NCERT Book Class 7 Maths Integers

Integers

1.1 INTRODUCTION

We have learnt about whole numbers and integers in Class VI. We know that integers form a bigger collection of numbers which contains whole numbers and negative numbers. What other differences do you find between whole numbers and integers? In this chapter, we will study more about integers, their properties and operations. First of all, we will review and revise what we have done about integers in our previous class.

1.2 RECALL

We know how to represent integers on a number line. Some integers are marked on the number line given below.

Can you write these marked integers in ascending order? The ascending order of these numbers is – 5, – 1, 3. Why did we choose – 5 as the smallest number?

Some points are marked with integers on the following number line. Write these integers in descending order.

The descending order of these integers is 14, 8, 3, ...

The above number line has only a few integers filled. Write appropriate numbers at each dot.

1.3 PROPERTIES OF ADDITION AND SUBTRACTION OF INTEGERS

1.3.1 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.

1.3.2 Closure under Subtraction

What happens when we subtract an integer from another integer? Can we say that their difference is also an integer? Observe the following table and complete it:

Statement Observation

(i) 7 – 9               = – 2 Result is an integer

(ii) 17 – (– 21)      = _______ ______________

(iii) (– 8) – (–14)   = 6 Result is an integer

(iv) (– 21) – (– 10) = _______ ______________

(v) 32 – (–17)        = _______ ______________

(vi) (– 18) – (– 18)  = _______ ______________

(vii) (– 29) – 0        = _______ ______________

What do you observe? Is there any pair of integers whose difference is not an integer?

Can we say integers are closed under subtraction? Yes, we can see that integers are closed under subtraction.

Thus, if a and b are two integers then a – b is also an intger. Do the whole numbers satisfy this property?

Please refer to attached file for NCERT Class 7 Maths Integers