Sunday, October 28, 2012

Convert Fractions to Decimals


How to convert fractions to decimals with calculator ?

In this article, let us learn what is fraction and what is decimal and how to convert fractions to decimals using calculator.

Fractions: Let us divide a circle into four parts and take a part away and ask yourself a question,"How many parts are taken away from the whole ?" It is one part from 4. we could represent this as 1/4. So, fraction is a number composed of two parts say top part which is called as numerator and the bottom part is called as denominator.So, numerator gives the required part whereas denominator part gives the number of parts in the whole.

Example: `(15)/(17)`

Decimals: Decimals are numbers which has a dot which we say it as decimal point.

Example: 0.234, 67.45

Convert Fractions to Decimal( Relation)


We could observe that 0.5 is in 1/10th position. It means that 0.5 = 5/10

We could observe 9 in 0.59 is in 1/100th position. It means that 0.59 = 59/100

We could observe 1 in 0.591  is in 1/1000th position. It means that 0.591= 591/1000

If any fraction has the denominator has 10, 100, 1000or any multiples of 10  then the fraction is called as decimal fraction.

Convert Fractions to Decimal( Examples)

Consider a fraction `(1)/(4)`

Let us see how to convert the above fraction to decimal using calculator.

Choose a number such that the number when multiplied with denominator becomes a number which is a multiple of 10.So, i am choosing the number 25 since 25 x 4 = 100

Multiply the number 25 with the numerator and denomiantor.

So, 1 x 25 = 25 and 4 x 25 = 100

1/4 = 25/100

Since 100 has two zeros keep decimal point after counting 2 numbers from the right.

So, 25/100 = 0.25

In some case, we could not make the denominator as multiples of 10. For eample, 2/3. We could not find a number such that when denominator multiplied by the number gives denominator as multiples of 10.But 3 x 333 = 999

Since 999 is nearest to 1000, multiply the numerator and denomiantor with 333. So,

2/3 = 2 x333 / 3 x 333 = 666/999 = 0.666 (approximately)

Otherwise, to convert fractions to decimals with calculator, enter the numerator in the calculator and press the division sign and then the denominator. The resulting number in the calculator is the decimal.

Tuesday, October 23, 2012

Solve Rational Equation Problems


In algebra solving rational equation is very simple,we have few rules to solve any type of equations. Whatever we do on  one side  of the equation, we must do to the other side also. If you have fractions, we can try to eliminate them by multiplying by the common denominator. If there are quadratics involved in our equations, we must get all the  terms to one side with zero on the other.The basic rational expression is in the form of fraction.where there is at least one variable in the denominator.

Solved Example Based on Rational Equation :

Ex 1:Solve `3/x+6=2/(4x)`

Sol:

Step 1: The given equation is

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

subtracting both sides by `2/(4x)`

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

Step 2: Rearrange the equation.

`3/x-2/(4x)+6=0`

subtracting both sides by 6.

`3/x-2/(4x)+6-6=0-6`

`3/x-2/(4x)=-6`

Step 3: Find the l.c.d(least common denominator) x and 4x

L.C.D=4x

`(12-2)/(4x)=-6`

`10/(4x)=-6`

Step 4:Multiply both sides by 4x.

`10/(4x)xx4x=-6xx4x`

10=-24x

Step 5:Divide both sides by -24

`10/(-24)=(-24x)/(-24)`

`x=-5/12`

The solution is  [x=-5/12]

Example Based on Rational Equation:

Ex 2: Solve `x/(x-2)+1/(x-4)=2/(x^2-6x+8)`

Sol:

Step 1:first factor the `x^2-6x+8`

factors=(x-4)(x-2)

Step 2:convert common denominator to all

`(x/(x-2))((x-4)/(x-4))+(1/(x-4))((x-2)/(x-2))=2/((x-2)(x-4))`

`(x^2-4x)/((x-2)(x-4))+(x-2)/((x-2)(x-4))=2/((x-2)(x-4))`

`(x^(2)-4x)+(x-2)=2`

`x^(2)-4x+x-2=2`

`x^(2)-3x-4=0`

`(x-4)(x+1)=0`

`x=4 or x=-1`

If we submit the x=4 in the denominator,it is division by zero,so x=4 is not considerable.

x=-1   is the answer

Friday, October 19, 2012

Positive Integers Tutoring



Tutoring means a tutor taking an interactive session to individual student or a group of student in a class through online. The learning integer is defined the equal to the whole number. The negative numbers are including in the learning integer tutor. The integers do not used the fraction number. Each positive integer contains same negative integers. Let us discuss about the positive integers tutoring.

Positive Integer Tutoring

The general structure of integer is {…, -4, -3, -2, -1, 0, 1, 2, 3, 4…}. The integer is commonly representing the three types of numbers.

The first type is positive counting number. The second type is negative counting number. The zero value is third type.

The positive integer is equal to the whole number. The general structure of the positive integer is {1, 2, 3, 4, 5…}. The positive integer is also called as the positive number counting. This number is specifying positive value only. The + is the sign of the positive integers.

The value +86 and 86 is representing the same value. The positive integers do not necessary for the sign representation. The value 55 is automatically representing the positive integer.

The non negative integer is equal representation of the positive integer. The main difference of the positive integer and non negative integer is the positive integer starts with 1 but the non negative integer starts with 0. Many operations are performing the positive integer tutoring.

Example Problem of Positive Integer Tutoring

Problem 1:

Calculate the following positive integer.

2415 + 1564 =?

Solution

2415
1564(+)
--------
3979
---------

Problem 2:

Calculate the following positive integer.

4698 - 2456 =?

Solution

4698
2456 (-)
--------
2242
---------

Practice problem of positive integer tutoring

1. Add the positive integers 568 + 637.

2. Subtract the integers 634 – 542.

Answer

1. 1205

2. 92

Wednesday, October 3, 2012

Theory of Proportions

Introduction to theory of proportions:
       The theory of proportion is one of the basic topic in mathematic. In our usual life, there are a lot of occasions as we compare two quantities by means of their measurements. As soon as we compare two quantities of the same type by division, we contain a ratio of those two quantities.
Definition of Ratio: Ratio means similarity of two like quantities by division.

Definition of Theory Proportions:

      Proportions is a correspondence of two ratios.
      Consider the proportions
                a: b = c: d
      The first and fourth terms (a and d) are knoen as the extreme terms or extremes.
      The second and third terms (b and c) are known as the middle terms or means.
Important property:
      Product of extremes = Product of means.

Examples of Theory Proportions:

Let us see some examples of theory of proportions.
Example 1:
      Verify 5: 6 = 10: 12 is a proportion or not.
Solution:
      Product of extremes = 5*12 = 60
      Product of means = 6*10 = 60.
             `:.`   60 = 60
       These two products are equal.
            `:.` 5:6 = 8: 6 is a proportion.
Example 2:
       Verify 6: 7 = 12: 15 is a proportion or not.
Solution:
       Product of extremes = 6*15 = 90
       Product of means = 7*12 = 84
                          `:.`    90 = 84
       These two products are not equal.
         So, 6: 7 =12: 15 is not a proportion.
Example 3:
       If 2: 3= 6:_ is a proportion, find the missing term.
Solution:
       Let us assume the missing value is x
       Product of extremes = 2*x
       Product of means = 3*6 =18
       Since it is a proportion, 2*x =18
                                          2x = 18
       Divide both sides by 2 on both sides we get,
                                        2x/2 = 18/2
                                             x = 18/2 = 9
       `:. ` The missing term is 9
       So the proportion is 2:3 =6: 9

Example 4:
       The income and Savings of a family are into the ratio 8: 3 If the income of the family is Rs. 3,300.Find how much is being saved.
Solution:
       Let us savings be Rs. x.
          `:.` The proportion is 8: 3 = 3300: x
                     (Income: saving) = (Income: saving)
                                       11x = 9900
                                   11x/11= 9900/11
                                           x= 900
      Therefore, the savings = Rs. 900.

Tuesday, October 2, 2012

Step by Step Adding Fractions

Introduction to step by step adding fractions:
                  A fraction is a number that can represent part of a whole. The earliest fractions were reciprocals of integers: ancient symbols representing one part of two, one part of three, one part of four, and so on. A much later development were the common or "vulgar" fractions which are still used today (½, ⅝, ¾, etc.) and which consist of a numerator and a denominator.

                                                                                                                                                 

Step by Step Adding Fractions:

1. Add the two fractions `20/3` and `22/4`
         Solution:
                                   The  two fractions are  `20/3` and `22/4`
                 Step1:             Add two fraction
                                              =`20/3` +`22/4`
                 Step2:          There the denominator are different  so we need to take lcm  to preform addition
                                                           =`(80+66)/12`
                  Step3:           By adding 80 and 66 the answer is 146
                                                         =`146/12`
                   Step4:                This can be simplified has
                                                           =12.1
 2. Add the two fractions `40/4` and `50/5`
            Solution:
                                  The  two fractions are `40/4` and `50/5`
                   Step1:                 Add two fraction
                                                     =`40/4` +`50/5`
                   Step2:     There the denominator is sameso we need to take lcm  to preform addition
                                                            =`(200+200)/20`
                   Step3:       By adding 200 and 200 the answer is 400
                                                                =`400/20`
                   Step4:           This can be simplified has
                                                       = 1
 3. Add the two fractions `60/5` and `70/6`
          Solution:
                                  The  two fractions are `60/5` and` 70/6`
                    Step1:          Add two fraction
                                                  =`60/5` +`70/6`
                    Step2:   There the denominator is same so we need to take lcm  to preform addition
                                                        =`(360+350)/30`
                    Step3:     By adding 360 and350 the answer is 710
                                                              =`710/30`
                    Step4:        This can be simplified has
                                                              = 23.66

Step by Step Adding Fractions:

4. Add the fractions `5/6` and `25/30`
      Solution:
                                        The two fractions are `5/6` and `25/30`
                 Step1:         The given Two fractions are equivalent fractions
                                         By simplifying `25/30` we get 5/6
                  Step2:
                                          Now we need to find the sum of `5/6` and `5/6`
                                                                   = `5/6` +`5/6`
                   Step3 :            There the denominator are same so add the numerators in the fractions together
                                                                   =`(5+5)/6`
                                              The sum of 5 and 5 is 10
                                               So `(5+5)/6` can be written as `10/6`
                  Step4:
                                             This can be reduced further as `5/3`
5. Add the two fractions `80/6` and `90/6`
        Solution:
                                     The  two fractions are `80/6` and `90/6`
                  Step1:             Add two fraction
                                                =`80/6` +`90/6`
                   Step2:       There the denominator is same so add the numerators in the fractions together
                                                            =`(80+90)/6`
                      Step3:        By adding 80 and 90 the answer is 170
                                                          =`170/6`
                      Step4:          This can be simplified has
                                                        = 28.33


 6. Add the two fractions `1000/3` and `120/4`
         Solution:
                                  The  two fractions are `100/3` and `120/4`
                Step1:           Add two fraction
                                         =`100/3` +`120/4`
                Step2:     There the denominator is same so we need to take lcm  to preform addition
                                           =`(400+3690)/12`
                Step3:      By adding 400 and 360 the answer is 760
                                                  =`760/12`
                Step4:        This can be simplified has
                                                  = 63.33

Monday, October 1, 2012

Multiply Mixed Numbers

  Here in this page we are going to discuss about multiplying mixed numbers.Mixed numbers can be written in form of improper fraction. The mixed numbers have summation of whole number and proper fraction. Proper fraction is nothing but the numerator of the fraction is less that that the denominator of the fraction. By multiplying the mixed numbers, we must follow certain procedure as follow.

How to Multiply Mixed Numbers
Let's see the procedure-
Step 1: Convert the given mixed numbers to improper fraction.
To make the mixed numbers to improper fraction, we multiply the whole number and denominator of the fraction and add the result to the numerator of the fraction.
Example: 2 ¼
Multiply 2 and 4 we get 8
Add the number 8 to the numerator of the fraction 1, we get 8 + 1 = 9.
Now get the improper fraction of the mixed number 2 ¼ = `(9)/(4)`
Step 2: Multiply the numerator and denominator of the improper fraction separately.
Example: consider the two improper fractions.
`(a)/(b)` * `(c)/(d)` , where, a > b and c > d
`(a * c)/(b * d)`  = `(p)/(q)`
Step 3: Now convert the improper fraction by mixed number as following procedure.
Example: `(8)/(5)`
5) 8 ( 1
       5

_________
        3
___________
Mixed number can be written as, quotient as the whole number, remainder is the numerator of the proper fraction and divisor is the denominator of the proper fraction.
`(8)/(5)`  = 1`(3)/(5)`

Examples:

Here are the examples on Multiplying Mixed Numbers
Example 1:
Multiplying the mixed numbers 3 ½ and 6 ¼.
Solution:
Step 1: Convert the mixed numbers 3 ½ to improper fraction, we get
3 ½ = `(7)/(2)`
Step 2: Convert the mixed numbers 6 ½ to improper fraction, we get
6 ¼ =  `(25)/(4)`
Step 3: Multiplying the improper fractions  `(7)/(2)` and `(25)/(4)`, we get
`(7)/(2)` * `(25)/(4)`  `(175)/(8)`
Step 4: Convert the improper fraction  `(175)/(8)` to mixed number.
8) 175 (21
    16
___________
       1 5
          8
___________
           7
Mixed number  `(175)/(8)`  `21(7)/(8)`
Answer:  `21(7)/(8)`
Example 2:
Multiplying the mixed numbers 4 ½ and 2 ¾.
Solution:
Step 1: Convert the mixed numbers 4 ½ to improper fraction, we get
4 ½ = `(9)/(2)`
Step 2: Convert the mixed numbers 2 ¾ to improper fraction, we get
2 ¾ = `(11)/(4)`
Step 3: Multiplying the improper fractions `(9)/(2)` and `(11)/(4)`, we get
`(9)/(2)` * `(11)/(4)` = `(99)/(8)`
Step 4: Convert the improper fraction `(99)/(8)` to mixed number.
8) 99 (12
    8
___________
     1 9
     1 6
___________
         3
Mixed number `(99)/(8)`   `12(3)/(8)`
Answer:   `12(3)/(8)`