NCERT Solutions for Class 6 Maths Chapter 10 - The Other Side of Zero Exercise 10.5

Exercise 10.5

1. Can you explain each of Brahmagupta’s rules in terms of Bela’s Building of Fun, or terms of a number line? 

Ans: 

Brahmagupta’s Rules

1. Addition of Positive Numbers:

Rule: When adding two positive numbers, the result is positive.
Bela’s Building: Imagine Bela starts on the 3rd floor. If she moves up 2 floors, she reaches the 5th floor.
Number Line: This is like moving from 3 to 5 by adding 2.
Example: 3 + 2 = 5

2. Addition of Negative Numbers:

Rule: Adding two negative numbers results in a negative number.
Bela’s Building: If Bela begins 3 floors below ground level (-3) and goes down another 2 floors, she ends up 5 floors below ground (-5).
Number Line: This is represented by moving from -3 to -5 by adding -2.
Example: −3 + (−2) = −5

3. Addition of a Positive and a Negative Number:

Rule: Subtract the smaller absolute value from the larger absolute value and keep the sign of the larger one.
Bela’s Building: If Bela starts on the 3rd floor and moves down 5 floors, she ends up 2 floors below ground (-2).
Number Line: This is like moving from 3 to -2 by adding -5.
Example: 3 + (−5) = −2

4. Subtraction of a Positive Number from a Negative Number:

Rule: Subtracting a positive number from a negative one is the same as adding both numbers and keeping the negative sign.
Bela’s Building: If Bela is 3 floors below ground (-3) and goes down 2 more floors, she ends up 5 floors below ground (-5).
Number Line: This is shown as moving from -3 to -5 by subtracting 2.
Example: −3 − 2 = −5

5. Subtraction of a Negative Number from a Positive Number:

Rule: Subtracting a negative number from a positive number is equivalent to adding the two numbers.
Bela’s Building: If Bela starts on the 3rd floor and goes up 2 floors, she reaches the 5th floor.
Number Line: This is like moving from 3 to 5 by subtracting -2.
Example: 3 − (−2) = 5

6. Subtraction of a Negative Number from a Negative Number:

Rule: Subtracting a negative number from another negative number is the same as adding their absolute values while keeping the negative sign.
Bela’s Building: If Bela is 3 floors below ground (-3) and moves up 2 floors, she ends up 1 floor below ground (-1).
Number Line: This is like moving from -3 to -1 by subtracting -2.
Example: −3 − (−2) = −1

2. Give your own examples of each rule.

Ans:

1. Addition of Positive Numbers:

Example: 6 + 3 = 9
Bela’s Building: Starting on the 6th floor and moving up 3 floors to reach the 9th floor.

2. Addition of Negative Numbers:

Example: −7 + (−4) = −11
Bela’s Building: Starting 7 floors below ground and moving down 4 more floors, reaching 11 floors below ground.

3. Addition of a Positive and a Negative Number:

Example: 9 + (−6) = 3
Bela’s Building: Starting on the 9th floor and moving down 6 floors, arriving at the 3rd floor.

4. Subtraction of a Positive Number from a Negative Number:

Example: −5 − 4 = −9
Bela’s Building: Starting 5 floors below ground and moving down 4 more floors to 9 floors below ground.

5. Subtraction of a Negative Number from a Positive Number:

Example: 4 − (−3) = 7
Bela’s Building: Starting on the 4th floor and moving up 3 floors to reach the 7th floor.

6. Subtraction of a Negative Number from a Negative Number:

Example: −6 − (−2) = −4
Bela’s Building: Starting 6 floors below ground and moving up 2 floors to end up 4 floors below ground.

Benefits of NCERT Solutions for Class 6 Maths Chapter 10 Exercise 10.5 The Other Side of Zero

• The solutions provide detailed explanations that help students grasp the concepts of positive and negative integers, enhancing their overall understanding.

• Each solution is presented step-by-step, allowing students to follow the logic behind each problem, which builds their problem-solving skills.

• The exercise connects mathematical concepts to real-life situations, making it easier for students to see the relevance of what they are learning.

• These solutions serve as a great resource for revision, helping students quickly review key concepts before exams.

• By practising with these solutions, students gain confidence in their ability to tackle integer problems, preparing them for future math challenges.

Class 6 Maths Chapter 10: Exercises Breakdown

Important Study Material Links for Class 6 Maths Chapter 10 - The Other Side of Zero

Conclusion

In Exercise 10.5, students learn the essential concepts of integers by applying them to real-life situations like historical timelines and temperature changes. This exercise strengthens their understanding of positive and negative numbers, helping them practice the addition and subtraction of integers. By using these concepts in practical problems, students build a strong foundation for future topics in mathematics. Using these solutions ensures that students can confidently solve integer-related problems, preparing them effectively for their exams.

Chapter-wise NCERT Solutions Class 6 Maths

The chapter-wise NCERT Solutions for Class 6 Maths are given below. Go through these chapter-wise solutions to be thoroughly familiar with the concepts.

Related Important Links for Class 6  Maths 

Along with this, students can also download additional study materials provided by Vedantu for Maths Class 6.