Divisibility checking

a number is a multiple of;	Then;
2	Number should be an even number (ends with 0,2,4,6,8).
3	Sum of the digits should be divisible by 3.
4	Last 2 digit of the number may be ‘00’ or the last two digits form a number, which may be divisible by 4.
5	Unit place of the number should be zero or five.
6	Sum of the digit should be divisible by 2 and 3.
8	Last three digits may be ‘000’ or the last 3 digits form a number which may be divisible by 8.
9	Sum of the digits should be divisible by 9.
10	Last digit should be zero.
11	Difference of the sum of the alternate numbers may be zero or divisible by 11.

NUMBER SYSTEM

NUMBER SYSTEM

REAL NUMBERS

 A real number is any element of the set R, which is the union of the set of rational numbers and the set of irrational numbers. in mathematical expressions, unknown or unspecified real numbers are usually represented by z.
ex: 2, 5.6,  9.75, 5½,√2,....

RATIONAL NUMBERS

A rational number is any number that can be expressed in the form of p/q, with denominator q not equal to zero. since q may be equal to 1, every integer is a rational number.

IRRATIONAL NUMBERS

An irrational number is any real number that cannot be expressed as a ratio of integers. it can not be represented as terminating or repeating decimals.ex:√2

INTEGER NUMBER

An integer is a number that can be written without a fractional component.
ex: 21, 4, 0, and −2048 are integers, while 9.75, 5½, and √2 are not.

N	Natural numbers	1, 2, 3, 4, ………
W	Whole numbers	0, 1, 2, 3, ……
Z	Integers	…….., -4, -3, -2, -1, 0, 1, 2, 3, 4, ……..
Q	Rational numbers	Any numbers in the form of  p/q ; where q not equal to zero.
	Irrational numbers	An irrational number is any real number that cannot be expressed as a ratio of integers. it cannot be represented as terminating or repeating decimals. ex:√2,
C	Complex numbers	Numbers in the form of the form a+ib

Basic operations

ARITHMETICS

Basic operations

addition
subtraction
multiplication
division

Addition and subtraction on integers:

·        If sign of the numbers match, add the numbers together and keep the  same sign.

Example 1)   -5 + (-1) = -8

                 2)   3 + 4 = 7

·        If the sign does not match, subtract the number and keep the sign of largest number.

Example: 1) -9 + 6  = -3             

                              2)  6 + (-12) = 6

·        For subtraction of two numbers, add the opposite of the number after subtraction sign.

            Example 1)   7 – 10 = 7 + (-10)   = -3      

                            2)   5 - (-3) = 5 + 3 = 8           3)   -9 - (-2) = -7

Multiplication and division:

(+ve) x (+ve) = (+ve)	(+ve) / (+ve) = (+ve)
(-ve) x (-ve) = (+ve)	(-ve) /  (-ve) = (+ve)
(-ve) x (+ve) = (-ve)	(-ve) /  (+ve) = (-ve)
(+ve) x (-ve) = (-ve)	(+ve) / (-ve) = (-ve)

Puzzle:

Einstein's Gardens Puzzle

The Puzzle:

Five friends have their gardens next to one another, where they grow three kinds of crops: fruits (apple, pear, nut, cherry), vegetables (carrot, parsley, gourd, onion) and flowers (aster, rose, tulip, lily).

 1. They grow 12 different varieties.
2. Everybody grows exactly 4 different varieties
3. Each variety is at least in one garden.
4. Only one variety is in 4 gardens.
5. Only in one garden are all 3 kinds of crops.
6. Only in one garden are all 4 varieties of one kind of crops.
7. Pear is only in the two border gardens.
8. Paul's garden is in the middle with no lily.
9. Aster grower doesn't grow vegetables.
10. Rose growers don't grow parsley.
11. Nuts grower has also gourd and parsley.
12. In the first garden are apples and cherries.
13. Only in two gardens are cherries.
14. Sam has onions and cherries.
15. Luke grows exactly two kinds of fruit.
16. Tulip is only in two gardens.
17. Apple is in a single garden.
18. Only in one garden next to Zick's is parsley.
19. Sam's garden is not on the border.
20. Hank grows neither vegetables nor asters.
21. Paul has exactly three kinds of vegetable.
Who has which garden and what is grown where?

PHYSICS

             Everything in the universe basically consist of matter and energy. Physics is the study of that matter and energy. From that it's clear physics covers most of our activities and many of the things that go on around us. You may wonder how it is possible to study all this. The task is simple if you have an understanding of the laws of physics, which apply to most of the happenings around us.

The Queen of Science

              We live in an age of advances. Behind all this wonders there are something deep and mysteriously powerful. it been called the language of universe and perhaps it's civilizations greatest achievement. It's name mathematics. it do so well in science also.it is the key to universe cosmoses. Albert Einstein wondered how this mathematics does so well in explaining universe. So ultimately mathematics is a key to explore universe secret.

About

                                MATHEMATICA

       This blog is a product of clear vision about to emphasize something which you may learn in class rooms. It’s not to make anything new, but can help you to get some basic ideas in mathematics and physics. Also it’s an attempt to coordinate basic formulas and concepts.