What is a Negative Integer?

S3-SA4-0361

Grade Level:

Class 6

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

Definition

What is it?

A negative integer is a whole number that is less than zero. It is always shown with a minus sign (-) in front of it, like -1, -5, or -100. Negative integers are opposite to positive integers and represent values below a starting point.

Simple Example

Quick Example

Imagine you have Rs. 50 in your wallet. If you spend Rs. 60 on a yummy vada pav and chai, you don't just have zero rupees; you actually owe Rs. 10. This 'owing Rs. 10' can be represented as -10 rupees, where -10 is a negative integer.

Worked Example

Step-by-Step

Let's say the temperature in Shimla at noon is 5 degrees Celsius. By midnight, it drops by 8 degrees Celsius.
1. Start with the noon temperature: 5 degrees Celsius.
2. The temperature drops, which means we subtract: 5 - 8.
3. Since 8 is greater than 5, the result will be a negative number.
4. Subtract the smaller number from the larger number: 8 - 5 = 3.
5. Apply the sign of the larger number (which was negative): -3.
Answer: The temperature at midnight is -3 degrees Celsius.

Why It Matters

Understanding negative integers is super important! In data science, they help analyze profit/loss. In physics, they describe temperatures below freezing or depths below sea level. Engineers use them to calculate forces, and even in computer science, they are used to represent memory addresses or error codes.

Common Mistakes

MISTAKE: Thinking -5 is greater than -2. | CORRECTION: Negative numbers work the opposite way of positive numbers. The further a negative number is from zero, the smaller its value. So, -5 is smaller than -2.

MISTAKE: Forgetting the minus sign when writing a negative integer. | CORRECTION: Always remember to put the '-' sign before the number to show it's negative. Without it, it's a positive number.

MISTAKE: Confusing negative integers with fractions or decimals. | CORRECTION: Negative integers are whole numbers (like -1, -2, -100) that are less than zero. Fractions (-1/2) and decimals (-0.5) are not integers.

Practice Questions

Try It Yourself

QUESTION: What integer represents a withdrawal of Rs. 500 from your bank account? | ANSWER: -500

QUESTION: If the ground floor is 0, what integer represents 3 floors below the ground? | ANSWER: -3

QUESTION: A submarine is at 150 meters below sea level. If it descends another 70 meters, what is its new depth as an integer? | ANSWER: -220 meters

MCQ

Quick Quiz

Which of the following is a negative integer?

-10

2026-01-02T00:00:00.000Z

The Correct Answer Is:

A negative integer is a whole number less than zero, marked with a minus sign. Option C, -10, fits this definition. 0 is neither positive nor negative, 5 is a positive integer, and 1/2 is a fraction.

Real World Connection

In the Real World

When you check the weather app on your phone, especially during winter in places like Ladakh or Kashmir, you might see temperatures like -5°C or -10°C. These are negative integers telling you how cold it is, below the freezing point (0°C). Even when you check your mobile data usage, if you've used more than your pack, sometimes your balance might show as a negative number, indicating overuse.

Key Vocabulary

Key Terms

INTEGER: A whole number (positive, negative, or zero) | POSITIVE INTEGER: A whole number greater than zero (e.g., 1, 2, 3) | NEGATIVE SIGN: The symbol '-' used to denote a negative number | NUMBER LINE: A visual representation of numbers in order

What's Next

What to Learn Next

Great job learning about negative integers! Next, you should explore 'Addition and Subtraction of Integers'. This will teach you how to perform calculations with both positive and negative numbers, which is a fundamental skill for more advanced math.