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.
- 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. - 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. - 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 - 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. - Additive Identity:
For any integer a, a + 0 = a = 0 + a
Zero is an additive identity for integers.
Important Questions for Practice:
- Write a pair of integers whose sum gives
a) a negative integer
b) zero - Write down a pair of integers whose
a) sum is -5
b) difference is -8
c) sum is zero - Write a negative integer and a positive integer whose difference is -3
- 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)] - Write the properties used here:
a) (-5) + (-2) = (-2) + (-5)
b) [(-1) + (-2)] + (-3) = (-1) + [(-2) + (-3)]
ANSWERS:
- a) (-2) and (-1)
b) 5 and (-5) - a) (-3) and (-2)
b) (-2) and 6
c) 10 and (-10) - (-1) and 2 because (-1) – (2) = (-1) + (-2) = (-3)
- a) (-9) + (-3) = (-3) + (-9)
b) (-25) + 0 = (-25)
c) 13 + (-13) = 0
d) [(-7) + (-8)] + (-2) = (-7) + [(-8) + (-2)] - a) Commutative property
b) Associative property