Decimal multiplication and division practice worksheet with six problems each for finding products and quotients.
A worksheet titled "Decimal Multiplication and Division" with six multiplication problems and six division problems involving decimals, designed for math practice.
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Show Answer Key & Explanations
Step-by-step solution for: Multiplying and Dividing Decimals Worksheets - Math Monks
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Show Answer Key & Explanations
Step-by-step solution for: Multiplying and Dividing Decimals Worksheets - Math Monks
Let’s solve each problem step by step.
---
Part 1: Find the product
Problem 1:
56.37 × 100
→ Multiplying by 100 moves the decimal point two places to the right.
56.37 → 5637.0
✔ Answer: 5637
---
Problem 2:
9.13 × 5.66
First, ignore decimals: 913 × 566
Calculate:
913 × 500 = 456,500
913 × 60 = 54,780
913 × 6 = 5,478
Add them: 456,500 + 54,780 = 511,280 + 5,478 = 516,758
Now count decimal places: 9.13 has 2, 5.66 has 2 → total 4 decimal places
So, 516,758 → move decimal 4 left → 51.6758
✔ Answer: 51.6758
---
Problem 3:
21.31 × 13.99
Ignore decimals: 2131 × 1399
Break it down:
2131 × 1000 = 2,131,000
2131 × 300 = 639,300
2131 × 90 = 191,790
2131 × 9 = 19,179
Add:
2,131,000 + 639,300 = 2,770,300
+191,790 = 2,962,090
+19,179 = 2,981,269
Decimal places: 2 + 2 = 4 → move decimal 4 left → 298.1269
✔ Answer: 298.1269
---
Problem 4:
139.66 × 9.99
Note: 9.99 is almost 10 → 139.66 × 10 = 1396.6, then subtract 139.66 × 0.01 = 1.3966
So: 1396.6 - 1.3966 = 1395.2034
Alternatively, direct multiplication:
13966 × 999 = ?
But easier: 139.66 × 9.99 = 139.66 × (10 - 0.01) = 1396.6 - 1.3966 = 1395.2034
✔ Answer: 1395.2034
---
Problem 5:
5.117 × 0.319
Ignore decimals: 5117 × 319
Calculate:
5117 × 300 = 1,535,100
5117 × 10 = 51,170
5117 × 9 = 46,053
Add: 1,535,100 + 51,170 = 1,586,270 + 46,053 = 1,632,323
Decimal places: 3 + 3 = 6 → move decimal 6 left → 1.632323
✔ Answer: 1.632323
---
Problem 6:
158.31 × 19.22
Ignore decimals: 15831 × 1922
This is big — let’s break it:
15831 × 1000 = 15,831,000
15831 × 900 = 14,247,900
15831 × 20 = 316,620
15831 × 2 = 31,662
Wait — better: 1922 = 2000 - 78
Or just multiply directly:
Actually, use calculator-style logic:
158.31 × 19.22
≈ 158 × 19 = 3002, but we need precision.
Better:
15831 × 1922 = ?
Let me compute step by step:
15831 × 1000 = 15,831,000
15831 × 900 = 14,247,900 → total so far 30,078,900
15831 × 20 = 316,620 → 30,395,520
15831 × 2 = 31,662 → 30,427,182
Total: 30,427,182
Decimal places: 2 + 2 = 4 → 3042.7182
✔ Answer: 3042.7182
---
Part 2: Find the quotient
Problem 1:
33.28 ÷ 19.3
Move decimal in divisor to make whole number: multiply both by 10 → 332.8 ÷ 193
Now divide:
193 × 1 = 193 → subtract from 332.8 → 139.8
Bring down 0 → 1398
193 × 7 = 1351 → subtract → 47
Bring down 0 → 470
193 × 2 = 386 → subtract → 84
Bring down 0 → 840
193 × 4 = 772 → subtract → 68
So approximately 1.724...
Let’s do exact:
33.28 ÷ 19.3 = ?
Use long division:
19.3 ) 33.28
Multiply numerator and denominator by 10: 332.8 ÷ 193
193 goes into 332 once → 193, remainder 139.8
Bring down 0 → 1398
193 × 7 = 1351 → remainder 47
Bring down 0 → 470
193 × 2 = 386 → remainder 84
Bring down 0 → 840
193 × 4 = 772 → remainder 68
So 1.724... and continuing → approximately 1.72435...
But let’s check with calculator logic:
33.28 / 19.3 ≈ 1.7243523316...
We can round to reasonable digits — since inputs have 2-3 decimals, answer to 4 decimals is fine.
✔ Answer: 1.7244 (rounded to 4 decimal places)
Wait — actually, let’s be precise. The problem doesn’t specify rounding, so perhaps keep as fraction or exact decimal? But these are terminating? Let’s see:
Actually, 33.28 ÷ 19.3 = 3328/1930 = simplify? Divide numerator and denominator by 2: 1664/965
Divide 1664 ÷ 965:
965 × 1 = 965 → 1664 - 965 = 699
6990 ÷ 965 ≈ 7 → 965×7=6755 → 6990-6755=235
2350 ÷ 965 ≈ 2 → 1930 → remainder 420
4200 ÷ 965 ≈ 4 → 3860 → remainder 340
So 1.724... same as before.
Since it's a worksheet, likely expects decimal answer rounded reasonably.
I’ll go with 1.724
But let’s verify with actual division:
19.3 × 1.724 = 19.3 × 1.7 = 32.81, 19.3 × 0.024 = 0.4632 → total 33.2732 ≈ 33.28 — close enough.
Actually, 19.3 × 1.72435 = let’s not overcomplicate.
Standard approach: perform division and stop at 4 decimals.
✔ Final for this: 1.7244 (if rounded up) or 1.724 — I’ll use 1.724 as it’s sufficient.
Wait — let’s do exact:
33.28 ÷ 19.3 = ?
Multiply both by 100: 3328 ÷ 1930
Divide 3328 by 1930:
1930 × 1 = 1930 → subtract → 1398
Add decimal, add 0 → 13980
1930 × 7 = 13510 → subtract → 470
Add 0 → 4700
1930 × 2 = 3860 → subtract → 840
Add 0 → 8400
1930 × 4 = 7720 → subtract → 680
Add 0 → 6800
1930 × 3 = 5790 → subtract → 1010
So 1.7243... → so 1.7243
I think 1.724 is acceptable, but to be accurate, let’s say 1.7243
But perhaps the worksheet expects exact value? Since it’s decimal division, likely decimal answer.
I’ll go with 1.724 for simplicity, but technically it’s repeating or non-terminating.
Actually, 33.28 / 19.3 = 3328/1930 = 1664/965
1664 ÷ 965 = 1.7243523316... so to 4 decimals: 1.7244
Yes, round up because next digit is 5.
✔ Answer: 1.7244
---
Problem 2:
81.29 ÷ 27.2
Multiply both by 10: 812.9 ÷ 272
272 × 2 = 544
812.9 - 544 = 268.9
Bring down 0 → 2689
272 × 9 = 2448 → subtract → 241
Bring down 0 → 2410
272 × 8 = 2176 → subtract → 234
Bring down 0 → 2340
272 × 8 = 2176 → subtract → 164
So 2.988... → approximately 2.9886
Check: 27.2 × 2.988 = ?
27.2 × 3 = 81.6 → too big
27.2 × 2.9 = 78.88
81.29 - 78.88 = 2.41
2.41 / 27.2 ≈ 0.0886 → so 2.9886
✔ Answer: 2.9886 (to 4 decimals)
---
Problem 3:
6.9 ÷ 3.2
Multiply both by 10: 69 ÷ 32
32 × 2 = 64 → remainder 5
5.0 → 50 ÷ 32 = 1 → remainder 18
180 ÷ 32 = 5 → 160 → remainder 20
200 ÷ 32 = 6 → 192 → remainder 8
80 ÷ 32 = 2 → 64 → remainder 16
160 ÷ 32 = 5 → exactly
So 2.15625
✔ Answer: 2.15625
---
Problem 4:
3.7 ÷ 0.007
Multiply both by 1000: 3700 ÷ 7
7 × 528 = 3696 → remainder 4
4.0 → 40 ÷ 7 = 5 → 35 → rem 5
50 ÷ 7 = 7 → 49 → rem 1
10 ÷ 7 = 1 → 7 → rem 3
30 ÷ 7 = 4 → 28 → rem 2
20 ÷ 7 = 2 → 14 → rem 6
60 ÷ 7 = 8 → 56 → rem 4 → repeats
So 528.571428... → repeating 571428
But since 3.7 / 0.007 = 3700 / 7 = 528.571428...
To 4 decimals: 528.5714
✔ Answer: 528.5714
---
Problem 5:
1082.18 ÷ 39.2
Multiply both by 10: 10821.8 ÷ 392
392 × 27 = 392×20=7840, 392×7=2744 → total 10584
10821.8 - 10584 = 237.8
Bring down 0 → 2378
392 × 6 = 2352 → subtract → 26
Bring down 0 → 260
392 × 0 = 0 → so 0.6? Wait
After 27, we have 237.8, which is 2378 tenths? Better:
10821.8 ÷ 392
392 × 27 = 10584
Subtract: 10821.8 - 10584 = 237.8
Now 237.8 ÷ 392 = 0.6066...
So total 27.6066...
Compute: 237.8 / 392 = ?
392 × 0.6 = 235.2 → subtract from 237.8 → 2.6
2.6 / 392 = 0.00663...
So 27.60663...
To 4 decimals: 27.6066
Check: 39.2 × 27.6066 ≈ ?
39.2 × 27 = 1058.4
39.2 × 0.6 = 23.52 → total 1081.92
39.2 × 0.0066 = 0.25872 → total 1082.17872 ≈ 1082.18 — good.
✔ Answer: 27.6066
---
Problem 6:
23.176 ÷ 19.2
Multiply both by 10: 231.76 ÷ 192
192 × 1 = 192 → subtract from 231.76 → 39.76
Bring down 0 → 397.6
192 × 2 = 384 → subtract → 13.6
Bring down 0 → 136.0
192 × 0 = 0 → so 0.07? Wait
After 1.2, we have 13.6, which is 136 tenths?
231.76 ÷ 192
192 × 1.2 = 230.4
231.76 - 230.4 = 1.36
1.36 / 192 = 0.007083...
So total 1.207083...
To 4 decimals: 1.2071
Check: 19.2 × 1.2071 = 19.2 × 1.2 = 23.04, 19.2 × 0.0071 = 0.13632 → total 23.17632 ≈ 23.176 — close.
Actually, 19.2 × 1.20708333... = 23.176 exactly? Let's see:
23.176 ÷ 19.2 = 23176 / 19200 = simplify
Divide numerator and denominator by 16: 1448.5 / 1200 — not integer.
23176 ÷ 19200 = ?
Do division: 23176 ÷ 19200 = 1.20708333...
So to 4 decimals: 1.2071
✔ Answer: 1.2071
---
Now compile all answers:
Products:
1. 5637
2. 51.6758
3. 298.1269
4. 1395.2034
5. 1.632323
6. 3042.7182
Quotients:
1. 1.7244
2. 2.9886
3. 2.15625
4. 528.5714
5. 27.6066
6. 1.2071
Note: For quotient 3, it's exact 2.15625, so no rounding needed.
Final Answer:
Products:
1. 5637
2. 51.6758
3. 298.1269
4. 1395.2034
5. 1.632323
6. 3042.7182
Quotients:
1. 1.7244
2. 2.9886
3. 2.15625
4. 528.5714
5. 27.6066
6. 1.2071
---
Part 1: Find the product
Problem 1:
56.37 × 100
→ Multiplying by 100 moves the decimal point two places to the right.
56.37 → 5637.0
✔ Answer: 5637
---
Problem 2:
9.13 × 5.66
First, ignore decimals: 913 × 566
Calculate:
913 × 500 = 456,500
913 × 60 = 54,780
913 × 6 = 5,478
Add them: 456,500 + 54,780 = 511,280 + 5,478 = 516,758
Now count decimal places: 9.13 has 2, 5.66 has 2 → total 4 decimal places
So, 516,758 → move decimal 4 left → 51.6758
✔ Answer: 51.6758
---
Problem 3:
21.31 × 13.99
Ignore decimals: 2131 × 1399
Break it down:
2131 × 1000 = 2,131,000
2131 × 300 = 639,300
2131 × 90 = 191,790
2131 × 9 = 19,179
Add:
2,131,000 + 639,300 = 2,770,300
+191,790 = 2,962,090
+19,179 = 2,981,269
Decimal places: 2 + 2 = 4 → move decimal 4 left → 298.1269
✔ Answer: 298.1269
---
Problem 4:
139.66 × 9.99
Note: 9.99 is almost 10 → 139.66 × 10 = 1396.6, then subtract 139.66 × 0.01 = 1.3966
So: 1396.6 - 1.3966 = 1395.2034
Alternatively, direct multiplication:
13966 × 999 = ?
But easier: 139.66 × 9.99 = 139.66 × (10 - 0.01) = 1396.6 - 1.3966 = 1395.2034
✔ Answer: 1395.2034
---
Problem 5:
5.117 × 0.319
Ignore decimals: 5117 × 319
Calculate:
5117 × 300 = 1,535,100
5117 × 10 = 51,170
5117 × 9 = 46,053
Add: 1,535,100 + 51,170 = 1,586,270 + 46,053 = 1,632,323
Decimal places: 3 + 3 = 6 → move decimal 6 left → 1.632323
✔ Answer: 1.632323
---
Problem 6:
158.31 × 19.22
Ignore decimals: 15831 × 1922
This is big — let’s break it:
15831 × 1000 = 15,831,000
15831 × 900 = 14,247,900
15831 × 20 = 316,620
15831 × 2 = 31,662
Wait — better: 1922 = 2000 - 78
Or just multiply directly:
Actually, use calculator-style logic:
158.31 × 19.22
≈ 158 × 19 = 3002, but we need precision.
Better:
15831 × 1922 = ?
Let me compute step by step:
15831 × 1000 = 15,831,000
15831 × 900 = 14,247,900 → total so far 30,078,900
15831 × 20 = 316,620 → 30,395,520
15831 × 2 = 31,662 → 30,427,182
Total: 30,427,182
Decimal places: 2 + 2 = 4 → 3042.7182
✔ Answer: 3042.7182
---
Part 2: Find the quotient
Problem 1:
33.28 ÷ 19.3
Move decimal in divisor to make whole number: multiply both by 10 → 332.8 ÷ 193
Now divide:
193 × 1 = 193 → subtract from 332.8 → 139.8
Bring down 0 → 1398
193 × 7 = 1351 → subtract → 47
Bring down 0 → 470
193 × 2 = 386 → subtract → 84
Bring down 0 → 840
193 × 4 = 772 → subtract → 68
So approximately 1.724...
Let’s do exact:
33.28 ÷ 19.3 = ?
Use long division:
19.3 ) 33.28
Multiply numerator and denominator by 10: 332.8 ÷ 193
193 goes into 332 once → 193, remainder 139.8
Bring down 0 → 1398
193 × 7 = 1351 → remainder 47
Bring down 0 → 470
193 × 2 = 386 → remainder 84
Bring down 0 → 840
193 × 4 = 772 → remainder 68
So 1.724... and continuing → approximately 1.72435...
But let’s check with calculator logic:
33.28 / 19.3 ≈ 1.7243523316...
We can round to reasonable digits — since inputs have 2-3 decimals, answer to 4 decimals is fine.
✔ Answer: 1.7244 (rounded to 4 decimal places)
Wait — actually, let’s be precise. The problem doesn’t specify rounding, so perhaps keep as fraction or exact decimal? But these are terminating? Let’s see:
Actually, 33.28 ÷ 19.3 = 3328/1930 = simplify? Divide numerator and denominator by 2: 1664/965
Divide 1664 ÷ 965:
965 × 1 = 965 → 1664 - 965 = 699
6990 ÷ 965 ≈ 7 → 965×7=6755 → 6990-6755=235
2350 ÷ 965 ≈ 2 → 1930 → remainder 420
4200 ÷ 965 ≈ 4 → 3860 → remainder 340
So 1.724... same as before.
Since it's a worksheet, likely expects decimal answer rounded reasonably.
I’ll go with 1.724
But let’s verify with actual division:
19.3 × 1.724 = 19.3 × 1.7 = 32.81, 19.3 × 0.024 = 0.4632 → total 33.2732 ≈ 33.28 — close enough.
Actually, 19.3 × 1.72435 = let’s not overcomplicate.
Standard approach: perform division and stop at 4 decimals.
✔ Final for this: 1.7244 (if rounded up) or 1.724 — I’ll use 1.724 as it’s sufficient.
Wait — let’s do exact:
33.28 ÷ 19.3 = ?
Multiply both by 100: 3328 ÷ 1930
Divide 3328 by 1930:
1930 × 1 = 1930 → subtract → 1398
Add decimal, add 0 → 13980
1930 × 7 = 13510 → subtract → 470
Add 0 → 4700
1930 × 2 = 3860 → subtract → 840
Add 0 → 8400
1930 × 4 = 7720 → subtract → 680
Add 0 → 6800
1930 × 3 = 5790 → subtract → 1010
So 1.7243... → so 1.7243
I think 1.724 is acceptable, but to be accurate, let’s say 1.7243
But perhaps the worksheet expects exact value? Since it’s decimal division, likely decimal answer.
I’ll go with 1.724 for simplicity, but technically it’s repeating or non-terminating.
Actually, 33.28 / 19.3 = 3328/1930 = 1664/965
1664 ÷ 965 = 1.7243523316... so to 4 decimals: 1.7244
Yes, round up because next digit is 5.
✔ Answer: 1.7244
---
Problem 2:
81.29 ÷ 27.2
Multiply both by 10: 812.9 ÷ 272
272 × 2 = 544
812.9 - 544 = 268.9
Bring down 0 → 2689
272 × 9 = 2448 → subtract → 241
Bring down 0 → 2410
272 × 8 = 2176 → subtract → 234
Bring down 0 → 2340
272 × 8 = 2176 → subtract → 164
So 2.988... → approximately 2.9886
Check: 27.2 × 2.988 = ?
27.2 × 3 = 81.6 → too big
27.2 × 2.9 = 78.88
81.29 - 78.88 = 2.41
2.41 / 27.2 ≈ 0.0886 → so 2.9886
✔ Answer: 2.9886 (to 4 decimals)
---
Problem 3:
6.9 ÷ 3.2
Multiply both by 10: 69 ÷ 32
32 × 2 = 64 → remainder 5
5.0 → 50 ÷ 32 = 1 → remainder 18
180 ÷ 32 = 5 → 160 → remainder 20
200 ÷ 32 = 6 → 192 → remainder 8
80 ÷ 32 = 2 → 64 → remainder 16
160 ÷ 32 = 5 → exactly
So 2.15625
✔ Answer: 2.15625
---
Problem 4:
3.7 ÷ 0.007
Multiply both by 1000: 3700 ÷ 7
7 × 528 = 3696 → remainder 4
4.0 → 40 ÷ 7 = 5 → 35 → rem 5
50 ÷ 7 = 7 → 49 → rem 1
10 ÷ 7 = 1 → 7 → rem 3
30 ÷ 7 = 4 → 28 → rem 2
20 ÷ 7 = 2 → 14 → rem 6
60 ÷ 7 = 8 → 56 → rem 4 → repeats
So 528.571428... → repeating 571428
But since 3.7 / 0.007 = 3700 / 7 = 528.571428...
To 4 decimals: 528.5714
✔ Answer: 528.5714
---
Problem 5:
1082.18 ÷ 39.2
Multiply both by 10: 10821.8 ÷ 392
392 × 27 = 392×20=7840, 392×7=2744 → total 10584
10821.8 - 10584 = 237.8
Bring down 0 → 2378
392 × 6 = 2352 → subtract → 26
Bring down 0 → 260
392 × 0 = 0 → so 0.6? Wait
After 27, we have 237.8, which is 2378 tenths? Better:
10821.8 ÷ 392
392 × 27 = 10584
Subtract: 10821.8 - 10584 = 237.8
Now 237.8 ÷ 392 = 0.6066...
So total 27.6066...
Compute: 237.8 / 392 = ?
392 × 0.6 = 235.2 → subtract from 237.8 → 2.6
2.6 / 392 = 0.00663...
So 27.60663...
To 4 decimals: 27.6066
Check: 39.2 × 27.6066 ≈ ?
39.2 × 27 = 1058.4
39.2 × 0.6 = 23.52 → total 1081.92
39.2 × 0.0066 = 0.25872 → total 1082.17872 ≈ 1082.18 — good.
✔ Answer: 27.6066
---
Problem 6:
23.176 ÷ 19.2
Multiply both by 10: 231.76 ÷ 192
192 × 1 = 192 → subtract from 231.76 → 39.76
Bring down 0 → 397.6
192 × 2 = 384 → subtract → 13.6
Bring down 0 → 136.0
192 × 0 = 0 → so 0.07? Wait
After 1.2, we have 13.6, which is 136 tenths?
231.76 ÷ 192
192 × 1.2 = 230.4
231.76 - 230.4 = 1.36
1.36 / 192 = 0.007083...
So total 1.207083...
To 4 decimals: 1.2071
Check: 19.2 × 1.2071 = 19.2 × 1.2 = 23.04, 19.2 × 0.0071 = 0.13632 → total 23.17632 ≈ 23.176 — close.
Actually, 19.2 × 1.20708333... = 23.176 exactly? Let's see:
23.176 ÷ 19.2 = 23176 / 19200 = simplify
Divide numerator and denominator by 16: 1448.5 / 1200 — not integer.
23176 ÷ 19200 = ?
Do division: 23176 ÷ 19200 = 1.20708333...
So to 4 decimals: 1.2071
✔ Answer: 1.2071
---
Now compile all answers:
Products:
1. 5637
2. 51.6758
3. 298.1269
4. 1395.2034
5. 1.632323
6. 3042.7182
Quotients:
1. 1.7244
2. 2.9886
3. 2.15625
4. 528.5714
5. 27.6066
6. 1.2071
Note: For quotient 3, it's exact 2.15625, so no rounding needed.
Final Answer:
Products:
1. 5637
2. 51.6758
3. 298.1269
4. 1395.2034
5. 1.632323
6. 3042.7182
Quotients:
1. 1.7244
2. 2.9886
3. 2.15625
4. 528.5714
5. 27.6066
6. 1.2071
Parent Tip: Review the logic above to help your child master the concept of multiplying and dividing decimals worksheet for 6th grade.
