NCERT Book Class 7 Maths Chapter 1 Integers

Chapter 1
Integers
1.1 PROPER TIES OF ADDITION AND SUBTRACTION OF
INTEGERS
We have learnt about whole numbers and integers in Class VI. We have also learnt about
addition and subtraction of integers.

1.1.1 Closure under Addition
We have learnt that sum of two whole numbers is again a whole number. For example,
17 + 24 = 41 which is again a whole number. We know that, this property is known as the
closure property for addition of the whole numbers.
Let us see whether this property is true for integers or not.
Following are some pairs of integers. Observe the following table and complete it.

Statement Observation
(i) 17 + 23 = 40 Result is an integer
(ii) (–10) + 3 = _____ ______________
(iii) (– 75) + 18 = _____ ______________
(iv) 19 + (– 25) = – 6 Result is an integer
(v) 27 + (– 27) = _____ ______________
(vi) (– 20) + 0 = _____ ______________
(vii) (– 35) + (– 10) = _____ ______________

What do you observe? Is the sum of two integers always an integer?
Did you find a pair of integers whose sum is not an integer?
Since addition of integers gives integers, we say integers are closed under addition.
In general, for any two integers a and b, a + b is an integer.