learn basic mathematics topics

Contents:

• Ancient Roman numeral                                                         
• Hindu-Arabic Numeral    
• Prime Numbers 
• successor and predecessor
• Co-prime numbers 
• Comparison of numbers
• Natural numbers  
• Odd-Even and Composite number
• Whole numbers 
• Forming of Greater and Smallest numbers
• Integers 
• Methods of reading and writing a large number
• Factors   
• Indian place value chart
• Ascending order 
• International methods of numbering
• Descending order
• BODMAS and ODMAS
• Face value of a digit
• Place value.

Ancient Roman Numeral:

1	5	10	50	100	500	1000
I	V	X	L	C	D	M

Hindu- Arabic Numeral

The Hindu-Arabic numeral system based on place value.

1	2	3	4	5	6	7	8	9	10
One	Two	Three	Four	Five	Six	Seven	Eight	Nine	Ten
11	12	13	14	15	16	17	18	19	20
Eleven	Twelve	Thirteen	Fourteen	Fifteen	Sixteen	Seventeen	Eighteen	Nineteen	Twenty
21	22	23	24	25	26	27	28	29	30
Twenty One	Twenty-Two	Twenty-Three	Twenty Four	Twenty Five	Twenty Six	Twenty Seven	Twenty Eight	Twenty Nine	Thirty
31	32	33	34	35	36	37	38	39	40
Thirty One	Thirty-Two	Thirty-Three	Thirty Four	Thirty-Five	THirty-Six	Thirty-Seven	Thirty-Eight	Thirty-Nine	Forty
41	42	43	44	45	46	47	48	49	50
Forty One	Forty Two	Forty Three	Forty Four	Forty Five	Forty-Six	Forty Seven	Forty Eight	Forty Nine	Fifty
51	52	53	54	55	56	57	58	59	60
Fifty-One	Fifty Two	Fifty Three	Fifty Four	Fifty Five	Fifty Six	Fifty Seven	Fifty Eight	Fifty Nine	Sixty
61	62	63	64	65	66	67	68	69	70
Sixty One	Sixty Two	Sixty Three	Sixty Four	Sixty Five	Sixty Six	Sixty Seven	Sixty-Eight	Sixty Nine	Seventy
71	72	73	74	75	76	77	78	79	80
Seventy One	Seventy Two	Seventy Three	Seventy Four	Seventy Five	Seventy Six	Seventy Seven	Seventy Eight	Seventy Nine	Eighty
81	82	83	84	85	86	87	88	89	90
Eighty One	Eighty Two	Eighty Three	Eighty Four	Eighty Five	Eighty Six	Eighty Seven	Eighty Eight	Eighty Nine	Ninty
91	92	93	94	95	96	97	98	99	100
Ninty One	Ninty Two	Ninty Three	Ninty Four	Ninty Five	Ninty Six	Ninty Seven	Ninty Eight	Ninty Nine	Hundred

Prime Numbers:

A number 2, 5, 13,19 ...etc is divisible only itself and 1. these numbers have only two factors 1 and itself they are called a prime number.

0 and 1 are not prime numbers. all prime number is odd, except 2. There are 25 prime numbers from 1 to 100.

The smallest even number is 2. And the smallest prime number is also 2. Thus, 2 is the smallest prime number. Which is also the smallest even number.


List of prime number:

2	3	5	7	11
13	17	19	23	29
31	37	41	43	47
53	59	61	67	71
73	79	83	89	97

Coprime Numbers:

Two numbers are coprime numbers if the only common factor they have is 1.
Example -
18 = 1 x 2  x 3 x 3 and 

35 = 1 x 7 x 5

18 and 35 have no common factor other than 1 so they are coprime numbers.



Natural Numbers: The counting numbers1,2,3,4,5,6,7.....etc are called natural numbers.



Whole numbers; All natural numbers including 0 are called whole numbers.

Example - 0,1,2,3,4,5,6,7,....etc are all whole numbers.



Integers: All whole numbers along with negative natural numbers are known as integers.

Example -  etc ....-7,-6,-5,-4,-3,-2,-1,0,1,2,3,4,5,6,7....etc



Fractions - numbers in the form of a/b  where a and b are whole numbers and b is not equal to 0 are called fractions.

Example - 
1/4,
4/5
6/9


Factor: The factor of a number divide the number without leaving a remainder.

12 x 8 = 96 12 and 8 are factor of 96

1. A number is a factor of itself.
2. 1 is the factor of every number.

Ascending order: Ascending order means arranging numbers from the smallest to the largest.

Example -  4035, 4217, 4315, 4479.



Descending order: Descending order means arranging numbers from the biggest to smallest.


Example - 9729, 9652, 9526, 9256.



Face value of a digit: The face value of a digit in a number is the value of the digit itself irrespective of its place in the number.

 Example:

In the number 345789.

Face value of 3 = 3

Face value of 4 = 4

Face value of 5 = 5

Face value of 7 = 7

Face value of 8 = 8

Face value of 9 = 9



Place value:

• The place value of a digit depends on its position in the number.
• place value of a digit = face value of the digit X value of the place

Example - Find the place value of 2,37,456

                     L     TTh      Th         H       T        O
                     2      3           7           4       5          6

2,37,456 = 2 lakhs 37 thounds 4 hundreds 5 tens 6 once

place value of 6 =  6 X 1 = 6

Place value of 5 =  5 X 10 = 5 tens

Place value of  4 = 4 X 100 = 400 = 4 hundred

Place value of  7 = 7 X 1000 = 7000 = 7 thousands

Place value of  3 = 3 X 10000 = 30,000 = 30 thousands

Place value of  2 = 2 X 100000 = 2,00,000 = 2 lakhs

Successor and predecessor of a number:

Successor - The successor of a number is one more than the number. we find a successor to add 1 to the number.

Example -

The successor of 543786 is 543787  ( 543786 + 1 = 543787 )

The successor of 999999 is 1000000 ( 999999 +   = 1000000).


Predecessor - The predecessor of a number is less than the number. so subtract 1 from the number to get predecessor.

Example -

A predecessor of 56903 is 56902  ( 56903 - 1 = 56902 )

A predecessor of 999999 is 999998  ( 999999 - 1 = 999998).

Comparison of numbers:

Rule 1 - The number with more number of a digit is always greater.

Example -

     7999  <  36541

    10001  > 9999

         99   < 100


Rule 2 - The number with a greater number of hundreds is greater.

Example -

678   <  734.

297    >  199


Rule 3 - If the digits at hundreds and tens place are the same the number with a greater number at once place is greater.

Example -

560 < 569.

426 > 420.

Rule 4 - If the digits at hundreds, tens, and once place are the same, the numbers are equal.

Example -

        567  = 567

2347658  = 2347658.


Note - To compare numbers, move to the left to right comparing the digits at each place. if the digit is the same in place compare the digit at the next pace.

1. If 100s place is the same, compare 10s place.

2. 7 > 6, it is called 7 is greater > than 6.

3. 7 < 8, it is called 7 is less  < than 8.

Odd, Even and Composite Numbers

Even numbers- Numbers that make an exact number of pairs are called even numbers. or any number that can be exactly divided by 2 is known as even numbers.


Even numbers:

2	4	6	8	10	12	14	16	18	20
22	24	26	28	30	32	34	36	38	40
42	44	46	48	50	52	54	56	58	60
62	64	66	68	70	72	74	76	78	80
82	84	86	88	90	92	94	96	98	100

Note - All numbers end with 2, 4, 6, 8, and 0 are even numbers.


Odd numbers - The numbers that do not make an exact number of pairs are known odd numbers.

1	3	5	7	9	11	13	15	17	19
21	23	25	27	29	31	33	35	37	39
41	43	45	47	49	51	53	55	57	59
61	63	65	67	69	71	73	75	77	79
81	83	85	87	89	91	93	95	97	99

Note - All numbers with end 1, 3,5,7, and 9 are odd numbers.

Composite numbers:

The number that has more than 2 factors. a composite number has a minimum of 3 factors. A whole number that can be divided by numbers other than 1 or itself.

Example - 

15 can be divided exactly by 3, 5,1, and itself so 15 is a composite number.

17 can not be divide other than 1 and itself so 17 is not a composite number, 17 is an odd number.

4	6	8	9	10	12	14	15	16	18
20	21	22	24	25	26	27	28	30	32
33	34	35	36	38	39	40	42	44	45
46	48	49	50	51	52	54	55	56	57
58	60	62	63	64	65	66	68	69	70
72	74	75	76	77	78	80	81	82	84
85	86	87	88	90	91	92	93	94	95
96	98	99	100

Note - there are 74 composite numbers between 1 to 100.

Forming the greatest and smallest digits numbers:

We know that there is no 2 digit number beyond 99. 99 is the largest number of 2 digits. Thus, 999 is the largest number of 3 digits. And the largest number of 4 digits is 9999. If 1 is added to 9999, the smallest number of 5 digits is obtained.

1. The largest number of one digit + 1 = the smallest number of two digits.
2. The largest number of two digits + 1 = the smallest number of three digits.
3. The largest number of three digits + 1 = the smallest number of four digits.

Example:
9 + 1 = 10
99 +1 = 100
999 +1 = 1000. 

Similarly, reducing one to the smallest 2-digit number gives the largest number of 1 digit. Subtracting 1 from the smallest three-digit number gives the largest 2-digit number. Reducing 1 to a 4 digit number gives the largest 3 digit number.

Example:

10 - 1 = 9
100 - 1 = 99
1000 - = 999                

Greatest numbers      

One digit -  9 

Two-digit -  99   

Three-digit-  999 

Four-digit -   9,999    

Five-digit -   99,999   

Six-digit -     9,99,999 

Seven digits -99,99,999 

Eight digits - 9,99,99,999   

Nine digits -  99,99,99,999 

Ten digits-     9,99,99,99,999   

Smallest numbers  

One digit -     1     
                   
Two-digits -   10 

Three-digits - 100      

Four-digits -    1,000 

Five-digits -     10,000

Six digits -       10,0000

Seven digits -   10,00,000 

Eight digits -    100,00,000

Nine digits -     10,00,00,000

Ten digits -       1,00,00,00,000 

Method of reading and writing large numbers

1. 347
2. 2456

H  T    O                   Expanded

3       4        7                          3 X 100 + 4 x 10+ 7 x1


Three hundred and forty-seven
Similarly 2456

Th     H      T        O              Expanded

 2       4       5        6                    2 x 1000 + 4 x 100 + 5 x 10 + 6 x 1


2,456 = Two thousand four hundred and fifty-six


Number                         Name


1                                     One

10                                  Ten

100                                Hundred

1000                              Thousand

10,000                           Ten thousand

1,00,000                        Lakh or hundred thousand

10,00,000                      Ten lakh or million

1,00,00,000                   Crore or ten million

10,00,00,000                 Ten crore or hundred million

100,00,00,000               Hundred crore or billion







                                                              Indian place value chart


Commas help us a lot in writing and reading large numbers. The Indian System of Numeration uses commas to display thousands, millions, and crores. First commas in place of a hundred (moving from right to third). The second comma is followed by the next 2 digits. The third comma is followed by the leading two digits.

                
253567240 =  200000000 + 50000000 + 3000000 +  500000  + 
                        20 crore                    5 crores                  30 lakh                 5 lakh

 60000      +   7000   +     200  +   40  + 0 
 60 thousand             7 thousand          2 hundred    forty



25,35,67,240 = twenty-five crore thirty-five lakh sixty-seven thousand two hundred and forty

The international system of numeration

In the international method of numbering, unit, tens, hundreds, thousands, and used in millions.
The first comma is followed by the third digit from the right. The second comma displays the millions.

Example: 40, 612, 505

It is read as Forty million six hundred twelve thousand five hundred and five in the international method of numbering.


In the Indian method, it is four crore six lakh twelve thousand five hundred and five.



One's period           Thousands period              Millions period            Billions period


Ones                      Thousand                          Million                        Billion


Tens                       Ten thousands                     Ten million                 Ten billion


Hundreds              Hundred thousand            Hundred million        Hundred billion



165,124,640 = one hundred and sixty-five million one hundred and twenty-four thousand six hundred and forty

BODMAS and ODMAS

Simplifications:

Opening and removing brackets

(  ) it is called first brackets, Parentheses, or round brackets

❴  ❵ It is second brackets, braces, or curly brackets

[  ] Square brackets  

< > Angle brackets  

Example :

(6 + 7) x 10
= 13 X 10
= 130

The use of parentheses clearly states that the numbers within parentheses () are first converted into a single number and then carried out.   



When there brackets in a simplification sum, the order to be done by BODMAS. If brackets within the brackets, simplify within brackets first.

B - Brackets

O - Of

D - Division

M - Multiplication

A - Addition

S -  Subtraction


Example :

= 3 - { ( 36 + 24) /  ( 90 - 60)}

= 3 - { 60 / 30 }

= 3 - 2

= 1



ODMAS is helpful for the simplification of addition, subtraction, multiplication,  and division.

O - Of

D - Division

M - Multiplication

A - Addition

S - Subtraction.

Simplify-

= 8720 - 15 of  50 ÷ 25 × 130 - 3250 + 912
= 8720 - 750 ÷25 x 130 - 3250 + 912
= 8720 - 30 x 130 - 3250 + 912
= 8720 + 912  - 3900 - 3250
= 9632 - 7150
= 2482