Adding & Subtracting Decimals

The two most basic operations with decimals are addition and subtraction. It is normally easier to perform these operations using a vertical format. The vertical addition/subtraction format will allow us to line up the decimal points in each number and then find the sum or difference in each column. We previously learned how to add and subtract numbers vertically when we studied multi-digit addition and multi-digit subtraction with whole numbers.

Adding Decimals

• Write the numbers vertically and line up the decimal points
  • Extra zeros may be written to the right of the decimal point after the final non-zero digit if desired
• Draw a plus sign "+" to the left of the bottom number and a line underneath
• Bring the decimal point straight down into the answer
• Add starting in the rightmost column and work left
  • Use carrying when the result of the addition from a column is larger than 9

Let's take a look at a few examples:
Example 1: Find each sum.
51.37 + 24.5
Let's begin by setting up the vertical addition. We will line up the decimal points in our numbers: We can write a zero after the 5 in the number 24.5. This zero will not add any value to the number. It only serves as a visual aid to help with our vertical addition: We will bring our decimal point straight down into our answer: Add starting in the rightmost column and work left:

Column	Addition	Result
hundredths' place	7 + 0	7
tenths' place	3 + 5	8
ones' place	1 + 4	5
tens' place	5 + 2	7

51.37 + 24.5 = 75.87
Let's look at an example where we add more than two decimal numbers.
Example 2: Find each sum.
6.02 + 94.85 + 13.719
Let's begin by setting up the vertical addition. We will line up the decimal points in our numbers: We can write in zeros after the 5 in the number 94.85 and after the 2 in the number 6.02. These zeros will not add any value to the numbers. They only serve as visual aids to help with our vertical addition: We will bring our decimal point straight down into our answer: Add starting in the rightmost column and work left:

Column	Addition	Result
thousandths' place	9 + 0 + 0	9
hundredths' place	1 + 5 + 2	8
tenths' place	7 + 8 + 0	15 - carry the 1
ones' place	1(carried) + 3 + 4 + 6	14 - carry the 1
tens' place	1(carried) + 1 + 9	11

13.719 + 94.85 + 6.02 = 114.589

Subtracting Decimals

• Write the numbers vertically and line up the decimal points
  • Extra zeros may be written to the right of the decimal point after the final non-zero digit
    • We will need to add in zeros in some cases (top number (minuend) has fewer digits after the decimal point than the bottom number (subtrahend)) for borrowing
• Draw a minus sign "-" to the left of the bottom number and a line underneath
• Bring the decimal point straight down into the answer
• Subtract starting in the rightmost column and work left
  • Use borrowing when the bottom number of a column is larger than the top number

Let's take a look at a few examples:
Example 3: Find each difference.
12.15 - 3.9
Let's begin by setting up the vertical subtraction. We will line up the decimal points in our numbers: We can write a zero after the 9 in the number 3.9. This zero will not add any value and serves as a visual aid for our subtraction: We will bring our decimal point straight down into our answer: Subtract starting in the rightmost column and work left:

Column	Addition	Result
hundredths' place	5 - 0	5
tenths' place	11 - 9 (borrow from the 2)	2
ones' place	11 - 3 (borrow from the 1)	8

12.15 - 3.90 = 8.25
Example 4: Find each difference.
5.1 - 2.37
Let's begin by setting up the vertical subtraction. We will line up the decimal points in our numbers: Notice how our top number (minuend » 5.1) has fewer digits after the decimal point when compared to our bottom number (subtrahend » 2.37). We will write a zero after the 1 in the number 5.1. This will allow us to subtract in this column with the help of the borrowing procedure: We will bring our decimal point straight down into our answer: Subtract starting in the rightmost column and work left:

Column	Addition	Result
hundredths' place	10 - 7 (borrow from the 1)	3
tenths' place	10 - 3 (borrow from the 5)	7
ones' place	4 - 2	2

5.1 - 2.37 = 2.73

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