How to multiply decimals

Introduction to Multiplying decimals:

         A number that contains the decimal point is called as decimal. The decimal numbers are always has ten as its base value. In Hindu-Arabic numeric system, decimal notation refers the positional notation of the number. It can also used to refer the non-positional system in Roman and Chinese numerals. Decimals are always can be represented as another form of fractions.

Place Value:

       To know the decimals, we need to understand the place value. The value of a digit can be determined by its position in a number is called as place value. Each place in a decimal number has a different place value.

For Example, 25.64

Here 2-tens

         5-ones

         6-tenths

         4-Hundredths      

Multiplying Decimals:

Rules for multiplying Decimals:

• Multiply the numbers normally, ignoring the decimal points.

•  After multiplying normally, put the decimal point in the answer – The answer will have as many decimal places as the two given numbers combined.

 Consider the following Example,

              13.7* 12.5

Step1: Multiply normally by ignoring the decimal points

              137*

              125

             685

           274

         137 

        17125

How to find the Mean and Median of a data set

INTRODUCTION:

           A group of variables or a set of information is referred as Data. In general, sets are the collections of numbers and set can contains any kind of data. Data set is nothing but a collection of data. Data set can be represented as tables and graphs. Data collection is the method of collecting or preparing the data. For a given data set, we can find the mean, median, mode and range which is explained below.

Mean of data set:
         For finding the mean of all the values in a given data set, we have to find the sum of all numbers given in data set and we have to divide the total sum by the total number of elements.
Example:
Find the mean of data set: {8, 18, 23, 35, 51}
Solution:
         Mean      =    Total sum of data set  / Total number of elements in data set
                         =    (8 + 18 + 23 +  35 + 51) / 5
                         = 135 / 5   = 27
Median of a data set:
        In general, median is referred as the middle value of the given data set.
Example 1 :
Find the median for the given values: {5, 6, 9, 25, 34}
Solution:
      Here, the middle value is 9. Hence median = 9. 

How to translate word problems into algebraic expression

Introduction:

             Translating words into algebraic expression is the process of translating the word problems into an algebraic expression which can be used to solve the word problem and produce the solution for the given words problem. It is the simple way to solve words problem. Let us discuss about translating the words into algebraic expression.

Example problems to translating words into algebraic expression:

Problem 1:
Flowers shop has thirty Roses and forty Lilly. How many pieces of flowers does flowers shop have? 
Solution:
            Let a = Total number of Flowers in the flowers shop.
            The sum of thirty Roses and forty Lilly is equal to the total number of flowers in the flowers shop. It translates the words problem into an algebraic expression.
            a = 30 + 40
Solve this expression.
            Let a = Total number Pieces of Flowers in the flowers shop
                  a = 70.
There are 70 Pieces of Flowers in the flowers shop.

Hope you like the above examplation. Please leave your comments, if you have any doubts.

Example on how to solve polynomial

Introduction:

          In math, variables and constants with the operations of addition, subtraction, multiplication, and non-negative, whole-number exponents of finite length is known as a polynomial or in-determinates. For example, x² − 4x + 7 is a polynomial, but x² − 4/x + 7x^3/2 is not, because its second term involves division by the variable x and because its third term contains an exponent that is not a whole number.

Example:

X²+4X-5=0,

                   X²-X+5X-5=0,

                   X(X-1) +5(X-1) =0,

                   (X-1)(X+5) =0.                         Therefore the roots are X =1, -5...

                       (OR)

USING THE FOMULAE:

                   X = ` (-B + sqrt (B^2 - 4AC))/(2A)`

                   X²+4X-5=0 -------------------> (2)

                    AX²+BX+C=0----------------> (3)

Comparing (2) and (3),

A = 1, B =4, C =-5 Substitute these values in one.

        x = `(-4 +- sqrt (4^2 - 4(1)(-5)))/(2(1))`

          x = `(-4 +- sqrt (16 +20))/(2)`

          x = `(-4 +- sqrt (36))/(2)`

         x = `(-4 +- 6)/(2)`

        x = `(-10)/(2)``(2)/(2)`

       x = -5, 1

Hope you like the above example. Please leave your comments, if you have any doubts.

Numeric sequence and Types

Introduction:

The numeric sequence is called linear sequence. The numeric sequence are communicable to the constant rates of change and form the straight lines which is graphed.

        The numeric sequence are  15, 17, 19, 21, 23, 25… is a linear sequence that are represented in the table. The numeric sequence is used to draw graph, they provide straight line.

Example:

15, 17,19,21,23 this example numeric sequence the constant value  is 2.

Numeric Sequence Explanation and Types:

The numeric sequences contain any one number series. Some of then numeric sequences are given below.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ….etc the constant numeric sequences value is one

15, 17, 19, 21, 23, 25, 27, 29…..etc. the constant numeric sequences value is one

The above are simple explanation of the numeric sequence.

Different types of numeric sequences are :

• Arithmetic sequence
• Geometric sequence  
• Fibonacci Sequence

How to solve rational equation

Introduction:

Solving rational equations is one of the important topics that we need to know. What we do to one side of the equation, must do to the other. If we have fractions, we try to eliminate them by multiplying by the common denominator. Suppose, If there are quadratics involved, we must get all terms to one side with zero on the another.

Steps involved in solving a rational equation

Solving rational equation is an important to see at an equation that not having a variable in the denominator to make confident that we see the pattern for calculating rational equations. The following steps we will use in the solution process.

1. First we need to determine the least common denominator of the fractions in the given rational equation.

2. We need to take out the fractions by multiplying All terms by the least common denominator.

3. Then we have to simplify the terms in rational equation.

4. Solve the resulting equation.

5. Check the answers to make confident the solution does not make the fraction undefined.

Let’s look at first, how we would handle the equations like x/3 + 2x/2 = 4

Our first step in solving this equation is to multiply each term by its least common denominator of the fractions, which is 6

(6) x/3 + (6) 3x/2 = (6) 4

Simplifying the above equation results in the linear equation which we can solve to get our final answer.

2x + 6x = 24

8x = 24

x = 3

Hope you like the above explanation. Please leave your comments, if you have any doubts.

Solve absolute value inequalities

Introduction:

        Other than algebra, there is one more important inequality. It is called as Absolute value inequality. The absolute value for any number is numerical value regardless of its sign.  For example, the absolute value of | -5 | is 5 and │+5 │ is 5. Here the vertical lines denotes absolute value.

It is a little more difficult when dealing with equations. There are three possible outcomes for absolute value inequalities. 

1. If x is any expression and a any positive number, and │x │= a, then it has either x = a or x = - a values.
2. If x is any expression and a any positive number, and │x │<>
3. If x is any expression and a any positive number, and │x │> a then it looks   x < -a and x > a.

Example

Solve: │4x – 4 │ = 8

Solution:

Use the result, if |x| = a, then x = a or x = -a

Here │4x – 4 │ = 8

So, it has either 4x – 4 = 8 or  4x – 4 = -8 values.

Solve each equation using the addition and multiplication principles.

4x = 12,    4x = -4

after solving the equation, we get

x = 3,     x = -1. Answer

Hope you like the above explanation to solve the absolute value inequalities, Please leave your comments, if you have any doubts.