# Chapter 6 – Integers

The following Topics and Sub-Topics are covered in this chapter and are available on MSVgo:

Introduction

We regularly deal with numbers. Numbers are an inherent part of our day to day life. Whatever simple numbers that we deal with can be classified as integers. Integers can also be used to depict your profits and losses. Integers always have 1 as their denominator.

You can convert real-life applications in numbers and integers, and check its functioning. For example, if you want to build a toy castle, then you must know the length and breadth of the castle, along with the length and breadth of each toy unit. This will require you to know about integers and the concept of numbering. Want to know how? Then check this exciting blog that covers the depth of integers and their concepts.

#### What are Integers?

Integers are numbers that can be depicted on a number line. They can be of three types and are not fractions. Integers are also not improper fractions and have a denominator 1. Let’s check the different types of integers along with the examples.

Integers can be used to perform different operations such as addition, multiplication, or subtraction. In any arithmetic operations if we use integers, then the result is also an integer. There are different properties of integers that are given below in this article.

#### Types of Integers

Integers can be classified into three broad types. They are as follows:

• Positive Integers: Numbers that are positive in nature are called positive integers. These numbers are depicted on the right side of the origin on a number line. Examples: 1, 5, 555, 6852, 884, etc.

• Negative Integers: Numbers that are negative in nature are called negative integers. These numbers are depicted on the left side of the origin on a number line. Example: -54, -65, -5425, etc.
• Zero: Zero comes in between the number line and is considered the origin for both the positive and negative integers.

#### Properties of an Integer

• Closure Property: It states that the result is an integer on addition or multiplication of two or more integers. For example, 5 + 6 = 11. Here, all the numbers (5, 6, and 11) are integers.
• Commutative Integers Property: Going by this integer property, the following conditions hold true:
A + B = B + A
A * B = B * A
Where A and B are unique numerical values that are integers.
• Associative Property: Going by this property, the following condition holds true for any three integers:
A + (B + C) = (A + B) + C
A * (B * C) = (A * B) * C
Where A, B, and C are unique numerical values that are integers.
• Distributive Property: Going by this property, the following condition holds true for any three integers:
A * (B + C) = A * B + A * C
Where A, B, and C are unique numerical values that are integers.
• Additive Inverse Property: Additive inverse of any integer is the negative of that integer. Essentially, the sum of the integer and additive inverse should be zero.
A + (-A) = 0, where A is any integer.
• Multiplicative Inverse Property: Multiplicative inverse of any integer is the reciprocal of that integer. Essentially, the multiplication of the integer and its multiplicative inverse should be 1.
A * (1/A) = 1, where A is any integer.

#### Functions that we can Perform on Integers

• Addition of Integers: We can add two or more integers to get an integer. For example, 5 + 54 = 59.
• Subtraction of Integers: We can subtract any integer from another integer. Example, 65 – 5 = 60. We can even depict the subtraction of integers with the help of a number line.

• Multiplication: We can perform multiplication on integers to get an integer.
• Division: Division of two integers results in an integer quotient and integer remainder.

#### Conclusion

Integers are an integral concept in our life and are the basis of studying maths and physics. In maths, we start with the number system, and integers are a part of the number system. You can find integers in almost everything in your life. For example, the money you withdraw from the ATM, or the loss that your business incurred can be depicted using negative integers and more.

#### FAQs

• What are integers?

Any number that cannot be a fraction or a complex number is integers. They can be negative, positive, or zero, and occupy a place on the number line.

• What is an integer formula?

There is no special formula for calculating integers, as they are the basic elements of the number line. However, we can perform various operations on the integers, such as addition, subtraction, multiplication, and division. We can even convert one form of integers to another form, such as positive to negative integers.

• What are the examples of integers?

Integers are common numbers that can be positive, negative, or zero. The examples of integers are 1, 3, 4, -5, -54, 0, etc.

• What are the types of integers?

Integers can be of three types. They can be a positive integer, negative integer, and zero.

• What is an integer number in math?

In maths, the integer is a class of numbers that can be positive, negative, and zero and can be depicted on the number line. They cannot be fractional or complex numbers.

• What are the integers from 1 to 10?

Integers from 1 to 10 are 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. There are a total of 10 positive integers between 1 to 10.

Try MSVgo, a video-based learning app that can help you understand different kinds of numbers easily. We have multiple varieties of numbers in maths, including integers. The video tutorials will help you understand the concept easily.

### High School Physics

• Alternating Current
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### High School Chemistry

• Acids, Bases and Salts
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### High School Math

• Algebra – Arithmatic Progressions
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### Middle School Science

• Acids, Bases And Salts
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• Basic Biology
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• Weather, Climate And Adaptations Of Animals To Climate
• Winds, Storms And Cyclones

### Middle School Math

• Area and Its Boundary
• Boxes and Sketches
• Data Handling
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• Heavy and Light
• How Many
• Long And Short
• Mapping
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• Money
• Multiplication and Factors
• Multiply and Divide
• Numbers
• Parts and Wholes
• Pattern Recognition
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• Play With Patterns
• Rupees And Paise
• Shapes And Angles
• Shapes And Designs
• Shapes and Space
• Similarity
• Smart Charts
• Squares
• Subtraction
• Tables And Shares
• Tenths and Hundredths
• Time