According to Brahmagupta's rules, what is the result of subtracting a negative number from zero?

The positive equivalent of the negative number

The negative equivalent of the positive number

According to Brahmagupta's rules, what is the result of adding a positive number and a negative number?

Subtract the smaller number from the larger number and take the sign of the larger number.

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The Other Side of Zero

Action Plan Notes Questions Mock-Test

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Addition and Subtraction of Integers

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Applications of Integers

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Brahmagupta's Rules for Integers

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Learning Objectives

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Learning Objectives

Understand the concept of integers, including positive and negative numbers.
Identify and use the additive inverse of numbers.
Apply addition and subtraction of integers using number lines.
Evaluate expressions involving positive and negative integers.
Recognize the significance of zero in the number system.
Solve problems related to bank account balances using integers.
Interpret temperature readings in relation to positive and negative integers.
Analyze and complete integer grids to find border sums.

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Revision Notes & Summary

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Chapter 10: The Other Side of Zero

Introduction to Integers

Counting Numbers: The first numbers learned in mathematics are counting numbers (1, 2, 3, 4).
Zero: Represents nothing and comes before 1. Important in the Indian number system.
Fractions: Numbers that exist between whole numbers (e.g., 2 1, 2 3).
Negative Numbers: Numbers that come before 0, completing the number line.

Understanding Positive and Negative Numbers

Banking Example:
- Credits (positive numbers) and debits (negative numbers) affect your bank balance.
- Example: Starting with ₹0, credits of ₹30, ₹40, ₹50, and debits of ₹40, ₹50, ₹60.
Geographical Cross Sections: Heights above sea level are positive, below sea level are negative.

Operations with Integers

Addition and Subtraction

Addition: Starting Position + Movement = Target Position.
Subtraction: Target Position - Starting Position = Movement.
Example Expressions:
- a. -125 + (-30)
- b. +105 - (-55)
- c. +80 - (-150)

Inverses

The additive inverse of a number is the number that, when added to the original number, results in zero.
- Example: The inverse of +4 is -4.

Evaluating Expressions Using Number Lines

Unmarked Number Line: Can visualize addition and subtraction.
Example: 85 + (-60) = 25.

Practical Applications

Geographical Heights: Heights measured from sea level (0m).
Example Questions:
1. What is the highest point above sea level?
2. What is the lowest point below sea level?

Conclusion

Negative numbers, zero, and positive numbers are critical in mathematics and have significant applications in various fields.

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Practice Test – MCQs, True/False

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Multiple Choice Questions

₹130

₹90

₹160

₹70

Correct Answer: A

Solution:

Starting with ₹100, adding a credit of ₹60 results in ₹160. Subtracting a debit of ₹30 gives a final balance of ₹130.

Chapter Concept:

Addition and Subtraction of Integers

Floor +3

Floor +4

Floor +5

Floor +6

Correct Answer: A

Solution:

Starting at Floor +2, pressing '+' three times takes you to Floor +5. Pressing '-' twice takes you back to Floor +3.

Chapter Concept:

Applications of Integers

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The Other Side of Zero

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True or False

Correct Answer: False

Solution:

Heights above sea level are represented by positive integers, while heights below sea level are represented by negative integers.

Chapter Concept :

Applications of Integers

Correct Answer: True

Solution:

Zero is a unique integer that is neither positive nor negative. It acts as a neutral point on the number line, separating positive and negative integers.

Chapter Concept :

Introduction to Integers

Correct Answer: True

Solution:

According to Brahmagupta's rules, the sum of two positive numbers is indeed positive, such as

2 + 3 = 5

Chapter Concept :

Brahmagupta's Rules for Integers

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The Redemption Arena

The Other Side of Zero

Study Action Plan (Sorted by Difficulty)

Addition and Subtraction of Integers

High

Applications of Integers

High

Brahmagupta's Rules for Integers

Learning Objectives

Learning Objectives

Practice, Analyze & Improve 🚀

Revision Notes & Summary

Chapter 10: The Other Side of Zero

Introduction to Integers

Understanding Positive and Negative Numbers

Operations with Integers

Addition and Subtraction

Inverses

Evaluating Expressions Using Number Lines

Practical Applications

Conclusion

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Practice Test – MCQs, True/False

Multiple Choice Questions

Q1.In a bank account, if you start with a balance of ₹100 and make a credit of ₹60 followed by a debit of ₹30, what will be your final balance?

Correct Answer: A

Q2.Bela's Building of Fun uses a lift system where pressing the '+' button moves you up a floor and pressing the '-' button moves you down a floor. If you start at the Art Centre on Floor +2 and press the '+' button three times followed by the '-' button twice, which floor will you reach?

Correct Answer: A

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True or False

Q1.The height of geographical features above sea level is represented by negative integers.

Correct Answer: False

Q2.The number zero is considered neither a positive nor a negative integer.

Correct Answer: True

Q3.Brahmagupta's rules for addition state that the sum of two positive numbers is positive.

Correct Answer: True

High

Historical Context of Integers

High

Introduction to Integers

High

Q3.According to Brahmagupta's rules, what is the result of subtracting a negative number from zero?

Correct Answer: C

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Q4.If you have a bank account starting at ₹0, and you make credits of ₹30, ₹40, and ₹50, and debits of ₹40, ₹50, and ₹60, what will be your final balance?

Correct Answer: D

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Q5.If you start at Floor +2 in Bela's Building of Fun and press the '-' button 3 times, where will you end up?

Correct Answer: B

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Q6.If you start at Floor +2 and press -3 in the lift, which floor will you reach?

Correct Answer: B

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Q7.Using Brahmagupta's rules, what is the result of subtracting -3 from +5?

Correct Answer: A

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Q8.What is the result of adding the integers +5+5+5 and −3-3−3 using the token model?

Correct Answer: A

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Q9.According to Brahmagupta's rules, what is the result of adding a positive number and a negative number?

Correct Answer: C

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Q10.In a bank account, credits are represented by positive integers and debits by negative integers. If your account starts with ₹100, you credit ₹60, debit ₹30, and then debit ₹150, what is your final account balance?

Correct Answer: A

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Q4.The sum of two positive integers is always positive.

Correct Answer: True

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Q5.The sum of a positive integer and its negative counterpart is always zero.