Addition of Decimal Fractions

In addition of decimal fractions we will discuss here how to add two or more decimals.

Addition of decimal numbers are similar to addition of whole numbers. We convert them to like decimals and place the numbers vertically one below the other in such a way that the decimal point lies exactly on the vertical line. Add as usual as we learnt in the case of whole numbers.

The rules of adding decimal numbers are:

(i) Write the digits of the given numbers one below the other such that all the decimal points are in the same vertical line.

(ii) Add as we add whole numbers.

(iii) Put the decimal point of the sum vertically below the other decimal points.

Let us consider some of the following examples on addition of decimal numbers.

1. Add 14.02, 198.3, 394.051.

First convert all the decimals to be added into like decimals i.e. 14.02 into 14.020, 198.3 into 198.300 and 394.051 will remain same.

14.020 + 198.300 + 394.051

Now write the decimals in column in such a way that the decimal points of all the decimals are in the same column and then add the decimal ignoring the decimal point.

$Convert Unlike Decimals into Like Decimals$

Atlast, put the decimal point in the sum directly under the decimal points of all the decimals.

Answers: 606.371

2. Add $ 205.40, $ 80.75 and $ 1493.50.

Here, all the decimal numbers are in like decimals.

$ 205.40 + $ 80.75 + $ 1493.50

Now write the decimals in column in such a way that the decimal points of all the decimals are in the same column and then add the decimal ignoring the decimal point.

$Addition of Decimal Fractions$

Answers: 1779.65

3. Add 143.21; 89.025;1001.002; 975.35

Here, all the decimal numbers are in like decimals.

143.210 + 89.025 + 1001.002 + 975.350

Now write the decimals in column and add as we add whole numbers.

$Adding with Decimal Fractions$

Answers: 2208.587

$Addition of Decimal Fractions$

4. Add: 7.035; 8005.007; 91.71; 15.9142

First convert all the decimals to be added into like decimals i.e. 7.035 into 7.0350, 8005.007 into 8005.0070, 91.71 into 91.7100 and 15.9142 will remain as it is.

7.0350 + 8005.0070 + 91.7100 + 15.9142

Now write the decimals in column and add as we add whole numbers.

$Adding Decimals$

Answers: 8119.6662

5. Add: 81.71; 198.001; 2071.1945; 9.09

Convert all the decimals to be added into like decimals i.e. 81.71 into 81.7100, 198.001 into 198.0010, 2071.1945 will remain as it is and 9.09 into 9.0900.

81.7100 + 198.0010 + 2071.1945 + 9.0900

$Addition of Decimal Fractions$

Answers: 2359.9955

6. Add: 43.91; 108.431; 832.01

Convert all the decimals to be added into like decimals i.e. 81.71 into 81.7100, 198.001 into 198.0010, 2071.1945 will remain as it is and 9.09 into 9.0900.

43.910 + 108.431 + 832.010

$Add Decimals$

Answers: 984.351

7. Add: 91.4; 31.83; 101

Convert all the decimals to be added into like decimals.

91.40 + 31.83 + 101.00

$Decimal Addition$

Answers: 224.23

8. Add: 79.03; 13; 55.05

Convert all the decimals to be added into like decimals.

79.03 + 13.00 + 55.05

$Addition of Decimal Number System$

Answers: 147.08

$Decimal Addition$

9. Add 19.405; 20.21 and 8.1

Solution:

Converting the given decimals into like decimals, we get 19.405; 20.210 and 8.100

Hence, 19.405 + 20.210 + 8.100 = 47.715

$Addition Decimals$

10. Add $15.25; $60.98 and $10.5

Solution:

Converting the given decimals into like decimals, we get $15.25; $60.98 and $10.50

Hence, 15.25 + 60.98 + 10.50 = $86.73

11. Complete the given magic square. The sum of all rows and column is 9.0.

$Decimal Magic Squares$

Solution:

$Decimal Magic Squares$

Sum of the first row = 4.8 + 0.6 + 3.6 = 9

Sum of the second row = 1.8 + 3.0 + 4.2 = 9

Sum of the third row = 2.4 + 5.4 + 1.2 = 9

Again,

Sum of the first column = 4.8 + 1.8 + 2.4 = 9

Sum of the second column = 0.6 + 3.0 + 5.4 = 9

Sum of the second column = 3.6 + 4.2 + 1.2 = 9

Working Rules for Addition of Decimals:

For addition of decimals, we have to follow these steps:

Step I: Change the given decimal into like decimals.

Step II: Write the numbers in columns, so that decimal points should come in one column.

Step III: Now, add the decimals just as we add the whole numbers.

Step IV: Put the decimal in the sum directly under the decimal points of all the decimals.

Solved Examples on Addition of Decimals:

1. Add 7.086, 12 and 17.24.

Solution:

Converting into like decimals.

7.086 → 7.086

12 → 12.000

17.24 → 17.240

7.086

+ 12.000

+ 17.240

36.326

Therefore, 7.086 + 12 + 17.24 = 36.326

2. Add 3.85 and 2.5

Solution:

Converting into like decimals.

3.85 → 3.85

2.5 → 2.50

+ 3 . 0 0

+ 2 . 5 0

6 . 3 5

Therefore, 3.85 + 2.5 = 6.35

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