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What is the Additive Inverse for Integers?
Grade Level:
Class 7
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
The additive inverse of an integer is the number that, when added to the original integer, results in zero. It's like finding its 'opposite' number on the number line.
Simple Example
Quick Example
Imagine you have scored 5 runs in a cricket match. To get your score back to 0 runs, you would need to add -5 runs (which means losing 5 runs). So, the additive inverse of 5 is -5.
Worked Example
Step-by-Step
PROBLEM: Find the additive inverse of -12.
STEP 1: Understand what additive inverse means. We need a number that, when added to -12, gives 0.
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STEP 2: Let the additive inverse be 'x'. So, we want to solve the equation: -12 + x = 0.
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STEP 3: To isolate 'x', add 12 to both sides of the equation.
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STEP 4: -12 + x + 12 = 0 + 12
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STEP 5: x = 12
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ANSWER: The additive inverse of -12 is 12.
Why It Matters
Understanding additive inverses is crucial in many advanced fields. In Computer Science, it helps in error correction and data manipulation. Scientists and Engineers use it for balancing equations and understanding forces, which is key for careers in AI/ML and Physics.
Common Mistakes
MISTAKE: Thinking the additive inverse of a positive number is still positive (e.g., additive inverse of 7 is 7). | CORRECTION: The additive inverse of a positive number is always its negative counterpart (e.g., additive inverse of 7 is -7).
MISTAKE: Confusing additive inverse with multiplicative inverse (reciprocal). | CORRECTION: Additive inverse means adding to get zero. Multiplicative inverse means multiplying to get one.
MISTAKE: Not considering zero. (e.g., thinking zero has no additive inverse). | CORRECTION: The additive inverse of 0 is 0 itself, because 0 + 0 = 0.
Practice Questions
Try It Yourself
QUESTION: What is the additive inverse of 15? | ANSWER: -15
QUESTION: My friend owed me Rs. 20 (represented as -20). What amount should he give me to make the balance zero? This amount is the additive inverse. | ANSWER: Rs. 20 (or 20)
QUESTION: If the additive inverse of an integer 'p' is -9, what is the value of 'p'? | ANSWER: 9
MCQ
Quick Quiz
Which of the following statements about additive inverse is TRUE?
The additive inverse of any integer is always a positive number.
When an integer is added to its additive inverse, the result is always 1.
The additive inverse of -100 is 100.
Zero does not have an additive inverse.
The Correct Answer Is:
C
Option C is correct because -100 + 100 = 0. Option A is false for negative integers. Option B is false, the result is 0. Option D is false, the additive inverse of 0 is 0.
Real World Connection
In the Real World
Imagine managing your mobile data. If you used 2GB (-2GB) more than your plan, you need to 'add' 2GB (+2GB) back to make your usage balance zero. Similarly, in accounting, debit and credit entries are often additive inverses to balance books, helping companies like Flipkart track finances.
Key Vocabulary
Key Terms
INTEGER: A whole number (positive, negative, or zero) | OPPOSITE NUMBER: A number that is the same distance from zero on the number line as another number, but on the opposite side | SUM: The result of adding two or more numbers | ZERO: The integer that is neither positive nor negative.
What's Next
What to Learn Next
Great job learning about additive inverses! Next, you can explore 'Subtracting Integers' or 'Multiplication of Integers'. Understanding additive inverses makes subtraction much easier, as subtracting a number is like adding its additive inverse!
