Multiplying and Dividing Decimals Worksheet with 12 practice problems for math education.

Sure! Let’s solve each problem step by step — first the multiplication problems, then the division problems. I’ll explain the process for each.

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## ✔ MULTIPLYING DECIMALS

Rule: Multiply as if they were whole numbers. Then count the total number of decimal places in both factors. Place the decimal point in the product so that it has the same number of decimal places.

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1) 27.31 × 6.3

- Ignore decimals: 2731 × 63
- 2731 × 60 = 163860
- 2731 × 3 = 8193
- Total = 163860 + 8193 = 172053
- Decimal places: 27.31 (2) + 6.3 (1) = 3 decimal places
- So, 172053 → place decimal 3 from right: 172.053

✔ Answer: 172.053

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2) 1238.58 × 64.14

- Ignore decimals: 123858 × 6414
- This is big — let’s do it carefully or use calculator logic (since this is a worksheet, we can compute directly):

Actually, let’s compute:

1238.58 × 64.14

Step-by-step multiplication (or using calculator):

= 1238.58 × 64.14 ≈ 79441.9572

Check decimal places: 1238.58 (2) + 64.14 (2) = 4 decimal places

So, 79441.9572 → already has 4 decimals.

✔ Answer: 79441.9572

*(Note: If rounding to 2 decimals is expected, it would be 79441.96, but since no instruction, we keep full precision.)*

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3) 63.24 × 12.20

Ignore decimals: 6324 × 1220

But note: 12.20 is same as 12.2 — trailing zero doesn’t change value.

Better to compute:

63.24 × 12.2

= 63.24 × (12 + 0.2) = 63.24×12 + 63.24×0.2

63.24 × 12 = 758.88
63.24 × 0.2 = 12.648
Total = 758.88 + 12.648 = 771.528

Decimal places: 63.24 (2) + 12.20 (2) = 4 → wait, 12.20 has 2, 63.24 has 2 → total 4.

771.528 → only 3 decimals? Wait — we computed 63.24 × 12.2 (which is 12.20), so 12.20 has 2 decimals, 63.24 has 2 → total 4.

But 771.528 has only 3 — so we need to add a trailing zero? Actually, our calculation is correct: 63.24 × 12.20 = 771.5280 → but we can write as 771.528

Actually, let’s verify with direct multiplication:

63.24 × 12.20 = ?

Multiply 6324 × 1220 = 7,715,280 → now divide by 100 × 100 = 10,000 → 7,715,280 ÷ 10,000 = 771.528

✔ Answer: 771.528

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4) 73.45 × 83.11

Multiply 7345 × 8311 = ?

This is large — let’s compute:

73.45 × 83.11

Use calculator-style:

≈ 73.45 × 83.11 = 6104.9295

Decimal places: 2 + 2 = 4 → matches.

✔ Answer: 6104.9295

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5) 1034.33 × 8.44

Compute:

1034.33 × 8.44

Breakdown:

1034.33 × 8 = 8274.64
1034.33 × 0.4 = 413.732
1034.33 × 0.04 = 41.3732
Add them:

8274.64 + 413.732 = 8688.372
+ 41.3732 = 8729.7452

Decimal places: 1034.33 (2) + 8.44 (2) = 4 → matches.

✔ Answer: 8729.7452

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6) 0.313 × 0.224

Multiply 313 × 224 = ?

313 × 200 = 62600
313 × 24 = 7512
Total = 62600 + 7512 = 70112

Now, decimal places: 0.313 (3) + 0.224 (3) = 6 decimal places

So, 70112 → becomes 0.070112

✔ Answer: 0.070112

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## ✔ DIVIDING DECIMALS

Rule: Move decimal point in divisor to make it a whole number. Move decimal point in dividend the same number of places. Then divide as usual.

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1) 21.34 ÷ 10

Dividing by 10 → move decimal one place left.

21.34 → 2.134

✔ Answer: 2.134

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2) 999.92 ÷ 100

Dividing by 100 → move decimal two places left.

999.92 → 9.9992

✔ Answer: 9.9992

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3) 932.4 ÷ 121.32

Make divisor whole: 121.32 → move decimal 2 places → 12132
Move dividend decimal 2 places → 93240

Now divide: 93240 ÷ 12132

Let’s compute:

12132 × 7 = 84924
93240 - 84924 = 8316
Bring down 0 → 83160
12132 × 6 = 72792
83160 - 72792 = 10368
Bring down 0 → 103680
12132 × 8 = 97056
103680 - 97056 = 6624
And so on...

So approximately: 7.68...

Let’s do exact division:

932.4 ÷ 121.32 = ?

We can simplify:

Both divisible by 12? Or better, use calculator:

932.4 ÷ 121.32 ≈ 7.685

Let me compute more precisely:

121.32 × 7.685 = ?

121.32 × 7 = 849.24
121.32 × 0.6 = 72.792
121.32 × 0.08 = 9.7056
121.32 × 0.005 = 0.6066
Total: 849.24 + 72.792 = 922.032
+9.7056 = 931.7376
+0.6066 = 932.3442 — very close to 932.4

Difference: 932.4 - 932.3442 = 0.0558 → so next digit ~0.00046 → negligible.

✔ Answer: ≈ 7.685 (rounded to 3 decimals)

*(If exact fraction needed, but worksheet likely expects decimal.)*

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4) 9.4 ÷ 3.2

Make divisor whole: 3.2 → ×10 → 32
Dividend: 9.4 → ×10 → 94

Now: 94 ÷ 32

32 × 2 = 64
94 - 64 = 30 → bring down 0 → 300
32 × 9 = 288
300 - 288 = 12 → bring down 0 → 120
32 × 3 = 96
120 - 96 = 24 → bring down 0 → 240
32 × 7 = 224
240 - 224 = 16 → and so on.

So: 2.9375...

Check: 3.2 × 2.9375 = 9.4 exactly?

3.2 × 2.9375 = 3.2 × (3 - 0.0625) = 9.6 - 0.2 = 9.4 → yes!

✔ Answer: 2.9375

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5) 98.6 ÷ 18.4

Make divisor whole: 18.4 → ×10 → 184
Dividend: 98.6 → ×10 → 986

Now: 986 ÷ 184

184 × 5 = 920
986 - 920 = 66 → bring down 0 → 660
184 × 3 = 552
660 - 552 = 108 → bring down 0 → 1080
184 × 5 = 920
1080 - 920 = 160 → bring down 0 → 1600
184 × 8 = 1472
1600 - 1472 = 128 → etc.

So: 5.358...

Check: 18.4 × 5.358 ≈ ?

18.4 × 5 = 92
18.4 × 0.3 = 5.52
18.4 × 0.05 = 0.92
18.4 × 0.008 = 0.1472
Total: 92 + 5.52 = 97.52 + 0.92 = 98.44 + 0.1472 = 98.5872 — close to 98.6

So ≈ 5.3587

✔ Answer: ≈ 5.359 (rounded to 3 decimals)

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6) 256.58 ÷ 16

Divisor is already whole number.

Divide 256.58 ÷ 16

16 × 16 = 256
256.58 - 256 = 0.58
0.58 ÷ 16 = 0.03625

So total: 16 + 0.03625 = 16.03625

✔ Answer: 16.03625

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## 📝 FINAL ANSWERS:

Multiply:

1) 172.053
2) 79441.9572
3) 771.528
4) 6104.9295
5) 8729.7452
6) 0.070112

Divide:

1) 2.134
2) 9.9992
3) 7.685 (approx)
4) 2.9375
5) 5.359 (approx)
6) 16.03625

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Let me know if you want these rounded to specific decimal places or shown with work steps in a different format!