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You are HERE >> Mathematics  > Grade 5

Adding and Subtracting Decimals
By Lisa Williams
January 24, 2002


Adding or Subtracting Decimals:

Rule #1- ALWAYS line up the decimal point in the problem.

.1 + .23 =    .1
                +.23
                --------
                  .33

Rule #2: You can add zeros to the beginning or end of the number and it doesn't change the value of the decimal. It just changes the decimal name. See lesson on comparing decimals. But never between the decimal point and the digits.
Example: 
   Add a zero to the beginning
       .01 ( one hundredth) = 0.01 ( one hundredth) 

 1        1
----  = -----
100    100

The value stays the same. It just looks different.

Add zeros to the end of a number

 change 0.01 ( one hundredth) =  0.01000  (1000 hundred-thousandths)

The name of the decimal changes but not the value. You can see this clearly by looking at the equivalent fractions for these decimals.

    1 ...........
---------   =  ------------ 
  100 ........

Never add zeros between the decimal point and the digit.
     0.01   0.001 
     one hundredth does not equal one thousandth.

You need to add zeros sometimes in order to add or subtract.

Sample problems:
   .23          .230                 4.1           4.100
   .1            .100            -     .657    -   0.657
+ .456    +  .456           ---------------  --------------
----------    -----------                               3.443
                 .786

Problems:

1.)   6.5            2.)  17.59              3.) 205.8               4.) 9,257.43            5.) 7.23
     15.87                 8.358                   17.9                         86.895               8.49
   +  3.96             +  7.6                   +168.435               +  168.9             +  13.58
-----------------        -----------------            -----------------            --------------------      ---------------
 
 
 

6.) 525.6           7.) 16.29       8.) 5.327          9.) 19.19          10.)  2,350.67
 -   115.684          --  7.84         -- 1.485          --  18.1896          --     199.678
------------------       --------------      --------------       ------------------        ----------------------
 
 
 

Answers:
First add extra zeros where necessary. Then add or subtract remembering to keep the decimal point lined up even in your answer. You should be able to draw a straight line through decimal point in all the numbers in the problem and the answer.

1.)   6.50          2.)  17.590              3.) 205.800             4.) 9,257.430            5.) 7.23
     15.87                  8.358                    17.900                      86.895                 8.49
   +  3.96             +   7.600               + 168.435                 + 168.900           +  13.58
-----------------        -----------------            -----------------            --------------------        ---------------
     26.33                 33.548                  392.135                 9,513.225               29.30
 

6.) 525.600        7.) 16.29       8.) 5.327          9.)19.1900       10.)  2,350.670
 --  115.684          --  7.84         -- 1.485          --  18.1896          --     199.678
------------------       --------------      --------------       ------------------        ----------------------
     409.916              8.45            3.842                1.0004              2,150.992
 

 


 
Submitted by: Copyright© Lisa Williams I'm a homeschooling mom of 3 elementary school age children. I run a clowning business from my home (Jingles the clown), am pianist for a local church, teach a Sunday School class, teach piano, tutor basic math see Math tutoring and algebra online and I enjoy making people smile. Send a note to Lisa
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