NCERT Solutions & Concepts for Class 7 Maths Integers Exercise 1.2

Welcome to CBSE Class 7 Maths Chapter 1, where we dive deep into the properties of integers. Exercise 1.2 is a critical turning point in this chapter. Instead of basic arithmetic, it challenges you to think logically about the underlying behaviors of integer operations. Here, you will master properties like Commutativity, Associativity, and the Additive Identity. Learning these concepts is not just about solving homework; it builds a strong foundation for future algebraic topics. In this guide, our YoLearn AI Tutor will help you break down each property, visualize calculations on the sketchpad, and walk you through every step to solve Ex 1.2 questions with absolute confidence. Let's get started!

Properties of Addition and Subtraction of Integers

To solve the problems in Integers Exercise 1.2, you must understand four crucial properties of integers:

  1. Closure Property under Addition and Subtraction: The sum or difference of any two integers is always an integer. For any integers a and b, (a + b) and (a - b) are also integers.
  2. Commutative Property of Addition: Changing the order of addends does not change the sum. For any integers a and b, a + b = b + a. Note that subtraction is NOT commutative (a - b is not equal to b - a).
  3. Associative Property of Addition: When adding three or more integers, the way they are grouped does not affect the sum. For any integers a, b, and c, a + (b + c) = (a + b) + c. Subtraction is NOT associative.
  4. Additive Identity: The integer 0 is the additive identity because adding zero to any integer leaves it unchanged. For any integer a, a + 0 = 0 + a = a.

How to Find Pairs of Integers with Specific Sums or Differences

  1. Identify the Operation — Determine if the question asks for a sum (addition) or a difference (subtraction), and note the sign of the target outcome.
  2. Choose the First Integer — Select any starting integer. If you need a negative sum, choose a negative integer with a larger absolute value than your target.
  3. Form and Solve the Equation — Write a simple equation. For a sum of -7, write: x + y = -7. Substitute your chosen integer for x and solve for y.
  4. Verify Using Integer Rules — Calculate the operation with your chosen pair to verify the outcome. Ensure you apply positive/negative sign rules correctly.

Step-by-Step Solved NCERT Examples

  • Example 1: Write down a pair of integers whose sum is -3. Solution: Let the first integer be -5. We want to find another integer x such that (-5) + x = -3. Adding 5 to both sides, we get x = -3 + 5 = 2. Thus, our pair is -5 and 2. Verification: (-5) + 2 = -3. This is correct!
  • Example 2: Write a pair of negative integers whose difference is 8. Solution: Let the two negative integers be -a and -b. We need (-a) - (-b) = 8, which simplifies to -a + b = 8. Let's choose a = 2, so our first integer is -2. Then, b - 2 = 8, which gives b = 10, so our second integer is -10. Verification: (-2) - (-10) = -2 + 10 = 8. Our negative integer pair is -2 and -10. This is correct!

Common Mistakes to Avoid in Exercise 1.2

Watch out for these classic pitfalls during your CBSE exams:

  • The Minus Sign Trap: Remember that subtracting a negative number is equivalent to adding its absolute positive value. For example, 5 - (-3) becomes 5 + 3 = 8, not 5 - 3 = 2.
  • Commutative Confusion: Do not apply the commutative property to subtraction. While 5 + (-3) = (-3) + 5, 5 - (-3) is NOT equal to (-3) - 5.
  • Not Reading Constraints: If the question specifically asks for a negative integer and a positive integer, check your final answer to make sure the signs match the exact constraints.

Practice Questions with Solutions

  • Q: Write down a pair of integers whose sum is -7. A: Step 1: Let the first integer be x and the second integer be y. We need x + y = -7. Step 2: Let's choose x = -10. Step 3: Substitute x into our equation: -10 + y = -7, which gives y = -7 + 10 = 3. Step 4: Verify the result: (-10) + 3 = -7. Final answer: One such pair of integers is -10 and 3.
  • Q: Write down a pair of integers whose difference is -10. A: Step 1: Let the first integer be x and the second integer be y. We need x - y = -10. Step 2: Let's choose the first integer x = 2. Step 3: Substitute x into our equation: 2 - y = -10, which gives y = 2 + 10 = 12. Step 4: Verify the result: 2 - 12 = -10. Final answer: One such pair of integers is 2 and 12.
  • Q: Fill in the blank to make the statement true: (-5) + (-8) = (-8) + (...) A: Step 1: Observe the structure of the equation. It is in the form of a + b = b + c. Step 2: Recall the Commutative Property of addition: a + b = b + a. Step 3: Match the terms. Here, a = -5 and b = -8. Thus, the missing number must be equal to a, which is -5. Final answer: -5
  • Q: Fill in the blank to make the statement true: -53 + (...) = -53 A: Step 1: Notice that the sum of the integer and the missing number results in the same integer. Step 2: Recall the Additive Identity property: a + 0 = a for any integer a. Step 3: Since adding 0 to an integer does not change its value, the missing number is 0. Final answer: 0

Frequently Asked Questions

Is subtraction of integers associative?

No, subtraction of integers is not associative. For example, (5 - 3) - 2 = 0, but 5 - (3 - 2) = 4, showing that grouping changes the outcome.

What is the additive identity for integers?

Zero is the additive identity for integers. Adding zero to any integer, positive or negative, does not change its value.

How do I find a pair of integers with a sum of 0?

To get a sum of zero, choose any integer and its negative opposite (additive inverse), such as 6 and -6.