Introduction to Integers:
Understanding integers is like exploring a number universe where you have positive numbers (like 1, 2, 3…), negative numbers (like -1, -2, -3…), and zero. Positive numbers are for counting things you have, like friends or candies. Negative numbers are for things like owing money or temperatures below zero. Zero is like a neutral point, neither positive nor negative. Integers help us make sense of the world around us, whether we’re counting, measuring, or keeping track of changes.
What are Integers?
An integer is a set of numbers that includes all whole numbers, both positive and negative, as well as zero. This means that integers can be represented on a number line that extends infinitely in both directions from negative infinity to positive infinity.
Here we see what they look like:
Positive numbers: These are numbers that we use to count objects or represent quantities greater than zero. Examples include 1, 2, 3, 4, 5, etc.
Negative numbers: These are numbers less than zero, represented by a minus sign (-) before the number. Examples include -1, -2, -3, -4, -5, etc.
Zero: It’s neither positive nor negative, but it’s still an integer. It serves as a reference point on the number line, separating positive and negative numbers.
Understand Positive Integers
Positive numbers are probably the numbers we are most familiar with. These are the ones we use when counting our allowance, our friends, or our favorite football team’s scores. Positive numbers are shown to the right of zero on the number line and increase as you move further to the right.
Exploring negative Integers
Let’s take a step in the opposite direction – to the left of zero on the number line. Here, we will find negative numbers. Negative numbers represent values less than zero and are indicated by a minus sign (-) before the number.
Negative numbers may seem a little tricky at first, but they are just as important as positive numbers. They come in handy when we’re dealing with situations like owing money, measuring below-freezing temperatures, or tracking elevation loss.
For example, if our friend owes someone ₹5, it will be shown as -5. If the temperature drops by 3 degrees below zero, it will be shown as -3. And if we are descending a mountain and our altitude drops by 100 meters, it will be shown as -100.
Zero: The Neutral Ground
Now, let’s talk about zero. Unlike positive and negative integers, zero doesn’t have a sign associated with it because it’s neither positive nor negative. Instead, it serves as a reference point on the number line, separating positive numbers from negative numbers.
Operations with Integers
Addition and Subtraction
When adding or subtracting integers, we need to pay attention to the signs:
If we add two positive integers, the result will be positive.
If we add two negative integers, the result will also be negative.
If we subtract a negative integer from a positive integer, it’s like adding a positive integer, so the result will be positive.
If we subtract a positive integer from a negative integer, it’s like adding a negative integer, so the result will be negative.
For example:
- 2+3=5 (Both positive)
- 2+(−3)=−1 (Positive and negative)
- −2+(−3)=−5 (Both negative)
- −2−3=−5 (Both negative)
Multiplication and Division
When multiplying or dividing integers, the rules are a bit simpler:
If the signs of the numbers are the same (both positive or both negative), the result will be positive.
If the signs of the numbers are different (one positive and other negative), the result will be negative.
For example:
- 2×3=6 (Both positive)
- 2×(−3)=−6 (Positive and negative)
- −2×(−3)=6 (Both negative)
- −6÷2=−3 (Positive and negative)
Real-World Application
You might be wondering, “When will you ever use integers in real life?” Well, the truth is, they are everywhere! Here are a few examples of how they’re used in everyday situations:
Banking: When we deposit money into our bank account, it’s represented as a positive integer. But if we withdraw money or have an overdraft, it’s represented as a negative integer.
Thermometers: Temperature readings can be positive or negative integers, depending on whether it’s above or below zero degrees Celsius.
Elevations: If we’re hiking up a mountain, our altitude might be represented as a positive integer. But if we’re descending into a valley, it would be represented as a negative one.
Gaming Scores: In video games, our score might increase (positive integers) or decrease (negative integers) depending on our performance.
Directions: If we’re driving north, your direction might be represented as a positive integer. But if we’re driving south, it would be represented as a negative .
FAQ
What is an integer and examples?
- An integer is a number that includes negative and positive numbers, including zero. It does not include any decimal or fraction. Example: -8, 0, 1, 5, 8, 33, etc.
How Are Integers Different from Whole Numbers?
In whole numbers we take all Natural Numbers as well as zero. Whereas in integers we have all whole numbers as well as all negative numbers.
Can Integers Be Represented on a Number Line?
- Yes, integers can be represented on a number line. Positive integers are plotted to the right of zero, negative integers to the left of zero, and zero itself is at the center.
What Are Absolute Values of Integers?
- The absolute value of an integer is its distance from zero on the number line, ignoring its sign. For example, the absolute value of -5 is 5, and the absolute value of 5 is also 5. Absolute values are used to represent magnitudes or distances and are denoted by vertical bars, such as |x|
What is additive inverse?
The additive inverse of a number is the value that, when added to the original number, results in zero. In simpler terms, it’s the opposite of the given number.
For example:
- The additive inverse of 5 is -5, because 5 + (-5) equals 0.
- The additive inverse of -8 is 8, because (-8) + 8 equals 0.
