What is Additive Inverse of a Rational Number? | Simple Explanation for Class 6

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What is the Additive Inverse of a Rational Number?

Grade Level:

Class 6

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

Definition

What is it?

The additive inverse of a rational number is the number that, when added to the original number, gives a sum of zero. It's simply the same number with the opposite sign. For example, the additive inverse of a positive number is negative, and the additive inverse of a negative number is positive.

Simple Example

Quick Example

Imagine you have Rs 50 in your piggy bank (+50). To make your balance zero, you need to spend Rs 50 (-50). So, -50 is the additive inverse of +50. If you owe your friend Rs 20 (-20), and you get Rs 20 (+20) to pay them back, your debt becomes zero. So, +20 is the additive inverse of -20.

Worked Example

Step-by-Step

Let's find the additive inverse of 3/4.

--- Step 1: Understand the concept. We need a number that, when added to 3/4, results in 0.

--- Step 2: Remember that adding a number and its opposite sign version gives zero. For example, 5 + (-5) = 0.

--- Step 3: To make 3/4 become 0 when added to another number, that other number must be -3/4.

--- Step 4: Check your answer: 3/4 + (-3/4) = 0.

--- Answer: The additive inverse of 3/4 is -3/4.

Why It Matters

Understanding additive inverses is key in fields like Computer Science for error correction and in Physics for balancing forces. It helps engineers design stable structures and helps in financial accounting to balance ledgers. This concept is fundamental for careers in data science, engineering, and even economics.

Common Mistakes

MISTAKE: Confusing additive inverse with multiplicative inverse (reciprocal). For example, saying the additive inverse of 2 is 1/2. | CORRECTION: Additive inverse is about changing the sign, not flipping the fraction. The additive inverse of 2 is -2.

MISTAKE: Forgetting to change the sign for negative numbers. For example, saying the additive inverse of -7 is -7. | CORRECTION: The additive inverse of -7 is +7 because -7 + 7 = 0. Always change the sign.

MISTAKE: Not considering fractions or decimals. For example, only thinking about whole numbers. | CORRECTION: The rule applies to all rational numbers, including fractions like -5/8 (additive inverse is 5/8) and decimals like 1.5 (additive inverse is -1.5).

Practice Questions

Try It Yourself

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

QUESTION: Find the additive inverse of 7/9. | ANSWER: -7/9

QUESTION: If the additive inverse of a number 'x' is -2.5, what is the number 'x'? | ANSWER: 2.5

MCQ

Quick Quiz

Which of the following is the additive inverse of -12/5?

2026-05-12T00:00:00.000Z

-5/12

2026-12-05T00:00:00.000Z

-12/5

The Correct Answer Is:

The additive inverse of a number is the same number with the opposite sign. Since the given number is -12/5 (negative), its additive inverse will be +12/5 (positive). Options A and B are incorrect because they are reciprocals. Option D is the original number itself.

Real World Connection

In the Real World

Imagine your bank account balance. If you have Rs 100 in your account (+100), and you withdraw Rs 100 (-100) using your ATM card, your balance becomes zero. This 'withdrawal' is the additive inverse of your 'deposit' to bring the net effect to zero. Similarly, in cricket, if a team scores +50 runs, and then loses 50 runs due to a penalty (-50), their net runs from that incident are zero.

Key Vocabulary

Key Terms

ADDITIVE INVERSE: A number that, when added to another number, results in zero. | RATIONAL NUMBER: A number that can be written as a fraction p/q, where p and q are integers and q is not zero. | OPPOSITE SIGN: Having a plus (+) or minus (-) sign that is contrary to another number's sign. | SUM: The result of adding two or more numbers.

What's Next

What to Learn Next

Great job learning about additive inverses! Next, explore 'Multiplicative Inverse of a Rational Number'. This will help you understand how numbers behave when multiplied to get 1, which is another crucial concept for solving equations and working with fractions.