integer ‘a’, its additive inverse is ‘–a’.

Multiplication of integers: The product of two positive integers is a positive integer. The product of a negative integer and a positive integer is a negative integer.

The product of two negative integers is a positive integer. The product of even number of negative integers is a positive integer. The product of odd number of negative integers is a negative integer.

Properties of multiplication of integers:

a) Integers are closed under multiplication. { a × b is an integer for any two integers a and b}

b) Multiplication is commutative for integers. { a × b = b × a}

c) The integer 1 is the identity under multiplication. {a × 1= a = 1 × a}

d) Integers are associative under multiplication. {(a × b) × c = a × (b × c)}

Distributive property of integers: a × (b + c) = a × b + a × c Division of a positive integer by a negative integer gives a negative integer as quotient and vice-versa. However, when a negative integer is divided by another negative integer, the quotient obtained is a positive integer. For any integer a, a ÷1 = a and a ÷ 0 is not defined. Keywords: ascending and descending order of integers, predecessor, successor

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  • Q1

    In a class test containing 20 questions, 3 marks are given for every correct answer and (-1) marks are given for every incorrect answer. Gurpreet attempts all questions but only 12 of her answer correct and 8 are incorrect. The total score of Gurpreet is

    Marks:1
    Answer:

    28.

    Explanation:

    Marks given for one correct answer = 3
    So, marks given for 12 correct answer = 3x12 = 36
    Marks given for one incorrect answer = -1
    So, marks given for 8 incorrect answer = -1x8 = -8
    Therefore, gurpreet’s total score = 36 +(-8) = 28

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  • Q2

    The multiplicative identity for integers is

    Marks:1
    Answer:

    1.

    Explanation:

    Since, 1 1 = 1
    1 = 2
    -1 = -3
    So, we can say that 1 is the multiplicative identity for integers.

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  • Q3

    (-25) (-100) = ...

    Marks:1
    Answer:

    2500.

    Explanation:
    In general, for any two positive integers a and b.
    (-a)  (-b) = a  b
    here, a =-25 and b =-100
    then, (-25)  (-100) = 25  100 = 2500
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  • Q4

    [8 +{ 5 –(4 3 -7) -5 +3 4} +9] = …

    Marks:1
    Answer:

    24.

    Explanation:

    By using the rule of Bodmas.
    [8 +{ 5 –(4 3 -7) -5 +3 4} +9] = [8 + {5 –(12-7) -5 + 3 4} +9]
    = [8 + {5 – 5 - 5 + 12} + 9]
    = [8 + {12 - 5} + 9]
    = [8 + 7 + 9]
    = [15 + 9]
    = 24

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  • Q5

    The integer whose product with (-1) is (-26), is

    Marks:1
    Answer:

    26.

    Explanation:

    Let required integer be x
    then, (-1) (x) = (-26)
    x = (-26) (-1) = 26

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