Adding and Subtracting Decimals
Objective Learn how to add and subtract
decimals.
The only idea needed to add or subtract decimals, beyond the
standard algorithms for addition and subtraction of whole
numbers, is the alignment of the numbers so the decimal points
line up one above the other.
The Algorithm
Let's begin by introducing the following algorithm, since it
will allow you to solve problems right away.
Addition and Subtraction Algorithm for Decimals
1. Write both decimals, one above the other, with the decimal
point of one directly over the decimal point of the other.
2. Add or subtract the numbers as if they were whole numbers,
ignoring the decimal point.
3. Place the decimal point in the answer directly below the
decimal points in the numbers being added or subtracted.
Example 1
Add 2.12 and 3.59.
Solution
Write the two numbers one above the other, with the decimal
points aligned.
Add the digits, ignoring the decimal points at this step.
Insert a decimal point in the answer, directly below the other
decimal points.
So, the sum of 2.12 and 3.59 is 5.71. 1
Example 2
Subtract 1.01 from 3.17.
Solution
3.17 

Line up the decimal points. 
 1.01 

Subtract as with whole numbers. 
2.16 

Place the decimal point in the answer. 
In some addition and subtraction problems, there will be more
digits to the right of the decimal point in one number than in
the other number. Therefore, it is very important to align the
decimal points in problems where this is true. It may be helpful
to insert one or more zeros to the right of the last digit of the
number with fewer decimal places so that both numbers have the
same number of digits to the right of the decimal point. The
example below shows this procedure.
Example 3
Add 2.1 and 5.432.
Solution
Be sure to align the decimal points even though the numbers do
not have the same number of digits.
2.100 

Annex zeros; 2.1 = 2.100. 
+ 5.432 


Now use the algorithm to find the sum.
So, the sum of 2.1 and 5.432 is 7.532.
Estimation
Just as when adding and subtracting whole numbers, estimation
should be used to check the reasonableness of the answer to a
decimal sum or difference. For example, consider the sum of 2.9
and 4.3. Since 2.9 is almost 3 and 4.3 is about 4, their sum
should be approximately 3 + 4 or 7. Using the algorithm, 2.9 +
4.3 = 7.2. The estimate of 7 indicates that 7.2 is a reasonable
result for the sum.
