Multiplying and Dividing Decimals Worksheets - Math Monks - Free Printable

Let’s solve each problem step by step. We’ll start with the multiplication problems, then move to division.

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Multiply Problems:

Problem 1: 27.31 × 6.3

Step 1: Ignore decimals and multiply as whole numbers:
2731 × 63

Break it down:
2731 × 60 = 163,860
2731 × 3 = 8,193
Add them: 163,860 + 8,193 = 172,053

Step 2: Count decimal places in original numbers:
27.31 → 2 decimal places
6.3 → 1 decimal place
Total = 3 decimal places

Step 3: Put decimal back in answer: 172.053

✔ Answer: 172.053

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Problem 2: 1238.58 × 64.14

This is big — let’s do it carefully.

First, ignore decimals: 123858 × 6414

We can break 6414 into 6000 + 400 + 10 + 4

But that’s messy. Let’s use standard multiplication:

Actually, better to use calculator-style steps (since this is for a student, we’ll simulate careful hand math):

Alternatively, since this is time-consuming, let’s compute accurately:

1238.58 × 64.14

= (123858 / 100) × (6414 / 100) = (123858 × 6414) / 10000

Compute 123858 × 6414:

Let me compute step by step:

First, 123858 × 6000 = 743,148,000
123858 × 400 = 49,543,200
123858 × 10 = 1,238,580
123858 × 4 = 495,432

Now add:

743,148,000
+ 49,543,200 = 792,691,200
+ 1,238,580 = 793,929,780
+ 495,432 = 794,425,212

Now divide by 10,000 → move decimal 4 places left: 79,442.5212

Wait — check decimal places:

Original: 1238.58 has 2 decimals, 64.14 has 2 decimals → total 4 decimals → yes.

✔ Answer: 79442.5212

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Problem 3: 63.24 × 12.20

Note: 12.20 is same as 12.2

Ignore decimals: 6324 × 1220

Or easier: 63.24 × 12.2

Compute 6324 × 122 = ?

6324 × 100 = 632,400
6324 × 20 = 126,480
6324 × 2 = 12,648
Add: 632,400 + 126,480 = 758,880 + 12,648 = 771,528

Now, since we multiplied 63.24 (2 decimals) × 12.2 (1 decimal) → total 3 decimals

So 771.528

But wait — original was 12.20, which is still 2 decimals? Actually, trailing zero doesn’t count — 12.20 is same as 12.2 → 1 decimal place? No!

Wait: 12.20 has two decimal places (even if last digit is zero). So:

63.24 → 2 decimals
12.20 → 2 decimals
Total = 4 decimals

So our product should have 4 decimal places.

We computed 6324 × 1220 = ?

Better: 63.24 × 12.20

Do 6324 × 1220 = ?

6324 × 1000 = 6,324,000
6324 × 200 = 1,264,800
6324 × 20 = 126,480
Wait — 1220 = 1000 + 200 + 20? No, 1220 = 1200 + 20

Easier: 6324 × 1220 = 6324 × (122 × 10) = (6324 × 122) × 10

We had 6324 × 122 = 771,528 → times 10 = 7,715,280

Now, since original numbers had 2 + 2 = 4 decimal places, divide by 10,000 → 771.5280

Which is 771.528

But to be precise: 7,715,280 ÷ 10,000 = 771.5280 → so 771.528

✔ Answer: 771.528

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Problem 4: 73.45 × 83.11

Ignore decimals: 7345 × 8311

This is large — let’s compute:

7345 × 8000 = 58,760,000
7345 × 300 = 2,203,500
7345 × 10 = 73,450
7345 × 1 = 7,345

Add:

58,760,000
+ 2,203,500 = 60,963,500
+ 73,450 = 61,036,950
+ 7,345 = 61,044,295

Decimal places: 73.45 (2), 83.11 (2) → total 4

So 6104.4295

✔ Answer: 6104.4295

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Problem 5: 1034.33 × 8.44

Ignore decimals: 103433 × 844

Compute:

103433 × 800 = 82,746,400
103433 × 40 = 4,137,320
103433 × 4 = 413,732

Add:

82,746,400
+ 4,137,320 = 86,883,720
+ 413,732 = 87,297,452

Decimal places: 1034.33 (2), 8.44 (2) → total 4

So 8729.7452

✔ Answer: 8729.7452

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Problem 6: 0.313 × 0.224

Ignore decimals: 313 × 224

313 × 200 = 62,600
313 × 20 = 6,260
313 × 4 = 1,252
Add: 62,600 + 6,260 = 68,860 + 1,252 = 70,112

Decimal places: 0.313 (3), 0.224 (3) → total 6

So 0.070112

✔ Answer: 0.070112

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Divide Problems:

Problem 1: 21.34 ÷ 10

Dividing by 10 moves decimal one place left: 2.134

✔ Answer: 2.134

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Problem 2: 999.92 ÷ 100

Dividing by 100 moves decimal two places left: 9.9992

✔ Answer: 9.9992

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Problem 3: 932.4 ÷ 121.32

This is trickier. Let’s make divisor whole number.

Multiply numerator and denominator by 100 to eliminate decimals:

932.4 × 100 = 93,240
121.32 × 100 = 12,132

Now compute 93240 ÷ 12132

Let’s divide:

12132 × 7 = 84,924
93,240 - 84,924 = 8,316

Bring down 0 → 83,160

12132 × 6 = 72,792
83,160 - 72,792 = 10,368

Bring down 0 → 103,680

12132 × 8 = 97,056
103,680 - 97,056 = 6,624

Bring down 0 → 66,240

12132 × 5 = 60,660
66,240 - 60,660 = 5,580

So approximately 7.685... but let’s see exact value.

Actually, better to use calculator or simplify.

Note: 932.4 ÷ 121.32

Let me compute directly:

121.32 × 7.68 = ?

121.32 × 7 = 849.24
121.32 × 0.6 = 72.792
121.32 × 0.08 = 9.7056
Sum: 849.24 + 72.792 = 922.032 + 9.7056 = 931.7376

Close to 932.4 → difference 0.6624

Now 121.32 × 0.005 = 0.6066 → close

So 7.685 → 121.32 × 7.685 = ?

Actually, let’s do proper division:

932.4 ÷ 121.32 = ?

Use long division or accept approximation.

But let’s compute exactly:

932.4 / 121.32 = 93240 / 12132 (multiply num and den by 100)

Simplify fraction:

Divide numerator and denominator by 12? Let’s find GCD.

Actually, 93240 ÷ 12132 ≈ 7.685

Check: 12132 × 7.685 = ?

12132 × 7 = 84924
12132 × 0.6 = 7279.2
12132 × 0.08 = 970.56
12132 × 0.005 = 60.66
Sum: 84924 + 7279.2 = 92203.2 + 970.56 = 93173.76 + 60.66 = 93234.42

But we have 93240 → difference 5.58

So 7.685 + (5.58/12132) ≈ 7.685 + 0.00046 ≈ 7.68546

But perhaps it's exact? Let me try 93240 ÷ 12132

Do division:

12132 ) 93240.000

12132 × 7 = 84924 → subtract from 93240 → 8316

Bring down 0 → 83160

12132 × 6 = 72792 → subtract → 10368

Bring down 0 → 103680

12132 × 8 = 97056 → subtract → 6624

Bring down 0 → 66240

12132 × 5 = 60660 → subtract → 5580

Bring down 0 → 55800

12132 × 4 = 48528 → subtract → 7272

And so on.

So quotient is 7.6854...

But for practical purposes, let’s say 7.685

Wait — maybe I made a mistake. Let me use another approach.

Note: 932.4 ÷ 121.32 = ?

Calculate numerically:

121.32 × 7.685 = as above ~932.34, very close to 932.4

Difference is small. Perhaps the problem expects rounding.

But let’s assume we need exact value.

Actually, 932.4 / 121.32 = 93240 / 12132 = reduce by dividing numerator and denominator by 12? Let’s see GCD.

Find GCD of 93240 and 12132.

Use Euclidean algorithm:

GCD(93240, 12132)

93240 ÷ 12132 = 7 times, remainder 93240 - 7*12132 = 93240 - 84924 = 8316

GCD(12132, 8316)

12132 ÷ 8316 = 1 time, remainder 12132 - 8316 = 3816

GCD(8316, 3816)

8316 ÷ 3816 = 2 times, remainder 8316 - 7632 = 684

GCD(3816, 684)

3816 ÷ 684 = 5 times, 5*684=3420, remainder 396

GCD(684, 396)

684 ÷ 396 = 1, remainder 288

GCD(396, 288)

396 ÷ 288 = 1, remainder 108

GCD(288, 108)

288 ÷ 108 = 2, remainder 72

GCD(108, 72) = 36

GCD(72, 36) = 36

So GCD is 36

Thus, 93240 ÷ 36 = 2590
12132 ÷ 36 = 337

So 2590 / 337

Now divide 2590 ÷ 337

337 × 7 = 2359
2590 - 2359 = 231

So 7 + 231/337 ≈ 7.68546

So approximately 7.685

But for worksheet, perhaps they expect rounded answer or exact fraction.

Since it's decimal worksheet, likely decimal answer.

Let’s take 7.685

But let’s verify with calculator simulation:

932.4 ÷ 121.32 = 7.68546... so to three decimals, 7.685

✔ Answer: 7.685 (rounded to three decimal places)

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Problem 4: 9.4 ÷ 3.2

Make divisor whole: multiply num and den by 10 → 94 ÷ 32

94 ÷ 32 = 2.9375

Because 32 × 2 = 64, 94-64=30, bring down 0 → 300, 32×9=288, remainder 12, bring down 0 → 120, 32×3=96, remainder 24, bring down 0 → 240, 32×7=224, remainder 16, bring down 0 → 160, 32×5=160, done.

So 2.9375

✔ Answer: 2.9375

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Problem 5: 98.6 ÷ 18.4

Multiply num and den by 10: 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
Bring down 0 → 1280
184 × 6 = 1104
1280 - 1104 = 176
etc.

So 5.3586...

Approximately 5.359

But let’s compute exactly:

986 ÷ 184 = 493 ÷ 92 (divide by 2)

493 ÷ 92

92 × 5 = 460
493 - 460 = 33
So 5 + 33/92 = 5.358695...

To three decimals: 5.359

✔ Answer: 5.359 (rounded)

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Problem 6: 256.58 ÷ 16

Divide directly.

16 into 256.58

16 × 16 = 256 → so 16.000

Remainder 0.58

0.58 ÷ 16 = 0.03625

So total 16.03625

Check: 16 × 16.03625 = 16×16 = 256, 16×0.03625=0.58, yes.

✔ Answer: 16.03625

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Now, compiling all answers:

Multiplication:
1. 172.053
2. 79442.5212
3. 771.528
4. 6104.4295
5. 8729.7452
6. 0.070112

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

For division problem 3 and 5, since they are repeating or long decimals, we'll round to three decimal places as typical for such worksheets.

Final Answers:

Final Answer:
Multiply:
1. 172.053
2. 79442.5212
3. 771.528
4. 6104.4295
5. 8729.7452
6. 0.070112

Divide:
1. 2.134
2. 9.9992
3. 7.685
4. 2.9375
5. 5.359
6. 16.03625