In Mathematics, we have come across different types of numbers, such as whole numbers, natural numbers, complex numbers, imaginary numbers, etc. Each number is different from other numbers, even if they share some common properties. To understand the differences and similarities between the numbers, Mathematicians have developed a grouping system that categorizes the numbers based on the characteristics.

A number is an arithmetic value that represents the quantity and helps in making the calculations. People have been using numbers for thousands of years to count something in their real life. Here, we are going to learn the definition of integers, properties and operations on integers.

In Math, integers are the numbers that include positive integers, negative integers and zero. Integers are the special group of numbers that consists of a set of numbers, such as {…., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, …}. All the positive and negative whole numbers are the integers, excluding the fractional and decimal numbers. The set of integers are represented using the symbol “Z”. The integers that follow each other in an order are called the ** consecutive integers**.

If ” n” can be any integer, then.

The general form of consecutive odd integer is 2n+1

The general form of consecutive even integers is 2n.

Some of the examples of integers include -9, -7, 4, 0, -2, and so on.

The numbers like ½, 3.14, 8/9, √2, √5, etc., are not integers as the numbers have the decimal part in them.

The various arithmetic operations in Maths are addition, subtraction, multiplication and division. We can perform these various operations using the integers. Integers use certain rules to perform the arithmetic operations. Now let us discuss the rules and operations on integers one by one.

The addition of two positive integers will result in the positive integer. Similarly, the addition of two negative integers will result in the addition operation with a negative sign.

For example,

- 3 + 2 = 5
- (-3) + (-2) = -5

In case if one number is positive and the other number is negative, the addition operation becomes a subtraction operation, and we have to consider the sign of the greatest integer.

- (-3) + 2 = -1

While subtracting two numbers, change the sign of the number which is being subtracted, and follow the same procedure of addition operation.

For example,

- (+5) – (+8) = +5 – 8 = -3
- (-5) – (-8) = -5 + 8 = 3
- (-5) – (+8) = -5 -8 = -13

The rule for the multiplication of integers is the same as the division of the integers.

While multiplying or dividing two integers, follow these two rules.

If the sign of the two numbers is the same, then the result is positive.

If the sign of the two numbers is different, then the result is negative.

For example:

- (2) × (3) = 6
- (-2) × (-3) = 6
- (-2) × (4) = -8
- (2) × (-4) = -8

As discussed above, each classification of numbers is based on the ** properties of numbers**. Now, let us discuss the properties of integer numbers.

Let a, b, c be any integers, and “b” is a non-zero integer, then the following properties hold for all integers.

- Addition: a+b ∈ Z
- Subtraction: a-b ∈ Z
- Multiplication: a × b ∈ Z
- Division: a ÷ b ∉ Z

- Addition: a + 0 = 0 + a = a
- Multiplication: a × 1 = 1 × a = a

- Addition: a+ b = b+a
- Multiplication: a × b = b × a

- Addition: a + (b + c) = (a + b) +c
- Multiplication: a × (b × c) = (a × b) × c

- Addition: a × (b + c) = (a × b) + (a× c)
- Subtraction: a × (b − c) = (a × b) − (a × c)

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Are you wondering what are typical temperatures in Celsius and Fahrenheit degrees you should be aware of? Read the short article about the most important temperatures that accompany you every day and find out how to convert Celsius to Fahrenheit.

It is worth to start from information that Celsius and Fahrenheit degrees are two of the most popular units of temperature used by people in science and everyday life. So, it is important to know typical temperatures specified on both units. It is also important to know __how to convert Celsius degrees to Fahrenheit degrees__**.**

When it comes to the title temperatures, below you can see a short list of them. In the beginning, let’s present typical temperatures in Celsius and Fahrenheit degrees:

0 °C / 32 °F – water freezing point,19 °C / 66.2 °F – typical room temperature,36.6 °C / 97.88 °F – normal body temperature,40 °C / 104 °F – typical bath water temperature,100 °C / 212 – boiling point of water.

As you can see, Celsius degrees are very different from Fahrenheit degrees. What is the relationship between Celsius and Fahrenheit, and why values presented on the list look like this?

The principle of the conversion from Celsius to Fahrenheit include two mathematical operation. If you want to convert Celsius to Fahrenheit, you have to multiply Celsius degrees by 1.8 and then add 32 to the obtained result.

Let’s check whether it works on the basis of an example of conversions of water freezing point and boiling point of water from Celsius degrees to Fahrenheit degrees.

- 0 Celsius degrees * 1.8 = 0

0 + 32 = 32 Fahrenheit degrees

- 100 Celsius degrees * 1.8 = 180

180 + 32 = 212 Fahrenheit degrees

Obtained results agree with the data on the list, so you can be sure that this principle of conversion from Celsius to Fahrenheit really works.

An interesting piece of information is that there is such a temperature in Celsius degrees which is equal to the same temperature, but in Fahrenheit degrees. More specifically, when you see -40 Celsius degrees on the thermometer you can be sure you also see -40 Fahrenheit degrees. How is this possible?

It results from the principle described earlier, when explained how to convert Celsius to Fahrenheit. According to his principle, conversion of -40 Celsius degrees to Fahrenheit degrees should look like this:

- -40 Celsius degrees * 1.8 = -72

-72 + 32 = -40 Fahrenheit degrees

** See? **After the change from -40 Celsius degrees to Fahrenheit degrees you know that -40 Celsius degrees is equal to -40 Fahrenheit degrees. It means this temperature is the point of equality of both units. It is worth to remember it, because this piece of information is useful in chemistry, physics and other science fields.

Are you interested in the topic of Celsius and Fahrenheit degrees? Visit our website and read the extensive articles about units of temperature and relationships between them.

Do you want to know typical temperatures in Celsius and Fahrenheit degrees? Read the article to find out them and learn how to convert Celsius to Fahrenheit correctly.

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