Addition of Decimal Fractions

This topic will discuss on addition of decimal fractions. For adding decimal numbers we will have to first convert the decimals to be added into like decimals. Then we will write the decimal numbers in proper column so that the decimal point of every number falls in one vertical line in same location.

Steps of Addition of Decimal Fractions:

Step I: Changing numbers to be added into like fractions.

Step II: Arranging the numbers in columns with decimal point in one vertical line.

Step III: Then perform the addition ignoring the decimal point.

Step IV: After completing the addition put the decimal point in proper place.

For Example:

1. Add 19.625, 9.63, and 2.65

Changing the decimal fractions into like fractions such that:

19.625, 9.630, 2.650

Now we have to arrange these numbers in column keeping the decimal point in one vertical line

            19.625

              9.630

          +  2.650

            31.905

In the thousandths column we get 5 + 0 + 0 = 5. Then in the hundredths column 2 + 3 + 5 = 10 but we will write 0 with 1 carrying in tenths column. In the tenths column 6 + 6 + 6 = 18 and add 1 carrying make it 19. So we write 9 in the tenths column and 1 carrying in units place. Now the addition in units place is 9 + 9 + 2 = 20 and 1 carrying from tenths place makes it 21. But we will write 1 in the units place and 2 carrying in the tens place. So the sum total of tens place is 3.

Here are few examples on addition of decimal fractions:

1. 5.01, 65.08, 96.369, 12.32

Changing the decimal fractions into like fractions such that:

5.010, 65.080, 96.369, 12.320

            5.010

          65.080

          96.369

       + 12.320

         178.779

In the thousandths column the sum total is 9 and there is no carryover. In the hundredths place the sum total is 1 + 8 + 6 + 2 = 17 where we write 7 in the hundredths place and 1 carryover in the tenths place. In the tenths place the sum total is 3 + 3 = 6 and 1 carryover making it 7. In the units place the sum total is 5 + 5 + 6 + 2 = 18 with no carryover. So we write 8 in the units place and 1 carryover in the tens place 6 + 9 + 1 = 16 and 1 carryover in the tens place.

2. 45.03, 65.032, 85.021, 25.02

Changing the decimal fractions into like fractions such that:

45.030, 65.032, 85.021, 25.020

            45.030

            65.032

            85.021

         + 25.020

          220.103

The sum total of thousandths place 2 + 1 = 3 with no carryover and the addition of hundredths place is 3 + 3 + 2 + 2 = 10. But we will only write 0 and 1 in the tenths place as carryover. The addition of the units place 5 + 5 + 5 + 5 = 20 and will write 0 in the units place with 2 as carryover, Lastly the addition of tens place is 4 + 6 + 8 + 2 = 20 and 2 as carryover making it 22.

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