Grade 4 Decimals Worksheet: Adding Decimals in Columns

Problem Description:

The task involves solving a series of decimal addition problems presented in columns. Each problem requires adding two decimal numbers and writing the sum.

Solution Approach:

1. Align the Decimal Points: Ensure that the decimal points of both numbers are aligned vertically.
2. Add Zeros if Necessary: If one number has fewer digits after the decimal point, add zeros to make the lengths equal.
3. Perform Column Addition: Add the numbers column by column, starting from the rightmost digit (the smallest place value).
4. Carry Over: If the sum in any column exceeds 9, carry over the extra digit to the next column on the left.
5. Write the Final Sum: Place the decimal point in the answer directly below the decimal points in the numbers being added.

Step-by-Step Solutions:

#### Problem 1: \( 5.5 + 4.0 \)
\[
\begin{array}{r}
5.5 \\
+ 4.0 \\
\hline
9.5 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 5 + 0 = 5 \).
- Add the ones place: \( 5 + 4 = 9 \).
- The sum is \( 9.5 \).

#### Problem 2: \( 3.3 + 9.1 \)
\[
\begin{array}{r}
3.3 \\
+ 9.1 \\
\hline
12.4 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 3 + 1 = 4 \).
- Add the ones place: \( 3 + 9 = 12 \). Write down 2 and carry over 1.
- Add the tens place: \( 0 + 0 + 1 = 1 \).
- The sum is \( 12.4 \).

#### Problem 3: \( 9.7 + 2.3 \)
\[
\begin{array}{r}
9.7 \\
+ 2.3 \\
\hline
12.0 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 7 + 3 = 10 \). Write down 0 and carry over 1.
- Add the ones place: \( 9 + 2 + 1 = 12 \). Write down 2 and carry over 1.
- Add the tens place: \( 0 + 0 + 1 = 1 \).
- The sum is \( 12.0 \).

#### Problem 4: \( 1.0 + 4.9 \)
\[
\begin{array}{r}
1.0 \\
+ 4.9 \\
\hline
5.9 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 0 + 9 = 9 \).
- Add the ones place: \( 1 + 4 = 5 \).
- The sum is \( 5.9 \).

#### Problem 5: \( 6.7 + 7.3 \)
\[
\begin{array}{r}
6.7 \\
+ 7.3 \\
\hline
14.0 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 7 + 3 = 10 \). Write down 0 and carry over 1.
- Add the ones place: \( 6 + 7 + 1 = 14 \). Write down 4 and carry over 1.
- Add the tens place: \( 0 + 0 + 1 = 1 \).
- The sum is \( 14.0 \).

#### Problem 6: \( 0.91 + 0.41 \)
\[
\begin{array}{r}
0.91 \\
+ 0.41 \\
\hline
1.32 \\
\end{array}
\]
- Align the decimal points.
- Add the hundredths place: \( 1 + 1 = 2 \).
- Add the tenths place: \( 9 + 4 = 13 \). Write down 3 and carry over 1.
- Add the ones place: \( 0 + 0 + 1 = 1 \).
- The sum is \( 1.32 \).

#### Problem 7: \( 9.5 + 7.1 \)
\[
\begin{array}{r}
9.5 \\
+ 7.1 \\
\hline
16.6 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 5 + 1 = 6 \).
- Add the ones place: \( 9 + 7 = 16 \). Write down 6 and carry over 1.
- Add the tens place: \( 0 + 0 + 1 = 1 \).
- The sum is \( 16.6 \).

#### Problem 8: \( 4.8 + 0.1 \)
\[
\begin{array}{r}
4.8 \\
+ 0.1 \\
\hline
4.9 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 8 + 1 = 9 \).
- Add the ones place: \( 4 + 0 = 4 \).
- The sum is \( 4.9 \).

#### Problem 9: \( 0.71 + 0.02 \)
\[
\begin{array}{r}
0.71 \\
+ 0.02 \\
\hline
0.73 \\
\end{array}
\]
- Align the decimal points.
- Add the hundredths place: \( 1 + 2 = 3 \).
- Add the tenths place: \( 7 + 0 = 7 \).
- Add the ones place: \( 0 + 0 = 0 \).
- The sum is \( 0.73 \).

#### Problem 10: \( 9.1 + 2.0 \)
\[
\begin{array}{r}
9.1 \\
+ 2.0 \\
\hline
11.1 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 1 + 0 = 1 \).
- Add the ones place: \( 9 + 2 = 11 \). Write down 1 and carry over 1.
- Add the tens place: \( 0 + 0 + 1 = 1 \).
- The sum is \( 11.1 \).

#### Problem 11: \( 7.4 + 4.1 \)
\[
\begin{array}{r}
7.4 \\
+ 4.1 \\
\hline
11.5 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 4 + 1 = 5 \).
- Add the ones place: \( 7 + 4 = 11 \). Write down 1 and carry over 1.
- Add the tens place: \( 0 + 0 + 1 = 1 \).
- The sum is \( 11.5 \).

#### Problem 12: \( 0.23 + 0.08 \)
\[
\begin{array}{r}
0.23 \\
+ 0.08 \\
\hline
0.31 \\
\end{array}
\]
- Align the decimal points.
- Add the hundredths place: \( 3 + 8 = 11 \). Write down 1 and carry over 1.
- Add the tenths place: \( 2 + 0 + 1 = 3 \).
- Add the ones place: \( 0 + 0 = 0 \).
- The sum is \( 0.31 \).

#### Problem 13: \( 6.6 + 2.1 \)
\[
\begin{array}{r}
6.6 \\
+ 2.1 \\
\hline
8.7 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 6 + 1 = 7 \).
- Add the ones place: \( 6 + 2 = 8 \).
- The sum is \( 8.7 \).

#### Problem 14: \( 7.8 + 0.8 \)
\[
\begin{array}{r}
7.8 \\
+ 0.8 \\
\hline
8.6 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 8 + 8 = 16 \). Write down 6 and carry over 1.
- Add the ones place: \( 7 + 0 + 1 = 8 \).
- The sum is \( 8.6 \).

#### Problem 15: \( 3.9 + 6.0 \)
\[
\begin{array}{r}
3.9 \\
+ 6.0 \\
\hline
9.9 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 9 + 0 = 9 \).
- Add the ones place: \( 3 + 6 = 9 \).
- The sum is \( 9.9 \).

#### Problem 16: \( 8.5 + 1.5 \)
\[
\begin{array}{r}
8.5 \\
+ 1.5 \\
\hline
10.0 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 5 + 5 = 10 \). Write down 0 and carry over 1.
- Add the ones place: \( 8 + 1 + 1 = 10 \). Write down 0 and carry over 1.
- Add the tens place: \( 0 + 0 + 1 = 1 \).
- The sum is \( 10.0 \).

#### Problem 17: \( 7.9 + 0.9 \)
\[
\begin{array}{r}
7.9 \\
+ 0.9 \\
\hline
8.8 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 9 + 9 = 18 \). Write down 8 and carry over 1.
- Add the ones place: \( 7 + 0 + 1 = 8 \).
- The sum is \( 8.8 \).

#### Problem 18: \( 5.0 + 0.3 \)
\[
\begin{array}{r}
5.0 \\
+ 0.3 \\
\hline
5.3 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 0 + 3 = 3 \).
- Add the ones place: \( 5 + 0 = 5 \).
- The sum is \( 5.3 \).

#### Problem 19: \( 5.7 + 0.8 \)
\[
\begin{array}{r}
5.7 \\
+ 0.8 \\
\hline
6.5 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 7 + 8 = 15 \). Write down 5 and carry over 1.
- Add the ones place: \( 5 + 0 + 1 = 6 \).
- The sum is \( 6.5 \).

#### Problem 20: \( 2.9 + 6.4 \)
\[
\begin{array}{r}
2.9 \\
+ 6.4 \\
\hline
9.3 \\
\end{array}
\]
- Align the decimal points.
- Add the tenths place: \( 9 + 4 = 13 \). Write down 3 and carry over 1.
- Add the ones place: \( 2 + 6 + 1 = 9 \).
- The sum is \( 9.3 \).

Final Answer:

\[
\boxed{
\begin{array}{cccc}
9.5 & 12.4 & 12.0 & 5.9 \\
14.0 & 1.32 & 16.6 & 4.9 \\
0.73 & 11.1 & 11.5 & 0.31 \\
8.7 & 8.6 & 9.9 & 10.0 \\
8.8 & 5.3 & 6.5 & 9.3 \\
\end{array}
}
\]