What is the Additive Inverse?

S3-SA1-0088

Grade Level:

Class 6

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

The additive inverse of a number is another number that, when added to the first number, gives a sum of zero. Think of it as the 'opposite' number on the number line. Every number has an additive inverse.

Simple Example

Quick Example

Imagine you have ₹50 in your wallet. If you spend ₹50 (which is -₹50), your balance becomes ₹0. So, the additive inverse of ₹50 is -₹50, because ₹50 + (-₹50) = ₹0.

Worked Example

Step-by-Step

Let's find the additive inverse of -12.

STEP 1: Understand the goal. We need to find a number that, when added to -12, results in 0.

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STEP 2: Let the unknown additive inverse be 'x'. So, we have the equation: -12 + x = 0.

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STEP 3: To isolate 'x', we need to 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 key in many fields like Computer Science for error correction, Physics for balancing forces, and Economics for calculating net profits or losses. It helps engineers design stable structures and AI/ML algorithms process data accurately by cancelling out effects.

Common Mistakes

MISTAKE: Thinking the additive inverse of a negative number is also negative. E.g., additive inverse of -7 is -7. | CORRECTION: The additive inverse of a negative number is always positive. The additive inverse of -7 is 7.

MISTAKE: Confusing additive inverse with multiplicative inverse (reciprocal). E.g., thinking the additive inverse of 5 is 1/5. | CORRECTION: Additive inverse deals with addition to get zero. Multiplicative inverse deals with multiplication to get one. The additive inverse of 5 is -5.

MISTAKE: Forgetting that zero is its own additive inverse. E.g., thinking zero has no additive inverse or it's 'undefined'. | CORRECTION: The additive inverse of 0 is 0, because 0 + 0 = 0.

Practice Questions

Try It Yourself

QUESTION: What is the additive inverse of 15? | ANSWER: -15

QUESTION: Find the additive inverse of -200. | ANSWER: 200

QUESTION: If the sum of two numbers is 0, and one number is -75, what is the other number? | ANSWER: 75 (The other number is the additive inverse of -75)

MCQ

Quick Quiz

Which of the following pairs shows a number and its additive inverse?

5 and 1/5

-10 and -10

12 and -12

0 and 1

The Correct Answer Is:

Option C is correct because 12 + (-12) = 0. Options A, B, and D do not sum to zero.

Real World Connection

In the Real World

In cricket, if a team scores +25 runs in an over and then loses -25 runs due to a penalty in the next over, their net change in runs from those two overs is 0. This 'cancelling out' effect uses the idea of additive inverses to track scores and balances, just like how banks manage credit and debit.

Key Vocabulary

Key Terms

OPPOSITE: A number with the same magnitude but different sign | SUM: The result of adding two or more numbers | INTEGER: Whole numbers and their negative counterparts (..., -2, -1, 0, 1, 2, ...) | ZERO: The number that represents nothing or the absence of quantity

What's Next

What to Learn Next

Great job understanding additive inverses! Next, you can explore 'multiplicative inverses' (reciprocals). This will show you how numbers can 'cancel out' through multiplication to give 1, which is another fundamental concept in mathematics.