The numbers are used for counting and measuring. Can be divided into negative numbers, zero, positive real numbers and they are said to be the main source of mathematics. All numbers are classified into sets and every number represented a unique representation.

Mathematical operations are only possible if one has the knowledge of numbers.
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The general format of the counting is {1, 2, 3, 4, 5,...…}.

Set of positive integers or non negative integers. It exclude zero, negative number, fraction number and decimal numbers.

The examples of the negative numbers are -86, -97 and -56 etc.

**Operations**

**numeral**, but in common usage the word number is used for both the abstract object and the symbol, as well as for the word for the number. In addition to their use in counting and measuring, numerals are often used for labels.

### Solved Examples

**Question 1: **How many apples are there in the picture?

** Solution: **

There are 5 apples in the picture.

**Question 2: **In the following picture, which is more? Number of parrots or number of flowers?

** Solution: **

Number of parrots = 4

Number of flowers = 3

Therefore, number of parrots are more than number of flowers in the given picture.

The numbers will not be over within 3 digits, 4 digits, or......N digit numbers. But we cannot keep counting them till N digit numbers hence, they go on forever till $\infty$ (infinity).
A number line is a line on which real numbers are placed according to their value. For example, the number 3.5 or 3 $\frac{1}{2}$ corresponds with the point on a number line that is halfway between the numbers 3 and 4. Each point on a number line corresponds to a real number, and each real number has a unique point on the Number line that corresponds only to that number. It is a valuable tools which are easily used to illustrate the mathematical concepts such as subtraction, addition and positive and negative numbers. In number line, right side of zero are positive numbers and left side of zero are negative numbers.

The number line is usually represented as a horizontal line.

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**Problem 1:** Classify the given numbers as rational or irrational. $\frac{22}{7}$, $\frac{22}{2}$, $\frac{22}{5}$

**Problem 2:** Out of 99 and 89, which number has greater distance from zero on the number line.

Set of positive integers or non negative integers. It exclude zero, negative number, fraction number and decimal numbers.

The examples of the negative numbers are -86, -97 and -56 etc.

Used for performing many operations like

- Addition
- Subtraction
- Multiplication
- Division

Addition operator is +,

Subtraction is -

For Multiplication we use * and

for division $\div$ or /.

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A notational symbol which represents a number is called a Subtraction is -

For Multiplication we use * and

for division $\div$ or /.

There are 5 apples in the picture.

Number of parrots = 4

Number of flowers = 3

Therefore, number of parrots are more than number of flowers in the given picture.

One of the most important manipulative devices, that is available for teaching mathematics. We can certainly count a numbers from a number chart. It used in mathematics for teaching a number patterns, number relationships, operations and problem solving.

Below you could see the number chart 1-100

The numbers will not be over within 3 digits, 4 digits, or......N digit numbers. But we cannot keep counting them till N digit numbers hence, they go on forever till $\infty$ (infinity).

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**1. Natural Numbers**

In learning algebra numbers, it is necessary to learn about Natural numbers. That can be represented by all Whole numbers except ' 0 '. And all these numbers are positive numbers only.

**Example: **(1, 2, 3, 4, 5, . . . )

**2. Whole Numbers**

In algebra numbers, the whole numbers can be represented by the set of numbers which is starting from 0 to infinity.

**Example: **(0, 1, 2, 3, . . . )

**3. Integers**

A set of numbers which contains all negative, positive numbers and also zero. There is no decimal numbers.

**Example: **(. . . . . . . . -4, -3, -2, -1, 0, 1, 2, 3, 4, . . . . . . . . . . . )

**4.** **Rational Numbers**** and Irrational Numbers**

The rational numbers and are the set of all numbers which can be written in fraction form. As a fraction $\frac{a}{b}$, where a and b are integers(b$\neq$0). Irrational is used only when a number which cannot be written in the form of simple fraction.

**Example: **$\sqrt{3}$: Irrational

$\sqrt{4}$ = 2 :Rational

$\sqrt{5}$, $\sqrt{6}$, $\sqrt{7}$, $\sqrt{8}$ : Irrational

$\sqrt{\frac{9}{4}}$: Rational

$\sqrt{2}$: Irrational

5. Real Numbers

The real numbers are the set of all numbers which contains both rational numbers and irrational numbers.

**6. Odd Numbers**

A number which is not divisible by 2 is called an odd number, such as (3, 5, 7, 9, 11, . . . . . . . ).

**Example:** Find out the all Odd numbers from (7, 2, 5, 3, 9, 22, 49, 18, 29, 36)

Answer : 3, 5, 7, 9, 29, 49

7. Even Numbers

A number which is divisible by 2 is called an even number, such as (2, 4, 6, 8, 10, . . . . . . . ).

**Example: **Find out the all Even numbers from (7, 2, 5, 3, 9, 22, 49, 18, 29, 36)

Answer : 2, 18, 22, 36

**8. Prime Numbers**

A number which is divisible by it self and it's not divisible by any numbers, such as (2, 5, 7, 11, . . . . . . . . . .).

**Example:** Find out the all prime numbers from the given below. (9, 2, 4, 7, 11, 29, 17, 49, 101)

Answer : 2, 7, 11, 17, 29, 101

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