Binary Numbers

Previously we have discussed about how to solve limits and In today's session we are going to discuss about Binary numbers that comes under board of ssc education andhra pradesh, It deals with only two numbers 0 and 1.it is also known as base-2 number system. It has a radix of 2. In todays gadgets and computers, the circuits are implemented using binary coding that uses Binary Numbers.The main reason is that it is easy to manipulate the equations with 0 and 1.
We can define Binary Numbers as the ones that contain only two digits: 0's and 1's.
00000011001011011101010111 is a binary number. We can define Binary numbers as a sequence of 0's and 1's. The binary number can be converted into decimal numbers and hexadecimal numbers using the conversion formulas. Any number can be represented in the form of 0 and 1 and can be converted back into its original form .
Counting in binary number starts by taking rightmost digits and moving toward left. Conversion of binary number can be converted to decimal number by multiplying each digit by the corresponding power of 2.
for example,

0 0 1 1 can be converted to decimal number as,

[ 0 0 1 1 ]₂ =[ ( 2⁰ * 1 ) + ( 2 ¹ * 1 ) + ( 2² * 0 ) + ( 2³ * 0 ) ]₁₀
= [ 1 + 2 + 0 + 0 ]₁₀
=[3]₁₀

Similary, we can convert any binary number to a decimal number.
Following is the table which shows binary numbers and their corresponding decimal numbers.

Binary number decimal number

0 0
1 1
1 0 2
1 1 3
1 0 0 4
1 0 1 5
1 1 0 6
1 1 1 7
1 0 0 0 8
1 0 0 1 9

Now. Let us do addition in of binary numbers.
There are following rules,
1 + 1 =1 0
1 + 0 = 1
0 + 1 = 1
0 + 0 = 0

let us add two binary numbers,

1 0 1 0 + 1 1 0 0

1 0 1 0
+1 1 0 0
---------------------------------------------
1 0 1 1 0

we can implement a binary adder using this rule.
In the next session we are going to discuss Properties of Irrational Number and Read more maths topics of different grades such as Binomial Theorem
in the upcoming sessions here and You can visit our website for getting information about Normal Distribution Examples.

Properties of Numbers

Hello students, Previously we have discussed about fourier transform of sine and Today we are going to discuss properties of numbers which is an important part of ap secondary education board. The numbers systems are a part of mathematics. Number systems have some basic properties like: commutative, distributive, and associative.
Associative property: associative word means to associate or to group; this property is a rule that refers to grouping. For addition, the rule is x + (y + z) = (x + y) + z. This property can be understood with the help of example: 4+ (5+7) = (4+5) + 7.
For multiplication, the operation x(yz)=(xy)z. We will understand this operation with the help of example 3(4*5)=(3*4)5.
Commutative property: commutative word means to move around or to commute; the commutative property is one of the parts that stated that you can rearrange digits in an expression. For addition, the commutative property rule is x + y = y + x; this means 6 + 4 = 4 + 6.
For multiplication, the commutative property rule is xy = yx this means 4*5 = 5*4. For example, we use the commutative property to restate 4 * 6 * a: 6*4*a, 6*a*4, a*6*4, 4*a*6, and 4*6*a
Why is it true that 4(6a) = (6a)(4)?
This is true by commutative property. (We can see that 4(6a) = (6a)(4) = 24a)
Distributive property: this property is easy to remember, this property can be stated as: x(y + z) = xy + xz. This means 3(4 + 5) = 3*4 + 3*5.
Why is it truethat3(a + b) = 3a + 3b?
This is true by the distributive property. Distributive Property operations can be performed in the real numbers.(Know more about Properties of Numbers in broad manner, here,)
The example of the number system properties: 4x - 5y + 6z (this is original statement).
4x - 5y + 6x: this is commutative property, (4x+6x)-5y: this is the associative property, x(4+6)-5y: this is distributive property.
In the next topic we are going to discuss about Binary Numbers
and Read more maths topics of different grades such as Binomial Experiments in the upcoming sessions here and and You can visit our website for getting information about Negative Correlation Coefficient.

Properties of Complex Numbers

Previously we have discussed about system of equations worksheet and Today we are going to discuss about the Complex numbers and their properties which comes under andhra pradesh education board. First of all we should know about the complex numbers. A complex number is a number which has a form of x + iy, here x and y are the real numbers and i is known as the imaginary part or unit of the complex number. The value of i is root of -1 or i>2= -1. In the form of the complex number the term x is the real part and iy is the imaginary part of the number. The complex number is known as purely imaginary number if its real part or x is equals to 0.(Know more about Complex Numbers in broad manner, here,)
Now here I will tell you about some of the Properties of Complex Numbers:
1.    Powers of   i = root of -1, i>2 = -1, i>3 = -1, i>4 = 1
2.     Equality of two complex numbers: Two complex numbers are said to be equal if their real and imaginary parts are equal say two complex numbers are

 x + iy = a + ib if x = a and y = b.

3.    Addition property: When we add two complex numbers then we have to add the real parts to one another and imaginary parts to one another of the numbers. Like if we have two complex numbers say a + ib and x + iy then their addition will be (a + x) + (b + y)i.
The subtraction is just opposite of the addition property of the complex numbers.
4.    Multiplication: To multiply two complex numbers simply use the FOIL method.

(a + bi)*(x + yi)= (ax - by) + (ay + bx)i.

5.     Complex Conjugation: The complex number x + yi can be conjugate and it will give value x –yi. One thing is to remember is that the product of a complex number and its conjugate is always a real value. That is (x + iy) (x - iy)= x2+ y2.
So these are the Complex Number Properties. In the next topic we are going to discuss Properties of Numbers and if anyone want to know about Solving Binomial Expansion then they can refer to Internet and text books for understanding it more precisely and if you need help with math you can visit our website.

How to do Estimate Quotients

Previously we have discussed about rational expressions calculator with steps and In today's session we are going to discuss about How to do Estimate Quotients which comes under school secondary board of andhra pradesh.
WHAT IS QUOTIENT??(Quotient Rule Derivatives)
Quotient is a result obtained by dividing one amount by another.
What is division?

The inverse process of multiplication is division. The number times a number can be broken into parts according to another number.
DIVISOR, DIVIDEND AND QUOTIENT:
    The number that is divided is called the dividend.
    The number that divides the dividend is called divisor.
    The number of times the dividend is divisible by the divisor is called the quotient.
    If the dividend is completely not divisible by the divisor it leaves behind a remainder.
10/2=5
Here,
10 is the dividend
2 is the divisor
5 is the quotient
Let us see how to find the dividend if we know the quotient, divisor and remainder
Dividend = Quotient x Divisor + Remainder
In the above example
Remainder=0
Quotient is 5
Divisor is 2
Dividend=2*5+0=10
Example:
5/4
Here divisor: 4
Remainder: 1
Quotient: 1
Dividend=4*1+1=5

Estimating is the process of finding the value of unknown quantity by proper steps.
How to do Estimate Quotients: Estimating of quotient means finding the value with which  a number can be divided with another number.(Know more about Quotients in broad manner, here,)

Compatible numbers:
What are compatible numbers:
Compatible numbers are numbers which we  can be divided  easily.
e.g.:
22 divided 2
2*1=2
again 2*1=2
=11
the quotient is 11
45/9
=5
The quotient is 5.
These are compatible numbers.
Now let us see how to estimate quotients for non compatible numbers:

315/5

Let us take 31..
Now 31 divided 5, we get 6
we get a remainder of 1
15 divided by 5 is 3
therefore the quotient is 63
Solve estimate quotients:
294/7
What number times 7 has a product close to 29?
? *7 = 28
4 * 7 = 28
So,
29 divided by 7 is about 4
Now ?*7=14
Answer here is 2
Therefore the quotient is 42

In The Next Session We Are Going To Discuss Properties of Complex Numbers
and if anyone want to know about Binomial Expansion then they can refer to Internet and text books for understanding it more precisely.

Math Blog on Estimating Quotients

Previously we have discussed about measures of central tendency worksheets and In today's session we are going to discuss about Estimating quotients of numbers which is  a part of board of secondary education ap, Its defined by some rules that help the students in understanding how to estimate quotients .The rules for defining the estimate the quotient are as follows with their examples:
Rule no 1 # Decimal number is rounded to the nearest whole number means if the decimal number is approximately equal or near to the its nearest whole number then it will change into that whole number .
Example : 5 . 9 / 3 = ?
6 / 3 = 2 so 5 . 9 / 3 is near about to 2.
Rule no 2 # Decimal number(learn how to divide decimals) may be renamed means if the decimal number is not exactly calculated in terms of easier calculation then it will be change into its close decimal number that makes the calculations easy.(Know more about Quotients in broad manner, here,)
Example : 2 .8 / 3 = ?
2 .7 is easily divided by the 3 that is equal to the .9 so rename the 2 .8 into the 2 .7 to make the calculation more easy and fast so in place of 2 .8 / 3 we can write 2 .7 / 3 = 0 .9 .
Rule no 3 # Division problems can be rewrite as Multiplication problems .
Example : 7 .7 / 6 = ?
6 * _ = 6 .0
6 * 1 .0 = 6 .0
6 * 1 .1 = 6 .6
6 * 1. 5 = 9 .0
Here 7 .7 / 6 is lies in between 1 .1 and 1. 5 that is near about 1 .3 .
Rule no 4 # When divide the number by 10 , 1000 , 1000 or 10000 and so on move the digits of the number to the right side by one , two or three places .
Example : 554 / 10 = 55 .4
554 / 100 = 5 .54
554 / 1,000 = 0 .554
554 / 10,000 = 0 .0554
In the next topic we are going to discuss How to do Estimate Quotients
and Read more maths topics of different grades such as Math Blogs on Solving Trinomial Multiplication in the upcoming sessions here.
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Types of Numbers

Number is the basic and very important object of mathematics. Today we are going to discuss about the numbers and their various types. Whenever we apply any mathematical operation then we need to take one or more numbers as an input and that produces an output which is also a number. We can apply many operations on numbers such as multiplication, division, subtraction, addition etc. Numeral is the notation which represents the numbers. (To get help on cbse boards click here)

Now I am going to tell you about the various types of the numbers.
NUMBER TYPES:
1.       Natural Number: These numbers are represented by “N”. Also known as counting numbers. These numbers start from one like: 1, 2, 3, 4, …..
2.       Integers: These numbers are represented as “Z”. These are of two types:

 a) Positive integers

                                                                         b) Negative integers
These are ………-4, -3, -2, -1, 0, 1, 2, 3, 4……………
3.       Rational Numbers: A rational number is represented by a fraction which is consisting of an integer numerator and denominator which is not equal to zero. These numbers are represented by Q. x/y where x is an integer and y is not equal to 0.
4.       Real Numbers: These numbers are all measuring numbers and written with decimal numerals. To represent them we use “R” notation. Example: 2.5342, 5.32 etc.
5.       Complex Numbers: A complex number consists of a number of the form x+iy where x, y are real numbers and i represents the imaginary part of the number and square root of -1. Represented as “C”.

Each number system is a proper subset of the other number set such as: C is the subset of R, R is subset of Q, Q is subset of Z and Z is subset of N (which in turn is Superset of Z).

Here I explained about the Numbers and types of numbers, in next session we will discuss about the various properties of the numbers and In the next session we will discuss about Math Blog on Estimating Quotients. 

How to perform Estimating and Rounding Numbers

Estimating and rounding is the basic need of math. These two things are used frequently in most of the math problems. Rounding and estimating comes in various physical quantities such as money, length of time, etc. Rounding off of any number is kind of or similar to estimation.
Here we will first learn rounding of the whole numbers.  In this, first we find the place value we want that is the rounding digit and then search the immediate digit to its right. If the immediate right digit is less than 5 then without changing the rounding digit just change the remaining right digit of it to zero. If that digit is greater than or equal to 5, then we will add 1 to the rounding digit and change all the right digits to zero.
Here are some examples to show estimating and rounding
1.       367 is the given number here then for estimating and rounding it we first look at the rounding digit that is 6. Now we will take the right digit of this rounding digit 6 that is 7. Here 7 is greater than 5 so we will add 1 to the rounding digit as 6 +1 = 7 and then we move to the right digit and make it 0. So we will get 370 that is the round up value. (To get help on icse text books click here)
Similarly
2.       Round off of 342 will be: 340 because here the rounding digit is 4 and the right digit is 2 that is less than 5 so we will place a zero at its place without changing the rounding digit.
So here I tell you about a very interesting part of math. Using this we can correctly answer the question by estimation. We should get it into habit so that we may be able to frequently solve estimation and round off based problems.
In next time we will discuss about Estimating Quotients and In the next session we will discuss about Types of Numbers. 

Number System Problems

Some of the real number examples are natural, positive and negative integers, fractions, decimal numbers, cube roots and square roots of any number. To solve the Number System Problems, we will first diagnose the type of problem and check which arithmetical calculation is to be done and this is a part of CBSE Board Syllabus.
We have some clues which help to analyze the type of problem.
If a word Add, Combine, sum, Join, together, all together, in all or total exist in the math problem then we add the numbers.
eg. :  Find the sum of 2.43, 23.09, and 3.9.
      What is the result if you Add 23.6 and 12.8 ?
      If you Join the line segment of 3.5 cm and 4.67, what is the total length?
      I have Rs34.65 and my sister has Rs 45.80, how much money do we have in all?
Similarly to diagnose the problem of difference we must look into following keywords
Left, subtract, difference, More, much and other such words.(want to Learn about Number ,click here),
 eg. : I had 24.500 kg sugar from which 12.470 kg sugar is used, how much sugar is left with me?
         Find the difference between 124.6 and 34.67.
        Subtract    34.67 from 56.34 and give the answer.
      I have Rs34.65 and my sister has Rs 45.80, how much money more does my sister have?
 Now we look into the keywords of multiplication:
      Product, multiply, To find the value of more than one when value of one is given. In all such cases we multiply.
Eg. Find the product of 34.6 and 32.90.
     What is the result , if you multiply 12.9 with 4.98?
     If the cost of 1 pen is Rs 45.00, find the cost of 23 pens.
Now we discuss the cases where division is done.
   To check the problem for division we must see divide, distribute, equally , and the problems where we need to find the unit value.
 Eg: Distribute 35 apples equally among 5 children.
       Divide 500 books on 25 shelves equally.
      If 5050 gms of grapes are to be distributed equally among 10 persons how much will each child get?

So students this is all about number system problem. In the next article we will discuss about How to perform Estimating and Rounding Numbers
and if anyone want to know about Simplifying Rational Expressions

then they can refer to Internet and text books for understanding it more precisely. 
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