CBSE Class 7 Mathematics/Integers

CBSE Class 7 Mathematics/Integers is about the properties of addition and subtraction of integers. Here you can find out practice problems from the chapter Integers.

CBSE Class 7 Mathematics /Integers – Chapter 1
Properties of Addition and Subtraction of Integers.

CBSE Class 7 Mathematics /Integers – Chapter 1
Properties of Addition and Subtraction of Integers.

  1. Closure under Addition:
    For any two integers a and b, a + b is an integer.
    Since addition of integers gives integers, we say integers are closed under addition.
  2. Closure under Subtraction:
    If a and b are two integers then a – b is also an integer.
    Since subtraction of integers gives integers, we say integers are closed under subtraction.
  3. Commutative Property:
    Addition is commutative for integers.
    For any two integers a and b, a + b = b + a
    We have 5 + (-6) = -1 and (-6) + 5 = -1
    So 5 + (-6) = (-6) + 5
  4. Associative property:
    Addition is associative for integers.
    For any integers a, b and c, a + (b + c) = (a + b) + c
    Consider the integers -3, -2 and -5
    Look at (-5) + [(-3) + (-2)] and [(-5) + (-3)] + (-2)
    (-5) + [(-3) + (-2)] = (-5) + (-5) = -10
    [(-5) + (-3)] + (-2) = (-8) + (-2) = -10
    In both the cases we get -10, so associativity holds.
  5. Additive Identity:
    For any integer a, a + 0 = a = 0 + a
    Zero is an additive identity for integers.

Important Questions for Practice:

  1. Write a pair of integers whose sum gives
    a) a negative integer
    b) zero
  2. Write down a pair of integers whose
    a) sum is -5
    b) difference is -8
    c) sum is zero
  3. Write a negative integer and a positive integer whose difference is -3
  4. Fill in the blanks to make the following statements true:
    a) (-9) + (-3) = (-3) + —–
    b) -25 + ——- = -25
    c) 13 + ——– = 0
    d) [(-7) + (-8)] + (-2) = —– + [(-8) + (-2)]
  5. Write the properties used here:
    a) (-5) + (-2) = (-2) + (-5)
    b) [(-1) + (-2)] + (-3) = (-1) + [(-2) + (-3)]

ANSWERS:

  1. a) (-2) and (-1)
    b) 5 and (-5)
  2. a) (-3) and (-2)
    b) (-2) and 6
    c) 10 and (-10)
  3. (-1) and 2 because (-1) – (2) = (-1) + (-2) = (-3)
  4. a) (-9) + (-3) = (-3) + (-9)
    b) (-25) + 0 = (-25)
    c) 13 + (-13) = 0
    d) [(-7) + (-8)] + (-2) = (-7) + [(-8) + (-2)]
  5. a) Commutative property
    b) Associative property

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