NCERT Solutions for Class 7 Maths Chapter 1 Exercise 1.2

NCERT Solutions for Class 7 Maths Chapter 1 Exercise 1.2 (Ex. 1.2) Integers in PDF file format free to download or use online without downloading. All the question answers with solutions are done according to latest NCERT Books for 2021-2022.

In class 7 math exercise 1.2, we will learn to add positive and negative integers and work with practical problems occurring in daily life. All the questions are easy to solve in ex. 1.2 of class 7 mathematics.

Class 7 Maths Chapter 1 Exercise 1.2 Solution




Class: 7Mathematics
Chapter: 1Integers
Exercise: 1.2PDF and Videos Solution

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Class 7 Maths Chapter 1 Exercise 1.2 Solution in Videos

Class 7 Maths Chapter 1 Exercise 1.2 Solution
Class 7 Maths Chapter 1 Exercise 1.2 Explanation




Subtraction of Integers

For any integers a and b, we define:
(i) a – b = a + (additive inverse of b) = a + (- b).
(ii) a – (- b) = a + [additive inverse of (- b)] = a + b.

Properties of Subtraction of Integers

I. Closure Property for Subtraction:

If a and b are any two integers, then (a – b) is always an integer.
Example: (i) 2 – 5 = 2 + (- 5) = – 3, which is an integer.
(ii) – 2 – (- 6) = – 2 + 6 = 4, which is an integer.

II. Subtraction of Integers is not Commutative:

Examples:
(i) Consider the integers 3 and 5.
We have: (3 – 5) = 3 + (- 5) = – 2 and (5 – 3) = 5 + (- 3) = 2.
So, (3 – 5) ≠ (5 – 3).
(ii) Consider the integers (- 4) and 2.
We have: (- 4) – 2 = (- 4) + (- 2) = – 6 and 2 – (- 4)
= (2 + 4) = 6.
So, (- 4) – 2 ≠ 2 – (- 4).

III. Subtraction of Integers is Not Associative:

Example:
Consider the integers 3, (- 4) and (- 5).
We have: {3 – (- 4)} – (- 5)
= (3 + 4) – (- 5) = 7 – (- 5) = (7 + 5) = 12.
And, 3 – {(- 4) – (- 5)} = 3 – {(- 4) + 5} = (3 – 1) = 2.
So, {3 – (- 4)} – (- 5) ≠ 3 – {(- 4) – (- 5)}.

Class 7 Maths Exercise 1.2 Important Questions

Subtract: (i) 9 from 4 (ii) – 8 from 5 (iii) 7 from (- 6) (iv) – 9 from – 5

We have:
(i) 4 – 9 = 4 + (- 9) = – 5
(ii) 5 – (- 8) = 5 + 8 = 13
(iii) (- 6) – 7 = (- 6) + (- 7) = – 13
(iv) – 5 – (- 9) = (- 5) + 9 = 4

What are the rules for subtraction of integers?

Steps on How to Subtract Integers:
(i) First, keep the first number (known as the minuend).
(ii) Second, change the operation from subtraction to addition.
(iii) Third, get the opposite sign of the second number (known as the subtrahend)
(iv) Finally, proceed with the regular addition of integers.

Why subtraction of integers is not associative?

Contrary to addition, subtraction doesn’t have the associative property. If we subtract the first two numbers, 10 minus 5, it gives us 5. … Changing the way of associating the numbers in subtraction changes the answer. Thus, subtraction doesn’t have the associative property.

Consider the integers (- 5) and (- 2), use associative law?

Consider the integers (- 5) and (- 2).
Then, (- 5) – (- 2) = (- 5) + 2 = – 3.
Clearly, – 3 > – 5 but – 3 is not greater than – 2.

Why is subtraction not commutative?

Subtraction is not commutative because changing the order of the numbers changes the answer. Addition is commutative, which means that the order in which we add numbers does not matter. Because both additions have a 3 and a 5 added together, the answer to both sums is the same.

NCERT Solutions for Class 7 Maths Chapter 1 Exercise 1.2
7 Maths exercise 1.2 solutions