What is Integers?

Integers are a set of whole numbers that include positive and negative numbers, as well as zero. They are different from fractions and decimals, which are not whole numbers. Some examples of integers are 1, -2, 0, 10, -100, and 500. Integers are used in many different contexts, such as temperature, money, and sports scores.

Integers Definition

An integer is a whole number that includes negative and positive numbers, including zero. It has no decimal or fractional part. A few examples of integers are: -4, 0, 2, 5, 8, 97.

A set of integers, which is represented as Z, includes:

• Positive Numbers: A number is positive if it is greater than zero. Example: 1, 2, 3, . . .
• Negative Numbers: A number is negative if it is less than zero. Example: -1, -2, -3, . . .
• Zero is defined as neither a negative number nor a positive number. It is a whole number.

Set of Integers

The set of integers is represented by the letter Z and it is written as shown below:

Z = {... -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5 ...}

Observe the figure given below to understand the definition of integers.

Opposite Integers

Positive integer and negative integers are opposit to each other.

Example:

• +8 and -8 are opposite to each other
• +12 and -12 are opposite to each other
• Opposite of 0 is 0

Absolute value of an Integer

The absolute value of an integer is its numerical value irrespective of its sign. It is represented by | |. While writing the absolute value of an integer, we don't consider its sign.

Example: Absolute value of -8 = |-8| = 8 Absolute value of 12 = |12| = 12

Integer Addition

Adding a positive integer means moving to the right side on the number line. Adding a negative integer means moving to the left side on the number line.

Example:

-3+5=?

Answer = 2

Integer Subtraction

subtraction of integers is an inverse process of addition.

To subtract an integer from another integer, we add the opposite of first integer to second integer.

Example:

Subtract -5 from 10

= 10 - (-5)

= 10 + 5 (opposite of first integer -5 is +5)

= 15.

Integers on a Number Line

On a straight line, a number line is a visual representation of numbers. This line is infinite, extending horizontally on both sides, with numbers placed at equal intervals for the purpose of comparing them. The set of integers, like other numbers, can also be represented on a number line.

Test your knowledge with Upfunda Quiz!

1. The maximum and minimum temperature of a city as 24 degree celsius and -4 degree celsius respectively. What was the difference between the minimum and the maximum temperature?
2. Ramesh thinks of an integer. He subtracts 12 from it and gets the result at -6. What was the integer he thought of?
3. Amit wants to some balls. If he bought 5 balls, he would still have $10 left in his wallet. If he wants to uy seven balls, he would have to borrow 22 dollars. How much is one ball (the price of a ball is an integer number)?
4. In an exam of 50 questions, 5 marks are awarded for every correct answer and -3 marks for every incorrect answers. If Radhika attempt all the questions and gave 21 incorrect answer, then what is her score in the exam? Choose:
5. If M and N are two integers such that M is 12 and N is the predecessor of M+6, then find the value of M-N