Dividing Decimals Worksheets - Math Monks - Free Printable

Let's solve each of the decimal division problems step by step. The goal is to find the quotient for each division problem.

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🔧 Key Tip:

When dividing decimals, you can eliminate the decimal in the divisor by multiplying both the divisor and dividend by the same power of 10 (to make the divisor a whole number). Then perform long division as usual.

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✔ Problem 1: $ 5.2 \div 30.58 $

We are dividing:
$$
5.2 \overline{)30.58}
$$

But actually, it’s written as:
$$
\frac{30.58}{5.2}
$$

To eliminate the decimal in the divisor (5.2), multiply both numbers by 10:

$$
\frac{30.58 \times 10}{5.2 \times 10} = \frac{305.8}{52}
$$

Now divide $ 305.8 \div 52 $

Let’s do long division:

```
5.88
________
52|305.80
-260
----
458
-416
----
420
-364
----
56 → remainder, but we can continue
```

So, $ 305.8 \div 52 = 5.8807... $ ≈ 5.88

✔ Answer: 5.88

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✔ Problem 2: $ 7.5 \div 145.13 $

Actually: $ \frac{145.13}{7.5} $

Multiply numerator and denominator by 10:

$$
\frac{1451.3}{75}
$$

Now divide $ 1451.3 \div 75 $

```
19.35
________
75|1451.30
-75
---
701
-675
----
263
-225
----
380
-375
----
50 → remainder
```

So, $ 1451.3 \div 75 = 19.35 $ (approximately)

✔ Answer: 19.35

---

✔ Problem 3: $ 68 \div 288.09 $

This is: $ \frac{288.09}{68} $

No need to adjust — divisor is already a whole number.

Divide $ 288.09 \div 68 $

```
4.236
________
68|288.090
-272
----
160
-136
----
240
-204
----
360
-340
----
200
-136
----
64 → stop here
```

So, $ 288.09 \div 68 \approx 4.236 $

✔ Answer: 4.236

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✔ Problem 4: $ 100 \div 581.30 $

This is: $ \frac{581.30}{100} $

Dividing by 100 moves decimal two places left:

$$
581.30 \div 100 = 5.813
$$

✔ Answer: 5.813

---

✔ Problem 5: $ 3 \div 281.30 $

This is: $ \frac{281.30}{3} $

Divide:

```
93.766...
________
3|281.300
-27
---
11
- 9
---
23
-21
---
20
-18
---
20
-18
---
2 → repeats
```

So, $ 281.30 \div 3 = 93.766... $ ≈ 93.77

✔ Answer: 93.77

---

✔ Problem 6: $ 66.8 \div 1889.37 $

This is: $ \frac{1889.37}{66.8} $

Multiply numerator and denominator by 10:

$$
\frac{18893.7}{668}
$$

Now divide $ 18893.7 \div 668 $

Estimate: $ 668 \times 28 = 18704 $, subtract from 18893.7:

$ 18893.7 - 18704 = 189.7 $

Bring down 0 → 1897

$ 668 \times 2 = 1336 $, subtract: $ 1897 - 1336 = 561 $

Bring down 0 → 5610

$ 668 \times 8 = 5344 $, subtract: $ 5610 - 5344 = 266 $

So far: 28.28...

Continue? Let’s go to two decimals.

So, $ 18893.7 \div 668 \approx 28.28 $

✔ Answer: 28.28

---

✔ Problem 7: $ 8.03 \div 58.34 $

This is: $ \frac{58.34}{8.03} $

Multiply numerator and denominator by 100:

$$
\frac{5834}{803}
$$

Now divide $ 5834 \div 803 $

Estimate: $ 803 \times 7 = 5621 $, subtract: $ 5834 - 5621 = 213 $

Add decimal: bring down 0 → 2130

$ 803 \times 2 = 1606 $, subtract: $ 2130 - 1606 = 524 $

Bring down 0 → 5240

$ 803 \times 6 = 4818 $, subtract: $ 5240 - 4818 = 422 $

So, $ 5834 \div 803 \approx 7.26 $

✔ Answer: 7.26

---

✔ Problem 8: $ 3.9 \div 9.204 $

This is: $ \frac{9.204}{3.9} $

Multiply numerator and denominator by 10:

$$
\frac{92.04}{39}
$$

Now divide $ 92.04 \div 39 $

```
2.36
________
39|92.04
-78
---
140
-117
----
234
-234
----
0
```

So, $ 92.04 \div 39 = 2.36 $

✔ Answer: 2.36

---

✔ Problem 9: $ 1000 \div 2867.18 $

This is: $ \frac{2867.18}{1000} $

Dividing by 1000 moves decimal three places left:

$$
2867.18 \div 1000 = 2.86718
$$

✔ Answer: 2.86718

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## ✔ Final Answers:

| Problem | Quotient |
|--------|----------|
| 1 | 5.88 |
| 2 | 19.35 |
| 3 | 4.236 |
| 4 | 5.813 |
| 5 | 93.77 |
| 6 | 28.28 |
| 7 | 7.26 |
| 8 | 2.36 |
| 9 | 2.86718 |

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📝 Summary:

- Always convert divisor to a whole number by multiplying both numbers by 10, 100, etc.
- Use long division when needed.
- Be careful with decimal placement.

Let me know if you'd like these answers rounded to specific decimal places or shown with full long division steps!