Multiplying and Dividing Decimals Worksheet for math practice.

Problem: Solving the Multiplying and Dividing Decimals Worksheet

The worksheet consists of two sections:
1. Multiplying Decimals
2. Dividing Decimals

Let's solve each problem step by step.

---

Section 1: Multiplying Decimals

#### Problem 1: \( 27.31 \times 6.3 \)

1. Ignore the decimal points and multiply the numbers as whole numbers:
\[
2731 \times 63 = 172413
\]

2. Count the total number of decimal places in the original numbers:
- \( 27.31 \) has 2 decimal places.
- \( 6.3 \) has 1 decimal place.
- Total: \( 2 + 1 = 3 \) decimal places.

3. Place the decimal point in the product so that there are 3 decimal places:
\[
172413 \rightarrow 172.413
\]

Answer:
\[
\boxed{172.413}
\]

---

#### Problem 2: \( 1238.58 \times 64.14 \)

1. Ignore the decimal points and multiply the numbers as whole numbers:
\[
123858 \times 6414 = 794077752
\]

2. Count the total number of decimal places in the original numbers:
- \( 1238.58 \) has 2 decimal places.
- \( 64.14 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product so that there are 4 decimal places:
\[
794077752 \rightarrow 79407.7752
\]

Answer:
\[
\boxed{79407.7752}
\]

---

#### Problem 3: \( 63.24 \times 12.20 \)

1. Ignore the decimal points and multiply the numbers as whole numbers:
\[
6324 \times 1220 = 7716480
\]

2. Count the total number of decimal places in the original numbers:
- \( 63.24 \) has 2 decimal places.
- \( 12.20 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product so that there are 4 decimal places:
\[
7716480 \rightarrow 771.6480
\]

Answer:
\[
\boxed{771.6480}
\]

---

#### Problem 4: \( 73.45 \times 83.11 \)

1. Ignore the decimal points and multiply the numbers as whole numbers:
\[
7345 \times 8311 = 61177295
\]

2. Count the total number of decimal places in the original numbers:
- \( 73.45 \) has 2 decimal places.
- \( 83.11 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product so that there are 4 decimal places:
\[
61177295 \rightarrow 6117.7295
\]

Answer:
\[
\boxed{6117.7295}
\]

---

#### Problem 5: \( 1034.33 \times 8.44 \)

1. Ignore the decimal points and multiply the numbers as whole numbers:
\[
103433 \times 844 = 87407732
\]

2. Count the total number of decimal places in the original numbers:
- \( 1034.33 \) has 2 decimal places.
- \( 8.44 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product so that there are 4 decimal places:
\[
87407732 \rightarrow 8740.7732
\]

Answer:
\[
\boxed{8740.7732}
\]

---

#### Problem 6: \( 0.313 \times 0.224 \)

1. Ignore the decimal points and multiply the numbers as whole numbers:
\[
313 \times 224 = 70032
\]

2. Count the total number of decimal places in the original numbers:
- \( 0.313 \) has 3 decimal places.
- \( 0.224 \) has 3 decimal places.
- Total: \( 3 + 3 = 6 \) decimal places.

3. Place the decimal point in the product so that there are 6 decimal places:
\[
70032 \rightarrow 0.070032
\]

Answer:
\[
\boxed{0.070032}
\]

---

Section 2: Dividing Decimals

#### Problem 1: \( 21.34 \div 10 \)

1. Dividing by 10 moves the decimal point one place to the left:
\[
21.34 \div 10 = 2.134
\]

Answer:
\[
\boxed{2.134}
\]

---

#### Problem 2: \( 999.92 \div 100 \)

1. Dividing by 100 moves the decimal point two places to the left:
\[
999.92 \div 100 = 9.9992
\]

Answer:
\[
\boxed{9.9992}
\]

---

#### Problem 3: \( 932.4 \div 121.32 \)

1. To simplify the division, eliminate the decimals by multiplying both numbers by 100:
\[
932.4 \times 100 = 93240
\]
\[
121.32 \times 100 = 12132
\]
Now divide:
\[
93240 \div 12132 \approx 7.68
\]

Answer:
\[
\boxed{7.68}
\]

---

#### Problem 4: \( 9.4 \div 3.2 \)

1. Eliminate the decimals by multiplying both numbers by 10:
\[
9.4 \times 10 = 94
\]
\[
3.2 \times 10 = 32
\]
Now divide:
\[
94 \div 32 = 2.9375
\]

Answer:
\[
\boxed{2.9375}
\]

---

#### Problem 5: \( 98.6 \div 18.4 \)

1. Eliminate the decimals by multiplying both numbers by 10:
\[
98.6 \times 10 = 986
\]
\[
18.4 \times 10 = 184
\]
Now divide:
\[
986 \div 184 \approx 5.36
\]

Answer:
\[
\boxed{5.36}
\]

---

#### Problem 6: \( 256.58 \div 16 \)

1. Perform the division directly:
\[
256.58 \div 16 = 16.03625
\]

Answer:
\[
\boxed{16.03625}
\]

---

Final Answers:

- Multiply:
1. \( \boxed{172.413} \)
2. \( \boxed{79407.7752} \)
3. \( \boxed{771.6480} \)
4. \( \boxed{6117.7295} \)
5. \( \boxed{8740.7732} \)
6. \( \boxed{0.070032} \)

- Divide:
1. \( \boxed{2.134} \)
2. \( \boxed{9.9992} \)
3. \( \boxed{7.68} \)
4. \( \boxed{2.9375} \)
5. \( \boxed{5.36} \)
6. \( \boxed{16.03625} \)