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
```

So, $ 305.8 \div 52 = 5.88 $ (approximately)

✔ Answer: 5.88

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✔ Problem 2: $ 7.5 \div 145.13 $

$$
\frac{145.13}{7.5}
$$

Multiply numerator and denominator by 10:

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

Now divide $ 1451.3 \div 75 $

Long division:

```
19.35
________
75|1451.30
-75
----
701
-675
----
263
-225
----
380
-375
----
5
```

So, $ 1451.3 \div 75 = 19.35 $ (approx.)

✔ Answer: 19.35

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✔ Problem 3: $ 68 \div 288.09 $

$$
\frac{288.09}{68}
$$

Divide directly:

```
4.236
________
68|288.09
-272
----
160
-136
----
240
-204
----
369
-340
----
29
```

So, $ 288.09 \div 68 = 4.236 $ (approx.)

✔ Answer: 4.236

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✔ Problem 4: $ 100 \div 581.30 $

$$
\frac{581.30}{100} = 5.813
$$

This is simple — dividing by 100 just moves the decimal two places left.

✔ Answer: 5.813

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✔ Problem 5: $ 3 \div 281.30 $

$$
\frac{281.30}{3}
$$

Divide:

```
93.766...
________
3|281.30
-27
----
11
- 9
----
23
-21
----
20
-18
----
20
-18
----
2
```

So, $ 281.30 \div 3 = 93.766... $ ≈ 93.77 (rounded to two decimals)

✔ Answer: 93.77

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✔ Problem 6: $ 66.8 \div 1889.37 $

$$
\frac{1889.37}{66.8}
$$

Multiply numerator and denominator by 10 to eliminate decimal:

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

Now divide $ 18893.7 \div 668 $

Estimate:
$ 668 \times 28 = 18,704 $
Subtract: $ 18,893.7 - 18,704 = 189.7 $

Now: $ 668 \times 0.28 = 186.24 $ → close

Try:
$ 668 \times 28.28 = ? $

Alternatively, use approximation:

$$
18893.7 \div 668 ≈ 28.28
$$

Check: $ 668 \times 28.28 = ? $

Break it down:
- $ 668 \times 28 = 18,704 $
- $ 668 \times 0.28 = 186.24 $
- Total = $ 18,704 + 186.24 = 18,890.24 $

Close to 18,893.7 → difference = 3.46

Add $ 3.46 / 668 ≈ 0.005 $

So total ≈ $ 28.285 $

✔ Answer: 28.285

---

✔ Problem 7: $ 8.03 \div 58.34 $

$$
\frac{58.34}{8.03}
$$

Multiply numerator and denominator by 100:

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

Now divide $ 5834 \div 803 $

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

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 far: 7.26...

Continue? But we can stop here.

So $ 5834 \div 803 ≈ 7.26 $

✔ Answer: 7.26

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✔ Problem 8: $ 3.9 \div 9.204 $

$$
\frac{9.204}{3.9}
$$

Multiply numerator and denominator by 10:

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

Now divide $ 92.04 \div 39 $

Estimate: $ 39 \times 2 = 78 $, $ 39 \times 2.3 = 39×2 + 39×0.3 = 78 + 11.7 = 89.7 $

Subtract: $ 92.04 - 89.7 = 2.34 $

Now $ 39 \times 0.06 = 2.34 $

So total = $ 2.3 + 0.06 = 2.36 $

✔ Answer: 2.36

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✔ Problem 9: $ 1000 \div 2867.18 $

$$
\frac{2867.18}{1000} = 2.86718
$$

Dividing by 1000 → move decimal three places left.

✔ 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 | 28.285 |
| 7 | 7.26 |
| 8 | 2.36 |
| 9 | 2.86718 |

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✔ Summary:

All answers are rounded to two or three decimal places, depending on precision needed. For exactness, some may be continued further, but these are reasonable approximations.

Let me know if you'd like the long division steps shown in detail for any specific problem!