CBSE Class 7 Mathematics/Integers/Chapter 1/Notes/Part 1

Welcome to our Class 7 Maths blog! Here, we’re diving into the basics of integers, focusing on the properties of addition and subtraction. We’ll cover everything you need to know from the new CBSE curriculum, including Exercise 1.1. Let’s get started on this fun Math adventure!

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.
   Example:
   (-2) + 5 = 3
   27 + (-27) = 0
2. Closure under subtraction:
   If a and b are two integers then a – b is also an integer.
   Example:
   (-21) – (-10) = (-21) + 10 = -11
   12 – (-20) = 12 + 20 = 32
3. Commutative property:
   For any two integers a and b, we can say a + b = b + a
   Example:
   We have 5 + (-6) = -1 and (-6) + 5 = -1
   So 5 + (-6) = (-6) + 5
4. Associative Property:
   For any integers a, b and c, we can say a + (b + c) = (a + b) + c
   Example:
   Consider the integers -3, -2 and -5
   LHS = (-3) + [(-2) + (-5)] = (-3) + (-7) = -10
   RHS = [(-3) + (-2)] + (-5) = (-5) + (-5) = -10
5. Additive Identity:
   For any integer a, a + 0 = a = 0 + a
   Example:
   (-8) + 0 = -8
   0 + (-23) = -23

Exercise 1.1

1. Write down a pair of integers whose:
   a) Sum is -7
   b) Difference is -10
   c) Sum is 0
   Solution:
   a) (-2) + (-5) = -7
   b) (-6) – 4 = (-6) + (-4) = -10
   c) (-3) + 3 = 0
2. a) Write a pair of negative integers whose difference gives 8.
   b) Write a negative integer and a positive integer whose sum is -5.
   c) Write a negative integer and a positive integer whose difference is -3.
   Solution:
   a) (-4) – (-12) = (-4) + 12 = 8
   b) (-7) + 2 = -5
   c) (-1) – 2 = (-1) + (-2) = -3
3. In a quiz, team A scored -40, 10, 0 and team B scored 10, 0, -40 in three successive rounds. Which team scored more? Can we say that we can add integers in any order?
   Solution:
   Total score of team A = (-40) + 10 + 0 = -30
   Total score of team B = 10 + 0 + (-40) = -30
   Scores of both the teams are same.
   Yes, we can add integers in any order.
4. Fill in the blanks to make the following statements true:
   i) (-5) + (-8) = (-8) + (—-)
   ii) -53 + —- = -53
   iii) 17 + —– = 0
   iv) [13 + (-12)] + (—-) = 13 + [(-12) + (-7)]
   v) (-4) + [15 + (-3)] = [-4 + 15] + ——
   Solution:
   i) -5
   ii) 0
   iii) -17
   iv) -7
   v) -3