hundredths are added to hundredths, tenths are added to tenths, ones are added to
ones, and so on. We write the decimal point in the sumso that it lines up with the
decimal points in the addends.For example, to find we proceed
as follows:
Ones column
Tenths column
Hundredths column
Vertical formSum of the hundredths digits: Think 1 3 5 9
Sum of the tenths digits: Think 2 2 4 8
Sum of the ones digits: Think 4 1 2 7The sum is 7.89.
In this example, each addend had two decimal places, tenths and hundredths. If
the number of decimal places in the addends are different, we can insert additional
zeros so that the number of decimal places match.
Write the decimal point in the sum directly
under the decimal points in the addends.The numbers that are being added, 4.21,
1 .23, and 2.45 are called addends.4. 2 1
1. 2 3
2. 4 5
7. 8 9
4.211.232.45,
4.2 Adding and Subtracting Decimals 331Adding DecimalsTo add decimal numbers:- Write the numbers in vertical form with the decimal points lined up.
- Add the numbers as you would add whole numbers, from right to left.
- Write the decimal point in the result from Step 2 directly below the
decimal points in the addends.
EXAMPLE (^1) Add:
StrategyWe will write the addition in vertical form so that the corresponding
place values and decimal points of the addends are lined up. Then we will add the
digits, column by column, working from right to left.
WHYWe can only add digits with the same place value.
SolutionTo make the column additions easier, we will write two zeros after the 6
in the addend 5.6 and one zero after the 8 in the addend 16.78. Since whole numbers
have an “understood” decimal point immediately to the right of their ones digit, we
can write the addend 68 as 68.000 to help line up the columns.
Line up the decimal points.
Now we add, right to left, as we would whole numbers, writing the sum from each
column below the horizontal bar.
Insert two zeros after the 6.
Insert a decimal point and three zeros: 68 68. 000.
Insert a zero after the 8.
31. 913
5. 6 00
68. 000
16. 78 0
31.9135.6 68 16.78
Self Check 1
Add:
Now TryProblem 1941.07 35 67.8884.1
Like whole number addition, if the sum of the digits in any place-value column is
greater than 9, we must carry.