Integers - Number of Integers Solutions from Our Ph.D. Experts

Integer: Definition and Meanings

Math has a lot of elements, and most of them can be confusing if you don't learn them well. Integers happen to be a crucial part of the subject and cover an important aspect. So, to start with, the word “integer” has been adapted from Latin. Generally, they are whole numbers, and they also include negative numbers.

If this gets confusing, here’s something to make things simple. Integers are numbers with no decimal or fractional part from a set of negative and positive numbers, including zero. The following image will make things clearer for you and help you understand the classification of integers:

Integers are all around you. Remember, any number without a decimal or fraction is an integer irrespective of whether it is positive or negative.

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What is an Integer?

As mentioned earlier, integers are any number, including zero, irrespective of it being positive or negative. An integer should always be a whole number and cannot be a decimal or fraction. The integers are represented by Z. For example,

Z= {…..,-3,-2,-1,0,1,2,3….}

If you want to learn about integers properly, you have to know the types and understand them. There are two types of integers, namely, positive and negative integers. Here's a look into the types:

Positive integer

Any number that's greater than zero is termed a positive integer.

For example, 1,2,3…

Negative integer

Numbers that are less than zero are termed negative integers.

For example, -1,-2,-3…

There’s a lot to learn if you want to know the lesson well. There are various types of numbers in the number system that can be included under integers; they are:

Whole numbers
Natural numbers
Odd and even integers
Prime and composite numbers

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Integers on a Number Line

There's a lot to learn in math. The subject explores various chapters, and you need to know the right ways to solve math problems. When you start learning integers, you cannot ignore the significance of number lines. The line will help you compare the numbers that must be placed at equal intervals. The line needs to extend to both sides horizontally, and the numbers must be placed exactly like the way it's shown in the image:

Understand the concept well to place integers correctly on the number line.

Graphing Integers on a Number Line

Visual representations in mathematics are important. You need to learn the best ways to do so. Graphing integers on a number line might be tough. You can look into the examples to understand how to place integers on a number line. Here are some tips that will make graphing integers on a number line easy for you:

The right horizontal side will have numbers that are always greater than the ones on the left
Positive numbers must be placed on the right side of “0” because they are greater than “0”
The negative numbers need to be placed on the left side of “0” cause they are smaller than “0”
The number zero is kept in the middle because it’s neither positive nor negative

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Integer Operations

Can any math lesson go without some calculation? Of course not. So, when you are studying integers, you have to know the integer operations. Here’s an insight into all the integer operations:

Addition of integers

Adding integers can be tricky. You have to understand what you are adding. There might be two negative integers or a combination of positive and negative integers. You will come across these cases when you start adding integers:

If both integers have the same signs, add them and provide the same sign in the answer; for example, (-2) + (-2) = -4
If one is positive and the other is negative, find the difference and provide the sign of the larger number in the result, for example, 3 + (-5) = -2

Here are some examples of adding integers using the number line:

Subtraction of integers

Here’s how you can carry out subtraction of integers:

Convert the problem into an addition problem by changing the sign of subtrahend
The rules will be the same as addition, apply them and solve the problems

Multiplication of integers

If you confront a multiplication problem, here’s what you should do:

Multiply the signs to get the resultant sign
Multiply the numbers, add the resultant sign to answer

Go through the table to understand the multiplication of integers properly:

Division of integers

Follow these tips to divide integers correctly:

Divide the signs of the two values to get the resultant sign
Divide the numbers, add the resultant sign to the quotient

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Rules of Integers

Every math problem must be solved following some rules. Here’s a look into the rules of integers:

The Sum of two positive integers is an integer
The Sum of two negative integers is an integer
The product of two positive integers is an integer
The product of two negative integers is an integer
Adding a positive integer and negative integer of the same value will result in zero
Multiplying integers and their reciprocal will give the result as one

Follow the rules and solve integer problems easily.

Properties of Integers

A math lesson has a lot of elements, and you have to understand each of them to learn the lesson well. Here’s a look into all of them:

Closure property

This property states that the particular set is closed for any mathematical operation.

Associative property

The property states that changing the grouping of two integers will not affect the result.

Commutative property

In this case, you will not see any change in the result if you change the positions of operands.

Distributive property

To calculate and find the right answer, you can distribute an operand among other operands.

Additive inverse property

This property states that adding an integer and its negative value will result in zero.

Multiplicative inverse property

The property states that multiplying an integer with its reciprocal will give one as a result.

Identity property

Solving integer problems might not be easy. The identity property applies to various operations, and you have to understand the same to solve the problems.

To end with,

It is impossible to solve math problems without understanding the lessons well. You have to know the essence of the subject and work on them correctly. The subject has a lot of significance, and everyone must learn it well. Instead of running away from complex problems, try solving them to enhance your skills and knowledge.

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Most Popular Questions Searched By Students:

Q. What are 5 examples of integers?

Ans: Integers are numbers, positive or negative, including zero. Here are five examples of integers: -2, -1, 0, 1, 2. Understanding what integers are is easy. Students must pay attention to the lessons that follow after the definition.

Q. How do you solve integer questions?

Ans: You can solve integer questions by following these rules:

The Sum of two positive integers is an integer
The Sum of two negative integers is an integer
The product of two positive integers is an integer
The product of two negative integers is an integer
Adding a positive integer and negative integer of the same value will result in zero
Multiplying integers and their reciprocal will give the result as one

Q. How do you solve integers in math?

Ans: You have to follow the rules and the properties to solve integer problems in math. Integers follow the same processes of addition, subtraction, multiplication and division.