NCERT Solutions for Class 7 Mathematics Chapter 2 Operating with Integers
NCERT Solutions for Class 7 Mathematics Chapter 2 Operating with Integers
NCERT Solutions for Class 7 Mathematics Chapter Operations with Integers
This worksheet provides complete and accurate NCERT Solutions for Class 7 Mathematics Chapter Operations with Integers. This worksheet helps students understand how integers work through simple explanations, number-based activities, and real-life examples like puzzles and movement on a number line. The chapter is important because it builds a strong foundation for arithmetic operations such as addition, subtraction, and multiplication of integers. These concepts are essential for higher-level mathematics and problem-solving skills. All solutions in this worksheet strictly follow NCERT structure and order, making it reliable for school learning and exam preparation.
Chapter summary: stories, poems & themes
This chapter includes number puzzles, activity-based questions, and visual learning through models like number lines and tokens. Students learn through Rakesh’s puzzle, carrom coin movement, and token-based explanations. These activities help students understand how integers behave in different situations such as movement in opposite directions and combining positive and negative values. The chapter is activity-based and concept-driven, focusing on understanding rather than memorisation.
What this NCERT chapter covers?
• Understanding integers through puzzles and real-life examples
• Addition and subtraction using number line and token model
• Concept of additive inverse
• Movement of integers in positive and negative directions
• Multiplication of integers using patterns and models
• Rules for multiplication of integers
How to use these NCERT solutions?
Students should first attempt all questions on their own and then check the answers using this worksheet. Parents and teachers can guide students step-by-step using the provided explanations. These solutions follow the exact NCERT order, ensuring that no concept or question is skipped. This helps in better revision, clear understanding, and accurate practice before exams.
Student tips & learning tricks
Students should carefully observe signs while performing operations with integers. A common mistake is ignoring the negative sign, which can change the entire answer. While solving problems, always check whether the movement or number is positive or negative. Use number lines or token methods to understand concepts clearly. Practice patterns in multiplication to avoid confusion in sign rules.
Why NCERT solutions are important?
NCERT Solutions are important because they follow the exact syllabus prescribed for CBSE schools. They help students build strong basics and improve problem-solving skills. These solutions also increase confidence and help students perform better in school exams. Using NCERT-based answers ensures accuracy and proper understanding of concepts.
Complete answer key – NCERT solutions
2.1 A quick recap of integers
Figure it out
1. (a) The two numbers are 18 and 9
(b) The two numbers are 8 and -4
(c) The two numbers are 5 and -5
(d) The two numbers are -5 and 5
(e) The two numbers are -4 and -3
(f) The two numbers are -10 and 3
2. First number = 7
Second number = 18
Sum: 7 + 18 = 25
Difference: 7 – 18 = –11
3. First strike = +4 units
Second strike = +3 units
Final position = 7 units
4. Final position formula:
P = a + b
5. Example:
First strike = 5
Second strike = –7
Final position = –2
6. The second movement is 9
7. The final position of the coin is –5
8. Figure 1
a is negative (leftward), b is positive (rightward)
Magnitude of a is greater than b
9. Figure 2
a and b are in opposite directions
Magnitude of a is equal to b
10. Figure 3
a is positive (rightward), b is negative (leftward)
Magnitude of a is greater than b
11. (+7) – (+18) = –11
12. (a) 7 – 18 = 7 + (–18)
Explanation:
Subtracting 18 is the same as adding its additive inverse.
The additive inverse of 18 is –18.
13. (b) 4 – (–12) = 4 + 12
Explanation:
Subtracting –12 is the same as adding its additive inverse.
The additive inverse of –12 is 12.
2.2 Multiplication of integers
1. There are 8 positives in the bag
Operation: 4 × 2 = 8
2. 4 × (–2) = –8
3. 4 × (–6) = –24
4. 9 × (–7) = –63
5. (–4) × 2 = –8
6. Rule for multiplying two integers:
Multiply their absolute values
If the integers have different signs, the product is negative
If both integers have the same sign, the product is positive
Figure it out
1. (a) –6
(b) 10
(c) 4
(d) –21
2. (a) –56088
(b) 56088
(c) –56088
3. Final Answer: In all cases, the integer we get is –8
Practice explanation
When the multiplicand is positive, for every unit decrease in the multiplier, the product decreases by the multiplicand.
Example pattern:
4 × 3 = 12
3 × 3 = 9
2 × 3 = 6
1 × 3 = 3
0 × 3 = 0
–1 × 3 = –3
–2 × 3 = –6
–3 × 3 = –9
This pattern continues even when the multiplier becomes negative.
Master Class 7 Mathematics with accurate NCERT Solutions and build strong concepts step by step