Grade 5 Math Worksheets: Adding decimals in columns | Worsheets library - Free Printable

Problem: Adding decimals in columns

The task is to add the given decimal numbers in each column. Here's how we solve each problem step by step:

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#### Step 1: Align the decimal points
When adding decimals, it's crucial to align the decimal points vertically. This ensures that the digits in the same place value are added together.

#### Step 2: Add the numbers
Add the numbers column by column, starting from the rightmost digit (the smallest place value) and moving left. If the sum of any column exceeds 9, carry over the extra digit to the next column.

#### Step 3: Write the final answer
Write the result below the line, making sure the decimal point is in the correct position.

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Solutions:

#### Problem 1:
$$
\begin{array}{r}
6.048 \\
+ 8.554 \\
\hline
14.602 \\
\end{array}
$$
- Align the decimal points.
- Add the thousandths: \(8 + 4 = 12\) → Write 2, carry 1.
- Add the hundredths: \(4 + 5 + 1 = 10\) → Write 0, carry 1.
- Add the tenths: \(0 + 5 + 1 = 6\).
- Add the units: \(6 + 8 = 14\).

#### Problem 2:
$$
\begin{array}{r}
35.38 \\
+ 59.94 \\
\hline
95.32 \\
\end{array}
$$
- Align the decimal points.
- Add the hundredths: \(8 + 4 = 12\) → Write 2, carry 1.
- Add the tenths: \(3 + 9 + 1 = 13\) → Write 3, carry 1.
- Add the units: \(5 + 9 + 1 = 15\) → Write 5, carry 1.
- Add the tens: \(3 + 5 + 1 = 9\).

#### Problem 3:
$$
\begin{array}{r}
81.88 \\
+ 81.66 \\
\hline
163.54 \\
\end{array}
$$
- Align the decimal points.
- Add the hundredths: \(8 + 6 = 14\) → Write 4, carry 1.
- Add the tenths: \(8 + 6 + 1 = 15\) → Write 5, carry 1.
- Add the units: \(1 + 1 + 1 = 3\).
- Add the tens: \(8 + 8 = 16\).

#### Problem 4:
$$
\begin{array}{r}
31.01 \\
+ 48.60 \\
\hline
79.61 \\
\end{array}
$$
- Align the decimal points.
- Add the hundredths: \(1 + 0 = 1\).
- Add the tenths: \(0 + 6 = 6\).
- Add the units: \(1 + 8 = 9\).
- Add the tens: \(3 + 4 = 7\).

#### Problem 5:
$$
\begin{array}{r}
32.91 \\
+ 34.08 \\
\hline
66.99 \\
\end{array}
$$
- Align the decimal points.
- Add the hundredths: \(1 + 8 = 9\).
- Add the tenths: \(9 + 0 = 9\).
- Add the units: \(2 + 4 = 6\).
- Add the tens: \(3 + 3 = 6\).

#### Problem 6:
$$
\begin{array}{r}
14.40 \\
+ 82.25 \\
\hline
96.65 \\
\end{array}
$$
- Align the decimal points.
- Add the hundredths: \(0 + 5 = 5\).
- Add the tenths: \(4 + 2 = 6\).
- Add the units: \(4 + 2 = 6\).
- Add the tens: \(1 + 8 = 9\).

#### Problem 7:
$$
\begin{array}{r}
66.00 \\
+ 11.86 \\
\hline
77.86 \\
\end{array}
$$
- Align the decimal points.
- Add the hundredths: \(0 + 6 = 6\).
- Add the tenths: \(0 + 8 = 8\).
- Add the units: \(6 + 1 = 7\).
- Add the tens: \(6 + 1 = 7\).

#### Problem 8:
$$
\begin{array}{r}
1.040 \\
+ 2.465 \\
\hline
3.505 \\
\end{array}
$$
- Align the decimal points.
- Add the thousandths: \(0 + 5 = 5\).
- Add the hundredths: \(4 + 6 = 10\) → Write 0, carry 1.
- Add the tenths: \(0 + 4 + 1 = 5\).
- Add the units: \(1 + 2 = 3\).

#### Problem 9:
$$
\begin{array}{r}
61.29 \\
+ 71.24 \\
\hline
132.53 \\
\end{array}
$$
- Align the decimal points.
- Add the hundredths: \(9 + 4 = 13\) → Write 3, carry 1.
- Add the tenths: \(2 + 2 + 1 = 5\).
- Add the units: \(1 + 1 = 2\).
- Add the tens: \(6 + 7 = 13\).

#### Problem 10:
$$
\begin{array}{r}
4.461 \\
+ 2.311 \\
\hline
6.772 \\
\end{array}
$$
- Align the decimal points.
- Add the thousandths: \(1 + 1 = 2\).
- Add the hundredths: \(6 + 1 = 7\).
- Add the tenths: \(4 + 3 = 7\).
- Add the units: \(4 + 2 = 6\).

#### Problem 11:
$$
\begin{array}{r}
93.88 \\
+ 77.49 \\
\hline
171.37 \\
\end{array}
$$
- Align the decimal points.
- Add the hundredths: \(8 + 9 = 17\) → Write 7, carry 1.
- Add the tenths: \(8 + 4 + 1 = 13\) → Write 3, carry 1.
- Add the units: \(3 + 7 + 1 = 11\) → Write 1, carry 1.
- Add the tens: \(9 + 7 + 1 = 17\).

#### Problem 12:
$$
\begin{array}{r}
8.763 \\
+ 2.832 \\
\hline
11.595 \\
\end{array}
$$
- Align the decimal points.
- Add the thousandths: \(3 + 2 = 5\).
- Add the hundredths: \(6 + 3 = 9\).
- Add the tenths: \(7 + 8 = 15\) → Write 5, carry 1.
- Add the units: \(8 + 2 + 1 = 11\).

#### Problem 13:
$$
\begin{array}{r}
2.902 \\
+ 4.633 \\
\hline
7.535 \\
\end{array}
$$
- Align the decimal points.
- Add the thousandths: \(2 + 3 = 5\).
- Add the hundredths: \(0 + 3 = 3\).
- Add the tenths: \(9 + 6 = 15\) → Write 5, carry 1.
- Add the units: \(2 + 4 + 1 = 7\).

#### Problem 14:
$$
\begin{array}{r}
2.400 \\
+ 8.391 \\
\hline
10.791 \\
\end{array}
$$
- Align the decimal points.
- Add the thousandths: \(0 + 1 = 1\).
- Add the hundredths: \(0 + 9 = 9\).
- Add the tenths: \(4 + 3 = 7\).
- Add the units: \(2 + 8 = 10\).

#### Problem 15:
$$
\begin{array}{r}
7.518 \\
+ 6.213 \\
\hline
13.731 \\
\end{array}
$$
- Align the decimal points.
- Add the thousandths: \(8 + 3 = 11\) → Write 1, carry 1.
- Add the hundredths: \(1 + 1 + 1 = 3\).
- Add the tenths: \(5 + 2 = 7\).
- Add the units: \(7 + 6 = 13\).

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Final Answers:

$$
\boxed{
\begin{array}{c}
14.602, \, 95.32, \, 163.54, \, 79.61, \, 66.99, \, 96.65, \, 77.86, \, 3.505, \, 132.53, \, 6.772, \, 171.37, \, 11.595, \, 7.535, \, 10.791, \, 13.731
\end{array}
}
$$