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NCERT Class 7 Maths Chapter 1 Integers MCQ Questions with Answers based on NCERT syllabus. Learn addition, subtraction, multiplication, division, and properties of integers with detailed solutions for
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Chapter Information
Subject: Mathematics
Class: 7
Chapter: Integers
Question Type: Multiple Choice Questions (MCQs)
Difficulty Level: Moderate to Difficult
Based On: NCERT Latest Syllabus
Introduction:
Integers include positive numbers, negative numbers, and zero. In this chapter, students learn how to represent integers on a number line and perform operations such as addition, subtraction, and multiplication. A good understanding of integers is essential for solving algebraic problems in higher classes.
What You Will Learn?
✔ Positive and Negative Integers
✔ Number Line Representation
✔ Addition of Integers
✔ Subtraction of Integers
✔ Multiplication of Integers
✔ Properties of Integers
✔ Opposite Integers
✔ Real-Life Applications of Integers
Why This Topic Is Important?
Integers are used in daily life to represent temperatures, profits and losses, heights above sea level, and bank transactions. Learning integers strengthens logical reasoning and mathematical skills.
Exam Relevance
These questions are useful for:
✔ CBSE Exams
✔ State Board Exams
✔ School Tests
✔ Unit Tests
✔ Half-Yearly Exams
✔ Annual Exams
✔ Scholarship Examinations
Q1. Which integer is the additive inverse of:
$$-11$$
A) $$11$$
B) $$-11$$
C) $$0$$
D) $$1$$
Answer:
$$11$$
Useful Formula for this Question:
The sum of an integer and its additive inverse is zero.
$$a+(-a)=0$$
Concept Behind This Question:
Students should understand the concept of additive inverse.
Step-by-Step Solution:
The additive inverse changes only the sign of the number.
Given integer:
$$-11$$
Its additive inverse is:
$$11$$
Verification:
$$(-11)+11=0$$
Hence, the correct answer is:
$$11$$
Exam Tip:
Opposite integers are additive inverses of each other.
Q2. Evaluate:
$$(-15)+9$$
A) $$24$$
B) $$-24$$
C) $$-6$$
D) $$6$$
Answer:
$$-6$$
Useful Formula for this Question:
For integers with different signs, subtract the smaller absolute value from the larger one and keep the sign of the larger absolute value.
Concept Behind This Question:
Students should add integers having different signs.
Step-by-Step Solution:
Given:
$$(-15)+9$$
Subtract the absolute values:
$$15-9=6$$
Since
$$15$$
has the larger absolute value and is negative, the result is negative.
Therefore,
$$(-15)+9=-6$$
Hence, the correct answer is:
$$-6$$
Exam Tip:
The sign of the integer with the greater absolute value determines the sign of the answer.
Q3. Find the value of:
$$-8-5$$
A) $$-13$$
B) $$13$$
C) $$-3$$
D) $$3$$
Answer:
$$-13$$
Useful Formula for this Question:
$$a-b=a+(-b)$$
Concept Behind This Question:
Students should subtract integers correctly.
Step-by-Step Solution:
Convert subtraction into addition:
$$-8-5=-8+(-5)$$
Add the integers:
$$-8+(-5)=-13$$
Hence, the correct answer is:
$$-13$$
Exam Tip:
Subtracting a positive integer moves left on the number line.
Q4. What is the product of:
$$7\times(-4)$$
A) $$28$$
B) $$-28$$
C) $$11$$
D) $$-11$$
Answer:
$$-28$$
Useful Formula for this Question:
$$(+)\times(-)=-$$
Concept Behind This Question:
Students should apply multiplication rules of integers.
Step-by-Step Solution:
Multiply the numbers:
$$7\times4=28$$
The signs are different.
Therefore,
$$7\times(-4)=-28$$
Hence, the correct answer is:
$$-28$$
Exam Tip:
The product of integers with unlike signs is always negative.
Q5. Which property is represented by:
$$5+0=5$$
A) Additive Identity
B) Multiplicative Identity
C) Closure Property
D) Associative Property
Answer:
Additive Identity
Useful Formula for this Question:
$$a+0=a$$
Concept Behind This Question:
Students should identify the identity properties of integers.
Step-by-Step Solution:
Adding zero to any integer does not change its value.
$$5+0=5$$
Therefore, zero is called the additive identity.
Hence, the correct answer is:
Additive Identity
Exam Tip:
Zero is the additive identity for integers.
Important Formulas & Concepts
1. Set of Integers
$$\ldots,-3,-2,-1,0,1,2,3,\ldots$$
2. Additive Inverse
$$a+(-a)=0$$
3. Subtraction of Integers
$$a-b=a+(-b)$$
4. Multiplication Rules
$$(+)\times(+)=+$$
$$(-)\times(-)=+$$
$$(+)\times(-)=-$$
$$(-)\times(+)=-$$
5. Additive Identity
$$a+0=a$$
6. Multiplicative Identity
$$a\times1=a$$
7. Commutative Property of Addition
$$a+b=b+a$$
8. Associative Property of Addition
$$(a+b)+c=a+(b+c)$$
FAQs
1. What are opposite integers?
Opposite integers have the same absolute value but different signs.
Example:
$$5\text{ and }-5$$
2. What is the additive identity of integers?
The additive identity is:
$$0$$
because
$$a+0=a$$
3. What is the multiplicative identity?
The multiplicative identity is:
$$1$$
because
$$a\times1=a$$
4. Is subtraction of integers commutative?
No.
$$7-3\ne3-7$$
5. What is the additive inverse of zero?
The additive inverse of zero is:
$$0$$
because
$$0+0=0$$
Common Mistakes
❌ Ignoring negative signs while calculations.
❌ Treating subtraction as commutative.
❌ Applying multiplication sign rules incorrectly.
❌ Confusing additive inverse with opposite numbers.
❌ Forgetting that zero is neither positive nor negative.
Quick Revision Notes
✔ Integers include positive numbers, negative numbers, and zero.
✔ Opposite integers have different signs.
$$a+(-a)=0$$
✔ Subtraction can be converted into addition.
$$a-b=a+(-b)$$
✔ Multiplication of unlike signs is negative.
$$(+)\times(-)=-$$
✔ Zero is the additive identity.
$$a+0=a$$
Conclusion
Integers is an important chapter in Class 7 Mathematics. Understanding integer operations and their properties helps students solve problems efficiently and prepares them for algebra and higher mathematics. Regular MCQ practice improves conceptual understanding, speed, and accuracy in examinations.
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