Dividing Decimals using Long Division (examples, solutions, videos ... - Free Printable

To solve the problems of dividing decimals by decimals, we need to follow a systematic approach. Here's how we can solve each problem step by step:

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1. \( 2.7 \div 79.65 \)

#### Step 1: Adjust the divisor to a whole number
- Move the decimal point in the divisor (2.7) one place to the right to make it a whole number (27).
- Move the decimal point in the dividend (79.65) one place to the right as well: \( 796.5 \).

#### Step 2: Perform the division
- Now, divide \( 796.5 \div 27 \).

\[
\begin{array}{r|l}
27 & 796.5 \\
\hline
& 29.5 \\
\end{array}
\]

- Explanation:
- \( 27 \times 29 = 783 \)
- Subtract: \( 796.5 - 783 = 13.5 \)
- Bring down the next digit (0): \( 135 \)
- \( 27 \times 5 = 135 \)
- Subtract: \( 135 - 135 = 0 \)

Thus, \( 2.7 \div 79.65 = 29.5 \).

---

2. \( 1.6 \div 51.52 \)

#### Step 1: Adjust the divisor to a whole number
- Move the decimal point in the divisor (1.6) one place to the right to make it a whole number (16).
- Move the decimal point in the dividend (51.52) one place to the right as well: \( 515.2 \).

#### Step 2: Perform the division
- Now, divide \( 515.2 \div 16 \).

\[
\begin{array}{r|l}
16 & 515.2 \\
\hline
& 32.2 \\
\end{array}
\]

- Explanation:
- \( 16 \times 32 = 512 \)
- Subtract: \( 515.2 - 512 = 3.2 \)
- Bring down the next digit (0): \( 32 \)
- \( 16 \times 2 = 32 \)
- Subtract: \( 32 - 32 = 0 \)

Thus, \( 1.6 \div 51.52 = 32.2 \).

---

3. \( 0.4 \div 13.96 \)

#### Step 1: Adjust the divisor to a whole number
- Move the decimal point in the divisor (0.4) one place to the right to make it a whole number (4).
- Move the decimal point in the dividend (13.96) one place to the right as well: \( 139.6 \).

#### Step 2: Perform the division
- Now, divide \( 139.6 \div 4 \).

\[
\begin{array}{r|l}
4 & 139.6 \\
\hline
& 34.9 \\
\end{array}
\]

- Explanation:
- \( 4 \times 34 = 136 \)
- Subtract: \( 139.6 - 136 = 3.6 \)
- Bring down the next digit (0): \( 36 \)
- \( 4 \times 9 = 36 \)
- Subtract: \( 36 - 36 = 0 \)

Thus, \( 0.4 \div 13.96 = 34.9 \).

---

4. \( 2.4 \div 45.6 \)

#### Step 1: Adjust the divisor to a whole number
- Move the decimal point in the divisor (2.4) one place to the right to make it a whole number (24).
- Move the decimal point in the dividend (45.6) one place to the right as well: \( 456 \).

#### Step 2: Perform the division
- Now, divide \( 456 \div 24 \).

\[
\begin{array}{r|l}
24 & 456 \\
\hline
& 19 \\
\end{array}
\]

- Explanation:
- \( 24 \times 19 = 456 \)
- Subtract: \( 456 - 456 = 0 \)

Thus, \( 2.4 \div 45.6 = 19 \).

---

5. \( 3.5 \div 84 \)

#### Step 1: Adjust the divisor to a whole number
- Move the decimal point in the divisor (3.5) one place to the right to make it a whole number (35).
- Move the decimal point in the dividend (84) one place to the right as well: \( 840 \).

#### Step 2: Perform the division
- Now, divide \( 840 \div 35 \).

\[
\begin{array}{r|l}
35 & 840 \\
\hline
& 24 \\
\end{array}
\]

- Explanation:
- \( 35 \times 24 = 840 \)
- Subtract: \( 840 - 840 = 0 \)

Thus, \( 3.5 \div 84 = 24 \).

---

6. \( 2.6 \div 96.2 \)

#### Step 1: Adjust the divisor to a whole number
- Move the decimal point in the divisor (2.6) one place to the right to make it a whole number (26).
- Move the decimal point in the dividend (96.2) one place to the right as well: \( 962 \).

#### Step 2: Perform the division
- Now, divide \( 962 \div 26 \).

\[
\begin{array}{r|l}
26 & 962 \\
\hline
& 37 \\
\end{array}
\]

- Explanation:
- \( 26 \times 37 = 962 \)
- Subtract: \( 962 - 962 = 0 \)

Thus, \( 2.6 \div 96.2 = 37 \).

---

7. \( 0.1 \div 79.23 \)

#### Step 1: Adjust the divisor to a whole number
- Move the decimal point in the divisor (0.1) one place to the right to make it a whole number (1).
- Move the decimal point in the dividend (79.23) one place to the right as well: \( 792.3 \).

#### Step 2: Perform the division
- Now, divide \( 792.3 \div 1 \).

\[
\begin{array}{r|l}
1 & 792.3 \\
\hline
& 792.3 \\
\end{array}
\]

- Explanation:
- \( 1 \times 792.3 = 792.3 \)
- Subtract: \( 792.3 - 792.3 = 0 \)

Thus, \( 0.1 \div 79.23 = 792.3 \).

---

8. \( 2.8 \div 5.6 \)

#### Step 1: Adjust the divisor to a whole number
- Move the decimal point in the divisor (2.8) one place to the right to make it a whole number (28).
- Move the decimal point in the dividend (5.6) one place to the right as well: \( 56 \).

#### Step 2: Perform the division
- Now, divide \( 56 \div 28 \).

\[
\begin{array}{r|l}
28 & 56 \\
\hline
& 2 \\
\end{array}
\]

- Explanation:
- \( 28 \times 2 = 56 \)
- Subtract: \( 56 - 56 = 0 \)

Thus, \( 2.8 \div 5.6 = 2 \).

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9. \( 0.2 \div 10.6 \)

#### Step 1: Adjust the divisor to a whole number
- Move the decimal point in the divisor (0.2) one place to the right to make it a whole number (2).
- Move the decimal point in the dividend (10.6) one place to the right as well: \( 106 \).

#### Step 2: Perform the division
- Now, divide \( 106 \div 2 \).

\[
\begin{array}{r|l}
2 & 106 \\
\hline
& 53 \\
\end{array}
\]

- Explanation:
- \( 2 \times 53 = 106 \)
- Subtract: \( 106 - 106 = 0 \)

Thus, \( 0.2 \div 10.6 = 53 \).

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Final Answers

\[
\boxed{
\begin{array}{ccc}
29.5 & 32.2 & 34.9 \\
19 & 24 & 37 \\
792.3 & 2 & 53 \\
\end{array}
}
\]