Dealing with Decimals

Introduction:
                  Decimal: A dot in between a decimal number, as like present in 85.937, to point out the position where values alter from positive to negative orders or powers of 10. Dealing with decimals, related with the operations which are said to be as addition, subtraction, multiplication and division.

Important while Dealing with Decimals:

Addition and Subtraction - when dealing with decimal, we require keeping in mind the rules for adding or subtracting you need to be careful while placing the decimal point in the same column as it is placed above.

Comparison - In case of dealing with decimal numbers first we have to think the whole number section. If the number has further number of digits in the left part of the decimal then it is without a doubt that is the larger number. On the other hand the case of equal whole number, we have to evaluate the integer towards the right of the decimal.

Multiplication - In case of dealing decimals with multiplications, we should not include the decimal points in the account at the beginning. Simply continue with the multiplication like any other multiplication. All we have to do is to total up the decimal places which are present from the right and place the decimal point in appropriate places. The count starts from the right hand side to the left.

Division - If the decimal dealing with division then the dividend allows a decimal and the divisor does not, then our requirement to do is put the decimal place in the quotient accurately on top of the decimal point in the dividend.

Example Problems for Dealing with Decimals:

Dealing decimal with addition:

Add the decimals 4.5 and 4.4

     4.5
 +  4.4     8.9

Add the decimals 5.61 and 4.2

     5.61
+  4.20
    9.81 

Dealing decimal with subtraction:

Subtract the decimals 3.5 and 2.2 

3.5

-2.2

--------

1.3 

Subtract the decimals 5.81 and 5.7

  5.81

-5.70  

  .11

Dealing decimal with Multiplication:

1)    4.36

    x 0.8

    ------

      3488 answer before adding the decimal point.

     3.488 answers - it have 3 (three) decimal positions because from the given original number, the result is obtained.

 2)    0.25

   x 0.125

   -------

      3125 is the answer without decimal point.

    .03125 answers - it have 5 (five) decimal positions because from the given original number, the result is obtained.

Dealing decimal with division: 

A. 10/100 = ten divided by hundred.

              .10

            -----

    100) 10.0

            10 0

             ----

    So 10/100 = .10  

B. what about 3/9 or 3 divided by 9?

             .5

           -----

        6) 3.0

            3 0

            ----

    So 3/6 = .5 (five tenths)

Mix Word Problems Math

Introduction :

Two different quantities having different percentage of needed substances can be mixed together to get the desired amount. This is called mix word problem in math. For example: Let X and Y be two different solutions. Each are having different percentage of Salt in it. Those two X and Y can be mixed together to get the required percentage of the final solutions.

Now let us see few problems of this kind.

Example Problems on Mix Word Problems Math:

Ex 1:  Two salt solutions having 12% and 36% of salts respectively in them. They are added together to form 40% of salt solution. If 280 liters of 12% salt solution is added, how many liters of 36% has to be added?

Soln: Let x be the salt solution.

Given: `36/100`   x   +   `12/100` `xx` 280 = `40/100`    (X + 80)

`=>` 36x + 3360 = 40x +3200

`=>` 40x – 36x = 3360 – 3200

`=>` 4x = 160   `=>` x = 40 liters.

Ex 2: Two oils have to be mixed together. One of the oil has 15% of the required content and the other has 30% of the required content. How many liters of 30% of oil have to be added to 290 liters of 15% of the oil, so that we can have a mix of 42% of the oil content?

Soln: Let X be the amount of oil with 30% content in it.

Given: `30/100` (x) + `15/100` (290)   =   `42/100` (x + 90)

`=>` 30x + 15`xx` 290 = 42x  + 42`xx` 90

`=>` 12x = 4350 – 3780

`=>` x = `570/12` = 47.50 liters

More Example Problem on Mix Word Problems Math:

Ex 3: Two herbals have to be mixed together. One of them has 25% of the required vitamins and the other has 35% of the required vitamins. How many liters of 25% of herbal have to be added to 120 liters of 45% of herbal, so that we can have a mix of 40% of vitamins?

Soln: Let x be the amount of herbal with 25% vitamin in it.

Given: `25/100` (x) + `45/100` (120) = 40/100 (x+120)

`=>` 25x + 5400 = 40x + 4800

`=>` 15x = 5400 – 4800 = 600 `=>`x = `600/15`

x = 40liters