• To add decimals and whole numbers, we are going to work with the wholes and the parts of the numbers separately.
• Suppose, we want to add \(12.2\) and \(15\).
• Since both numbers have different place values, so first make the place values same by adding a zero. Thus, \(15\) is written as \(15.0\)
• Write one number just below the other such that the bottom decimal point is directly below and lined up with the top decimal point.

\(\begin{array} {c} \hline &\text{Tens}&\text{Ones}&\text{Decimal point}&\text{Tenths}\\ \hline &1&2&\cdot&2\\ +&1&5&\cdot&0\\ \hline &&&\cdot&\\ \hline \end{array}\)

• Now we add the columns vertically starting from the right most column and moving towards left.
• Add the digits of tenths column,

\(2+0=2\)

Write \(2\) in the tenths column.

\(\begin{array} {c} &1&2&\cdot&2\\ +&1&5&\cdot&0\\ \hline &&&\cdot&2\\ \hline \end{array}\)

• Now, add the digits of ones column.

\(2+5=7\)

Write \(7\) in the ones column.

\(\begin{array} {c} &1&2&\cdot&2\\ +&1&5&\cdot&\\ \hline &&7&\cdot&2\\ \hline \end{array}\)

• At last, add the digits of tens column.

\(1+1=2\)

Write \(2\) in the tens column.

\(\begin{array} {c} \hline &\text{Tens}&\text{Ones}&\text{Decimal point}&\text{Tenths}\\ \hline &1&2&\cdot&2\\ +&1&5&\cdot&\\ \hline &2&7&\cdot&2\\ \hline \end{array}\)

\(\therefore\) The sum of \(12.2\) and \(15\) is \(27.2\)

• To add decimals and whole numbers, we are going to work with the wholes and the parts of the numbers separately.
• Suppose, we want to add \(2.4\) and \(1.2\)

i.e., \(2.4+1.2\)

• Write one number just below the other, so that the bottom decimal point is directly below and lined up with the top decimal point.

\(\begin{array} {c} \hline &\text{Ones}&\text{Decimal point}&\text{Tenths}\\ \hline &2&\cdot&4\\ +&1&\cdot&2\\ \hline &&\cdot&\\ \hline \end{array}\)

• First, add the digits of tenths column.

\(4+2=6\)

Write \(6\) in the tenths column.

\(\begin{array} {c} &2&\cdot&4\\ +&1&\cdot&2\\ \hline &&\cdot&6\\ \hline \end{array}\)

• Now, add the digits of ones column.

\(2+1=3\)

Write \(3\) in the ones column.

\(\begin{array} {c} \hline &\text{Ones}&\text{Decimal point}&\text{Tenths}\\ \hline &2&\cdot&4\\ +&1&\cdot&2\\ \hline &3&\cdot&6\\ \hline \end{array}\)

\(\therefore\;3.6\) is the sum of \(2.4\) and \(1.2\)

• To add decimals and whole numbers, we are going to work with the wholes and the parts of the numbers separately.
• Suppose, we want to add \(4.96\) and \(1.38\)

i.e., \(4.96+1.38\)

• Write one number just below the other so that the bottom decimal point is directly below and lined up with the top decimal point.

\(\begin{array} {c} \hline &\text{Ones}&\text{Decimal point}&\text{Tenths}&\text{Hundredths}\\ \hline &4&\cdot&9&6\\ +&1&\cdot&3&8\\ \hline &&\cdot&\\ \hline \end{array}\)

• First, add the digits of hundredths column.

\(6+8=14\)

Now, \(4\) is to be written in the hundredths column and \(10\) is carried to the next column (tenths).

\(\begin{array} {c} &4&\cdot&^\underline{\color{red}1}9&6\\ +&1&\cdot&\;\;\;3&8\\ \hline &&\cdot&&4\\ \hline \end{array}\)

• Add the digits of tenths column.

\(1+9+3=13\)

\(3\) is to be written in the tenths column and \(10\) is carried to the next column (ones).

\(\begin{array} {c} &^\underline{\color{red}1}4&\cdot&9&6\\ +&\;\;\;1&\cdot&3&8\\ \hline &&\cdot&3&4\\ \hline \end{array}\)

• Add the digits of ones column.

\(1+4+1=6\)

\(6\) is to be written in the ones column.

\(\begin{array} {c} \hline &\text{Ones}&\text{Decimal point}&\text{Tenths}&\text{Hundredths}\\ \hline &4&\cdot&9&6\\ +&1&\cdot&3&8\\ \hline &6&\cdot&3&4\\ \hline \end{array}\)

\(\therefore\;6.34\) is the sum of \(4.96\) and \(1.38\)

• To add decimals and whole numbers, we are going to work with the wholes and the parts of the numbers separately.
• Suppose, we want to add \(31.343\) and \(42.456\)
• Write one number just below the other so that the bottom decimal point is directly below and lined up with the top decimal point.

\(\begin{array} {c} \hline &\text{Tens}&\text{Ones}&\text{Decimal point}&\text{Tenths}&\text{Hundredths}&\text{Thousandths}\\ \hline &3&1&\cdot&3&4&3\\ +&4&2&\cdot&4&5&6\\ \hline &&&\cdot&&&\\ \hline \end{array}\)

• First, add the digits of thousandths column.

\(3+6=9\)

\('9'\) is to be written in the thousandths column.

\(\begin{array} {c} &3&1&\cdot&3&4&3\\ +&4&2&\cdot&4&5&6\\ \hline &&&\cdot&&&9\\ \hline \end{array}\)

• Now, add the digits of hundredths column.

\(4+5=9\)

\('9'\) is to be written in the hundredths column.

\(\begin{array} {c} &3&1&\cdot&3&4&3\\ +&4&2&\cdot&4&5&6\\ \hline &&&\cdot&&9&9\\ \hline \end{array}\)

• Add the digits of tenths column.

\(3+4=7\)

\('7'\) is to be written in the tenths column.

\(\begin{array} {c} &3&1&\cdot&3&4&3\\ +&4&2&\cdot&4&5&6\\ \hline &&&\cdot&7&9&9\\ \hline \end{array}\)

• Now add the digits of ones column.

\(1+2=3\)

\(3\) is to be written in the ones column.

\(\begin{array} {c} &3&1&\cdot&3&4&3\\ +&4&2&\cdot&4&5&6\\ \hline &&3&\cdot&7&9&9\\ \hline \end{array}\)

• Add the digits of tens column.

\(3+4=7\)

\(7\) is to be written in the tens column.

\(\begin{array} {c} \hline &\text{Tens}&\text{Ones}&\text{Decimal point}&\text{Tenths}&\text{Hundredths}&\text{Thousandths}\\ \hline &3&1&\cdot&3&4&3\\ +&4&2&\cdot&4&5&6\\ \hline &7&3&\cdot&7&9&9\\ \hline \end{array}\)

\(\therefore\;73.799\) is the sum of \(31.343\) and \(42.456\)

• To add decimals and whole numbers, we are going to work with the wholes and the parts of the numbers separately.
• Suppose, we want to add \(8.6,\;4.310\) and \(10.6055\)

i.e. \(8.6+4.310+10.6055\)

• Write each number just below the other, so that the bottom decimal point is directly below and lined up with the middle and the top decimal points.
• Add zeros, so that all the numbers have the same place values.
• The given decimal numbers can be written as:

\(\begin{array} {c} \hline &\text{Tens}&\text{Ones}&\text{Decimal point}&\text{Tenths}&\text{Hundredths}&\text{Thousandths}&\text{Ten thousandths}\\ \hline &&8&\cdot&6&0&0&0\\ &&4&\cdot&3&1&0&0\\ +&1&0&\cdot&6&0&5&5\\ \hline &&&\cdot&&&&\\ \hline \end{array}\)

• First, we add the digits of ten-thousandths.

\(0+0+5=5\)

\(5\) is to be written in the ten-thousandths column.

\(\begin{array} {c} &&8&\cdot&6&0&0&0\\ &&4&\cdot&3&1&0&0\\ +&1&0&\cdot&6&0&5&5\\ \hline &&&\cdot&&&&5\\ \hline \end{array}\)

• Now, add the digits of thousandths column.

\(0+0+5=5\)

\(5\) is to be written in the thousandths column.

\(\begin{array} {c} &&8&\cdot&6&0&0&0\\ &&4&\cdot&3&1&0&0\\ +&1&0&\cdot&6&0&5&5\\ \hline &&&\cdot&&&5&5\\ \hline \end{array}\)

• Add the digits of hundredths column.

\(0+1+0=1\)

\(1\) is to be written in the hundredths column.

\(\begin{array} {c} &&8&\cdot&6&0&0&0\\ &&4&\cdot&3&1&0&0\\ +&1&0&\cdot&6&0&5&5\\ \hline &&&\cdot&&1&5&5\\ \hline \end{array}\)

• Now, add the digits of tenths column.

\(6+3+6=15\)

\(5\) is to be written in the tenths column and \(10\) is carried to the next column (ones).

\(\begin{array} {lrc} \text{Carried}\to&&^\underline{\color{red}1}8&\cdot&6&0&0&0\\ &&4&\cdot&3&1&0&0\\ +&1&0&\cdot&6&0&5&5\\ \hline &&&\cdot&5&1&5&5\\ \hline \end{array}\)

• Add the digits of ones column.

\(1+8+4+0=13\)

\(3\) is to be written in the ones column and \(10\) is carried to the next column (tens).

\(\begin{array} {lrc} &&8&\cdot&6&0&0&0\\ &\text{Carried}\to\underline{\color{red}1}&4&\cdot&3&1&0&0\\ +&1&0&\cdot&6&0&5&5\\ \hline &&3&\cdot&5&1&5&5\\ \hline \end{array}\)

• Now, add the digits of tens column.

\(1+1=2\)

\(2\) is to be written in the tens column.

\(\begin{array} {c} \hline &\text{Tens}&\text{Ones}&\text{Decimal point}&\text{Tenths}&\text{Hundredths}&\text{Thousandths}&\text{Ten thousandths}\\ \hline &&8&\cdot&6&0&0&0\\ &&4&\cdot&3&1&0&0\\ +&1&0&\cdot&6&0&5&5\\ \hline &2&3&\cdot&5&1&5&5\\ \hline \end{array}\)

\(\therefore\;23.5155\) is the sum of \(8.6,\;4.310\) and \(10.6055\).

• We can add decimals with the help of grid.
• For example: We want to add \(0.25\) and \(0.35\)

• In the first grid, \(25\) squares are shaded, so first grid represents \(0.25\)
• In the second grid, \(35\) squares are shaded, so second grid represents \(0.35\)
• By combining them we get-

Here, there are \(60\) shaded squares in total. So, now the grid represents \(0.60\)

Thus, \(0.25+0.35=0.60\)