Addition and Subtraction of Decimals

 

  1. Addition of Decimals

    Adding decimals is very similar to adding whole numbers except with a few extra technical details and bookkeeping.  Recall that decimals are just fractions.  We add fractions by adding the whole number parts and the fractional parts separately, carrying the 1 from the fractional part if necessary to the whole number part.  For decimals, we line up the decimal points so that the whole number parts line up and the decimal parts line up.  Then add each.

    To add decimal numbers follow the step below.

    Step 1:  Line up the numbers vertically so that the decimal points all lie on a vertical line.

    Step 2:  Add extra zeros to the right of the number so that each number has the same number of digits to the right of the decimal place.

    Step 3:  Add the numbers as you would whole numbers.  Place the decimal point of the result in line with the other decimal points.


    Example

    Add

            93.59 + 4.7


    Solution
    1. 93.59    Notice the decimal points in line.
              4.7

    2. 93.59        We added this 0 so both numbers have 2 digits to the right
              4.70         of the decimal point.

                1
    3.   93.59
      +  4.70
        98.29

    Example

    Add

            135 + 44.571 + 2.01


    Solution

    1. 135.    Notice the decimal points in line.
              44.571
                2.01

    2. 135.000        We added these 0s so all three numbers have 3 digits
              44.571         to the right of the decimal point.
                2.010


                1
    3.   135.000        
                44.571       
      +    2.010
        181.581

    Exercises

    Add  (Hold your mouse over the yellow rectangle for the solution)

    1. 28.53 + 34.921    63.451

    2. 34.7 + 8.901 + 192    235.192

  2. Subtraction of Decimals

    Subtraction of decimals is carried out in a similar way.  We line up the decimals vertically, tack on extra zeros to the right, and subtract downward.  More specifically, follow the steps below

    Step 1:  Line up the numbers vertically so that the decimal points all lie on a vertical line.

    Step 2:  Add extra zeros to the right of the number so that each number has the same number of digits to the right of the decimal place.

    Step 3:  Subtract the numbers as you would whole numbers.  Place the decimal point of the result in line with the other decimal points.


    Example

    Subtract

            34.91 - 14.214


    Solution

    1. 34.91    Notice the decimal points in line.
      14.214

    2.   34.910         We added this 0 so both numbers have 3 digits to the right
              14.214         of the decimal point.

          
    3.    34.8910110
      -  14. 2   1  4
         20. 6   9   6

    Example

    Subtract

            12.00942 - 12.0087


    Solution

    1. 12.00942    Notice the decimal points in line.
              12.0087


    2. 12.00942        We added these 0 so all three numbers have 5 digits
      12.00870         to the right of the decimal point.
        


        
    3.     12.0089142       
      +  12.00 8  70
           0 .00072              Notice the zeros to the right of the decimal point.

    Example

    Find the value of x if 

            x + 52.98  =  67.3


    Solution

    We want to determine what number must be added to 52.78 to get 67.3.  The is the reverse of an addition problem, that is a subtraction problem.

            667.12310
        -   5 2.   9  8
              14.32

    Exercises

    Add  (Hold your mouse over the yellow rectangle for the solution)

    1. 159.02 - 87.835    71.185

    2. 198.9 - 198.132    0.768

  3. Applications

    Example

    You have purchased a new bicycle for     $389.98 and a helmet for $23.64.  How much is your total bill?


    Solution

    Since you are seeking the     total, this is an addition problem.  We have 
                1 1 1  1
            389.Example

    A nurse needs to make sure that a patient receives 1.12 liters of fluid during a 24 hour period.  The IV bottle originally contained 2.1 liters of fluid.  How much fluid should be left in the IV bottle when the patient has been given the necessary amount of fluid for the day?

    Solution

    Since we are taking away 1.12 liters from a 2.1 liter bottle, this is a subtraction problem.  

            12.10110
        -    1.   1  2
              0.98


    The nurse should remove the IV when it has 0.98 liters of fluid left in it.

 

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