Addition and Subtraction of Decimals
 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
 93.59
Notice the decimal points in line.
4.7
 93.59
We added this 0 so both numbers have 2
digits to the right
4.70
of the decimal point.
_{1}
 93.59
+ 4.70
98.29
Example
Add
135
+ 44.571 + 2.01
Solution
 135.
Notice the decimal points in line.
44.571
2.01
 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}
 135.000
44.571
+ 2.010
181.581
Exercises
Add (Hold your mouse over the yellow rectangle for the
solution)
 28.53 + 34.921
 34.7 + 8.901 + 192
 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
 34.91
Notice the decimal points in line.
14.214
 34.910
We added this 0 so both numbers have
3 digits to the right
14.214
of the decimal point.
 34.^{8}
9^{10}1^{1}0
 14. 2 1 4
20. 6 9 6
Example
Subtract
12.00942  12.0087
Solution
 12.00942
Notice the decimal points in line.
12.0087
 12.00942
We added these 0 so all three numbers have
5 digits
12.00870
to the right of the decimal point.
 12.00^{8}
9^{1}42
+ 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.
6^{6}7.^{12}3^{1}0
 5 2. 9 8
14.32
Exercises
Add (Hold your mouse over the yellow rectangle for the
solution)
 159.02  87.835
 198.9  198.132
 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.
^{1}2.^{10}1^{1}0
 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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