Multiply and Divide Decimals worksheet - Free Printable

Let's solve each problem step by step.

---

Problem 1: \( 6.208 \div 1.6 \)

To divide decimals, we can eliminate the decimal by multiplying both the numerator and denominator by a power of 10 that makes the divisor a whole number.

1. Multiply both numbers by 10:
\[
6.208 \times 10 = 62.08
\]
\[
1.6 \times 10 = 16
\]
So, the problem becomes:
\[
62.08 \div 16
\]

2. Perform the division:
- How many times does 16 go into 62? It goes 3 times (since \( 16 \times 3 = 48 \)).
- Subtract \( 48 \) from \( 62 \):
\[
62 - 48 = 14
\]
- Bring down the next digit (0):
\[
140
\]
- How many times does 16 go into 140? It goes 8 times (since \( 16 \times 8 = 128 \)).
- Subtract \( 128 \) from \( 140 \):
\[
140 - 128 = 12
\]
- Bring down the next digit (8):
\[
128
\]
- How many times does 16 go into 128? It goes 8 times (since \( 16 \times 8 = 128 \)).
- Subtract \( 128 \) from \( 128 \):
\[
128 - 128 = 0
\]

So, the result is:
\[
6.208 \div 1.6 = 3.88
\]

---

Problem 2: \( 8.3 \times 7 \)

Multiply as if they were whole numbers, then place the decimal point in the product.

1. Multiply \( 83 \times 7 \):
\[
83 \times 7 = 581
\]

2. Count the total number of decimal places in the original numbers:
- \( 8.3 \) has 1 decimal place.
- \( 7 \) has 0 decimal places.
- Total: \( 1 + 0 = 1 \) decimal place.

3. Place the decimal point in the product:
\[
581 \rightarrow 58.1
\]

So, the result is:
\[
8.3 \times 7 = 58.1
\]

---

Problem 3: \( 4.8 \times 1.8 \)

Multiply as if they were whole numbers, then place the decimal point in the product.

1. Multiply \( 48 \times 18 \):
\[
48 \times 18 = 864
\]

2. Count the total number of decimal places in the original numbers:
- \( 4.8 \) has 1 decimal place.
- \( 1.8 \) has 1 decimal place.
- Total: \( 1 + 1 = 2 \) decimal places.

3. Place the decimal point in the product:
\[
864 \rightarrow 8.64
\]

So, the result is:
\[
4.8 \times 1.8 = 8.64
\]

---

Problem 4: \( 0.56 \div 0.02 \)

To divide decimals, eliminate the decimal by multiplying both the numerator and denominator by a power of 10 that makes the divisor a whole number.

1. Multiply both numbers by 100:
\[
0.56 \times 100 = 56
\]
\[
0.02 \times 100 = 2
\]
So, the problem becomes:
\[
56 \div 2
\]

2. Perform the division:
\[
56 \div 2 = 28
\]

So, the result is:
\[
0.56 \div 0.02 = 28
\]

---

Problem 5: \( 0.42 \div 0.07 \)

To divide decimals, eliminate the decimal by multiplying both the numerator and denominator by a power of 10 that makes the divisor a whole number.

1. Multiply both numbers by 100:
\[
0.42 \times 100 = 42
\]
\[
0.07 \times 100 = 7
\]
So, the problem becomes:
\[
42 \div 7
\]

2. Perform the division:
\[
42 \div 7 = 6
\]

So, the result is:
\[
0.42 \div 0.07 = 6
\]

---

Problem 6: \( 0.05 \times 0.8 \)

Multiply as if they were whole numbers, then place the decimal point in the product.

1. Multiply \( 5 \times 8 \):
\[
5 \times 8 = 40
\]

2. Count the total number of decimal places in the original numbers:
- \( 0.05 \) has 2 decimal places.
- \( 0.8 \) has 1 decimal place.
- Total: \( 2 + 1 = 3 \) decimal places.

3. Place the decimal point in the product:
\[
40 \rightarrow 0.040 \quad \text{(or simply } 0.04\text{)}
\]

So, the result is:
\[
0.05 \times 0.8 = 0.04
\]

---

Problem 7: \( 0.5 \sqrt{5.246} \)

This appears to be a square root problem, but it is written incorrectly. Assuming it means \( \sqrt{5.246} \div 0.5 \):

1. First, find the square root of \( 5.246 \):
\[
\sqrt{5.246} \approx 2.29
\]

2. Divide the result by \( 0.5 \):
\[
2.29 \div 0.5 = 4.58
\]

So, the result is:
\[
\sqrt{5.246} \div 0.5 \approx 4.58
\]

---

Problem 8: \( 1.6 \sqrt{7.124} \)

This appears to be a square root problem, but it is written incorrectly. Assuming it means \( \sqrt{7.124} \div 1.6 \):

1. First, find the square root of \( 7.124 \):
\[
\sqrt{7.124} \approx 2.67
\]

2. Divide the result by \( 1.6 \):
\[
2.67 \div 1.6 \approx 1.67
\]

So, the result is:
\[
\sqrt{7.124} \div 1.6 \approx 1.67
\]

---

Problem 9: \( 5.32 \times 0.42 \)

Multiply as if they were whole numbers, then place the decimal point in the product.

1. Multiply \( 532 \times 42 \):
\[
532 \times 42 = 22344
\]

2. Count the total number of decimal places in the original numbers:
- \( 5.32 \) has 2 decimal places.
- \( 0.42 \) has 2 decimal places.
- Total: \( 2 + 2 = 4 \) decimal places.

3. Place the decimal point in the product:
\[
22344 \rightarrow 2.2344
\]

So, the result is:
\[
5.32 \times 0.42 = 2.2344
\]

---

Problem 10: \( 43.21 \times 2.1 \)

Multiply as if they were whole numbers, then place the decimal point in the product.

1. Multiply \( 4321 \times 21 \):
\[
4321 \times 21 = 90741
\]

2. Count the total number of decimal places in the original numbers:
- \( 43.21 \) has 2 decimal places.
- \( 2.1 \) has 1 decimal place.
- Total: \( 2 + 1 = 3 \) decimal places.

3. Place the decimal point in the product:
\[
90741 \rightarrow 90.741
\]

So, the result is:
\[
43.21 \times 2.1 = 90.741
\]

---

Final Answers:

\[
\boxed{
\begin{aligned}
1. & \ 3.88 \\
2. & \ 58.1 \\
3. & \ 8.64 \\
4. & \ 28 \\
5. & \ 6 \\
6. & \ 0.04 \\
7. & \ 4.58 \\
8. & \ 1.67 \\
9. & \ 2.2344 \\
10. & \ 90.741
\end{aligned}
}
\]