CLASS 6 MATHS NOTES

 

Prime Numbers

 Prime Numbers are those numbers which can be divided by itself and 1 only for example 1,3,5,7,11,13.......ans so on.

For example, 5 is prime because the only ways of writing it as a product, 1 × 5 or 5 × 1, involve 5 itself. 

Irrational Numbers

 An irrational number can be written as a decimal, but not as a fraction. An irrational number has endless non-repeating digits to the right of the decimal point. All most all real numbers are irrational

Like all real numbers, irrational numbers can be expressed in positional notation, notably as a decimal number. In the case of irrational numbers, the decimal expansion does not terminate, nor end with a repeating sequence . For example, the decimal representation of π starts with 3.14159, but no finite number of digits can represent π exactly, nor does it repeat.

Rational Numbers

Rational numbers: They represents the ratios of two integers. The set of all rational numbers is countable.A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, a numerator p and a non-zero denominator q. Since q may be equal to 1, every integer is a rational number.

For example - 3/4 is a rational number.

24/8 is a rational number.

1.1 is a rational number → 11/10

π is irrational, as it cannot be represented as a fraction of two integers. (Read 22/7 is rational but π is not rational, so what is the ratio for π? for clarification

The digits in pi go on for infinity, but they never repeat. A number whose digits go on for infinity without repeating is irrational.

Any decimal number that terminates is rational because it can be written with a power of ten in the denominator

• 9.2651 = 9265110000$\frac{92651}{10000}$

Any decimal number that ends in repeating digits is rational because the value of those repeating digits can be written as a fraction.

• 6.4212121212121… = 2119330

ational number, in mathematics, a number that can be represented as the quotient p/ q of two integers similar that q ≠ 0. In addition to all the pieces, the set of rational figures includes all the integers, each of which can be written as a quotient with the integer as the numerator and 1 as the denominator. In decimal form, rational figures are moreover terminating or repeating numbers. For illustration,1/7 = 0.142857, where the bar over 142857 indicates a pattern that repeats ever

                                          

                                                  

Even Numbers

Even Numbers are those numbers that can be divided into two equal groups or pairs and are exactly divisible by 2. For example, 2, 4, 6, 8, 10, and so on. 

ODD NUMBERS

 A whole number that is not able to be divided by two into two equal whole numbers The numbers 1, 3, 5, and 7 are odd numbers.

Odd numbers are positive integers that cannot be categorized into groups of two. For example: 1, 3, 5, 7, etc. Let's visualize it using an example of footwear and cherries. Let us assume that we have footwear in counts of 1, 3, 5, and 7. On the other hand, we have cherries in pairs of 2, 4, 6, and 8. Look at the image given below in order to understand how the pairing of these numbers will work.

Properties of Odd Numbers

If you try to carry out a few arithmetic operation the odd numbers, can you come to a common conclusion of all of the numbers? Well yes, there does exist a set of properties that applies not only for the odd numbers given in the list of 1 to 200 but are applicable to any odd number that you may come across. Given below is a list of the properties that will always apply for an odd number. Each of these properties can be explained in a detailed way as given below:

• Addition: The addition of two odd numbers will always give an even number, i.e., the sum of two odd numbers is always an even number. For example, 3 (odd) + 5 (odd) = 8 (even).
• Subtraction: subtract of two odd numbers will always give an even number. For example, 7 (odd) - 1 (odd) = 6 (even).
• Multiplication: it is of two odd numbers will always give an odd number. For example, 3 (odd) × 7 (odd) = 21 (odd).
• Division: division of two odd numbers will always give an odd number. For example, 33 (odd) ÷ 11 (odd) = 3 (odd).

Natural Numbers

A natural number is a number that occurs commonly and obviously in nature. As such, it is a whole, non-negative number. The set of natural numbers, denoted N, can be defined in either of two ways: N = {0, 1, 2, 3, ..} , N = (1, 2, 3, 4, .)

Whole Numbers

Number which are started from 0 are called whole numbers.

For Example: 0, 1, 2, 3, 4, 5, 6, and 7 are all whole numbers. Numbers such as -3, 2.7, or 3 ½ are not whole numbers.

 Let's sing!

Zero, one, two, three and four.

Whole numbers are many more.

Go on! Count on my friend!

Whole numbers just don’t end!

 Fun Facts

• There is no 'largest' whole number. 
• Except 0, every whole number has an immediate predecessor or a number that comes before.
• A decimal number or a fraction lies between two whole numbers, but are not whole numbers. 
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CLASS(9th) NUMBER SYSTEM

 NUMBER SYSTEM

Types Of Number System

1-Whole Numbers

2-Natural Numbers

3-Odd Numbers

4-Even Numbers

5-Rational Number

6-Irrational Numbers

7-Prime Numbers

POLYNOMIALS

Poly means many and nomials means terms so polynomial is working with many terms. 

           According to term they are of three types

           Monomial-one term

           Binomial  -two term

           Trinomial-three term

            According to degree they are also three types

            Linear polynomial-Degree One

            Quadratic polynomial-Degree Two

             Cubic polynomial-Degree Three

              

           

          

           

                     

HINDI GRAMMAR

 

• विराम चिन्ह
• संज्ञा
• सर्वनाम
• क्रिया
• विशेषण
• लिंग
• संधि
• संस्कृत शब्द रूप
• अनेकार्थी शब्द
• एकार्थक शब्द
• अनेक शब्दों के लिए एक शब्द
• विलोम शब्द
• पर्यायवाची शब्द
• रस
• कारक
• समास
• शब्द विचार
• वर्णमाला
• पद परिचय
• वाक्य
• क्रिया विशेषण
•  समुच्चय बोधक
• विस्मयादिबोधक
• वचन
• उपसर्ग
• प्रत्यय
• छन्द
• अलंकार
• पर्यायवाची शब्द
• तत्सम-तद्भव शब्द
• मुहावरे
• हिंदी निबंध

ENGLISH GRAMMAR

 Nouns

The easy way to remember nouns is that they relate to people, places, or effects. Indeed impalpable or abstract generalities like ideas or studies are effects. In the following rulings, the nouns are stressed
.
Sally does n’t use an iPhone. Jared does n’t eat subs. The Earth isn't the center of the macrocosm.

Pronouns
Pronouns are words that replace nouns I, me, she, we, they, who, that, yours, his, her, etc.
Pronouns need antecedents. That means that the thing (or person, or place) that the pronoun refers to requirements to have been mentioned formerly by name nearly before in the judgment orparagraph.However, the anthology can get relatively confused, If it’s not clear which thing the pronoun refers to.

I swam in the ocean. You swam in the ocean. He swam in the ocean. She swam in the ocean. It swam in the ocean.
Adjectives
Adjectives are descriptive words that add detail to a judgment. They can give important or necessary information (e.g., Please hand me the blue paper), or they can just make the judgment more intriguing (e.g. A frigid wind blew around the icy city). Adjectives describe nouns. Please suture the red dress. The rainfall is hot and sticky. The stuffed toy is fuzzy and round.

Verbs
Verbs are action words that’s a rather simplified explanation, but it’s the clearest one. Verbs tell you what the subject of the judgment is over to.

He ran into the wall. She buys new shoes. The cat licks its fur.
Adverbs
Adverbs describe verbs, adjectives, or indeed a whole judgment. Adverbs frequently end with the suffix-ly (for illustration, poorly, hungrily), but some look the same as their adjective forms (for illustration, the word presto is used as both an adjective and adverb).

Prepositions
Prepositions are little words that tell where or when (among other effects) commodity is. The monkey is on his reverse. The cement is behind the board. The dreamcatcher is above the bed.

Convergences
Convergences are words like and, but, and or that connect generalities, clauses, or corridor of rulings.

I wanted to meet her there on time, but I got stuck in business. You ca n’t wear socks and sandals.

Exclamations
Exclamations are words like wow and yay. They ’re sounds we make to convey extreme emotion or to produce emphasis when we ’re talking, occasionally when we ca n’t suppose of a good way to express ourselves. The problem with exclamations is that they bear a great deal of environment to be understood. For case, hey can mean hello, or that’s great, or stop doing that. Hey! How’s it going? Wow! Those fireworks are emotional. Yay! I passed math