Decimal operations practice worksheet with problems and answer section.

Let’s solve each problem one by one. I’ll show the steps clearly so you can follow along.

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1) 77.2 - 43.778

Align decimals:

```
77.200
- 43.778
________
```

Subtract from right to left:

- 0 - 8 → borrow → 10 - 8 = 2 (but we borrowed, so next digit becomes 9)
- 9 - 7 = 2
- 1 (after borrowing) - 7 → borrow again → 11 - 7 = 4
- 6 (after borrowing) - 3 = 3
- 7 - 4 = 3

Wait — let me do it carefully:

Actually:

77.200
-43.778
= ?

Start from thousandths place:
0 - 8 → can’t do → borrow from hundredths → but hundredths is 0 → keep going.

Better to write as:

77.200
-43.778
________

Thousandths: 0 - 8 → borrow → 10 - 8 = 2 (hundredths becomes 9 after borrow? Wait no — let's line up properly and subtract step by step.

Actually, easier way:

77.200 minus 43.778:

Do 77.200 - 43.000 = 34.200
Then subtract 0.778 more: 34.200 - 0.778 = 33.422

Check with direct subtraction:

```
77.200
- 43.778
________
33.422
```

Yes! Because:

From right:
- 0 - 8 → borrow → 10 - 8 = 2 (tenths place now has 9 instead of 0? Let’s track borrows.)

Actually, standard algorithm:

Write:

77.200
- 43.778
_________

Start at thousandths: 0 < 8 → borrow from hundredths → but hundredths is 0 → go to tenths → also 0 → go to units.

Units digit is 7 (in 77.200). So:

Borrow 1 from units → units become 6, tenths get 10 → but we need to borrow for hundredths and thousandths.

So:

After borrowing chain:

Thousandths: 10 - 8 = 2
Hundredths: 9 (because we borrowed 1 for thousandths) - 7 = 2
Tenths: 9 (borrowed 1 for hundredths) - 7 = 2
Units: 6 (borrowed 1 for tenths) - 3 = 3
Tens: 7 - 4 = 3

Wait — that gives 33.222? That’s wrong.

I think I messed up.

Let me use calculator-style thinking:

77.2 - 43.778 = ?

Convert to same decimal places: 77.200 - 43.778

Now subtract:

77.200
-43.778
= ?

Do 77.200 - 43.778:

Think: 77.200 - 43.778 = (77.200 - 43.000) - 0.778 = 34.200 - 0.778

34.200 - 0.778:

34.200
- 0.778
= 33.422

Yes! Because:

34.200 - 0.700 = 33.500
33.500 - 0.078 = 33.422

So answer is 33.422

✔ Confirmed.

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2) 2.072 ÷ 5.6

To divide decimals, make divisor whole number.

Multiply numerator and denominator by 10:
→ 20.72 ÷ 56

Now divide 20.72 by 56.

56 goes into 207 how many times? (since 20.72 → think 2072 ÷ 5600? Better to set up long division.)

Actually: 20.72 ÷ 56

56 > 20 → so 0. something.

Add decimal point and zeros: 20.720 ÷ 56

56 into 207 → 3 times (56×3=168), subtract: 207-168=39

Bring down 2 → 392

56 into 392 → exactly 7 times (56×7=392)

So we have 0.37

But wait — original was 20.72 ÷ 56 → which is 0.37

But we multiplied numerator and denominator by 10 earlier? No:

Original: 2.072 ÷ 5.6

We did: multiply both by 10 → 20.72 ÷ 56 → yes.

So 20.72 ÷ 56 = 0.37

Check: 56 × 0.37 = 56×0.3=16.8, 56×0.07=3.92 → total 20.72 ✔

So answer is 0.37

Wait — but 2.072 ÷ 5.6 should be same as 20.72 ÷ 56 = 0.37

Yes.

But let me confirm with another way:

2.072 / 5.6 = ?

Divide both by 0.8? Or just calculate:

5.6 × 0.37 = 5.6 × 0.3 = 1.68, 5.6 × 0.07 = 0.392 → total 2.072 ✔

Perfect.

Answer: 0.37

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3) 6.811 × 4.997

This is multiplication of two decimals.

First, ignore decimals: 6811 × 4997

That’s big — maybe approximate or compute step by step.

Note: 4.997 is almost 5, so 6.811 × 5 = 34.055, then subtract 6.811 × 0.003

Because 4.997 = 5 - 0.003

So:

6.811 × 4.997 = 6.811 × (5 - 0.003) = 6.811×5 - 6.811×0.003

6.811 × 5 = 34.055

6.811 × 0.003 = 0.020433

So 34.055 - 0.020433 = 34.034567

Is that accurate?

Let me verify with direct multiplication.

Set up:

6.811
× 4.997
________

First, multiply 6811 × 4997

But easier to do:

6.811 × 4.997

Compute step by step:

Break 4.997 = 4 + 0.9 + 0.09 + 0.007? Maybe not.

Use:

6.811 × 5 = 34.055
Minus 6.811 × 0.003 = 0.020433
So 34.055 - 0.020433 = 34.034567

Now, check decimal places: 6.811 has 3 decimals, 4.997 has 3 decimals → total 6 decimals in product.

34.034567 has 6 decimals? 34.034567 → that’s 6 digits after decimal? No:

34.034567 → digits after decimal: 034567 → 6 digits → yes.

But is this exact?

Let me compute 6811 × 4997.

6811 × 5000 = 34,055,000
Minus 6811 × 3 = 20,433
So 34,055,000 - 20,433 = 34,034,567

Since we had 3+3=6 decimal places, so 34.034567

Yes!

So answer is 34.034567

But perhaps round? The problem doesn't say, so keep full precision.

In context of worksheet, probably expect full answer.

So 34.034567

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4) 27.001 - 7.5

Align decimals:

27.001
- 7.500
_______

Subtract:

1 - 0 = 1 (thousandths)
0 - 0 = 0 (hundredths)
0 - 5 → can't → borrow from units.

Units is 7, but 7.001 → actually:

27.001
- 7.500

Start from right:

Thousandths: 1 - 0 = 1
Hundredths: 0 - 0 = 0
Tenths: 0 - 5 → can't → borrow from units.

Units digit is 7 (of 27), so borrow 1 → units become 6, tenths become 10.

Now tenths: 10 - 5 = 5
Units: 6 - 7 → can't → borrow from tens.

Tens is 2, borrow 1 → tens become 1, units become 16.

Units: 16 - 7 = 9
Tens: 1 - 0 = 1

So result: 19.501

Check: 27.001 - 7.5 = 27.001 - 7.500 = 19.501 ✔

Answer: 19.501

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5) 4.23 × 9

Simple multiplication.

4.23 × 9:

4 × 9 = 36
0.23 × 9 = 2.07
Total: 36 + 2.07 = 38.07

Or directly:

4.23
× 9
_____
38.07

Yes.

Answer: 38.07

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6) 19.2 + 31.82

Align decimals:

19.20
+31.82
______
51.02

Because:

0 + 2 = 2 (hundredths)
2 + 8 = 10 → write 0, carry 1 (tenths)
9 + 1 + 1(carry) = 11 → write 1, carry 1 (units)
1 + 3 + 1(carry) = 5 (tens)

So 51.02

Answer: 51.02

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7) 97.68 - 32.3

Align:

97.68
-32.30
______
65.38

Because:

8 - 0 = 8
6 - 3 = 3
7 - 2 = 5
9 - 3 = 6

So 65.38

Answer: 65.38

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8) 0.468 ÷ 6.5

Make divisor whole: multiply numerator and denominator by 10 → 4.68 ÷ 65

Now divide 4.68 by 65.

65 > 4.68 → so 0.point something.

4.680 ÷ 65

65 into 468 (move decimal)

65 × 7 = 455
468 - 455 = 13
Bring down 0 → 130
65 × 2 = 130 → exactly

So 0.072

Because: 4.68 ÷ 65 = 0.072

Check: 65 × 0.072 = 65 × 0.07 = 4.55, 65 × 0.002 = 0.13 → total 4.68 ✔

Original was 0.468 ÷ 6.5 = same as 4.68 ÷ 65 = 0.072

Answer: 0.072

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9) 0.6144 ÷ 1.6

Multiply num and den by 10: 6.144 ÷ 16

Divide 6.144 by 16.

16 into 61 (from 6.144) → 3 times (16×3=48), subtract: 61-48=13

Bring down 4 → 134

16 into 134 → 8 times (16×8=128), subtract: 134-128=6

Bring down 4 → 64

16 into 64 → 4 times

So 0.384

Because: 6.144 ÷ 16 = 0.384

Check: 16 × 0.384 = 16×0.3=4.8, 16×0.08=1.28, 16×0.004=0.064 → total 4.8+1.28=6.08, +0.064=6.144 ✔

Answer: 0.384

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10) 4.4 × 2.727

Multiply decimals.

First, 44 × 2727, then adjust decimals.

4.4 has 1 decimal, 2.727 has 3 decimals → total 4 decimals in product.

Compute 44 × 2727.

Easier: 4.4 × 2.727

Break it:

4.4 × 2 = 8.8
4.4 × 0.7 = 3.08
4.4 × 0.027 = ? First, 4.4 × 0.02 = 0.088, 4.4 × 0.007 = 0.0308 → total 0.1188

Now sum:

8.8 + 3.08 = 11.88
11.88 + 0.1188 = 11.9988

Direct multiplication:

4.4
×2.727
_______

First, 44 × 2727 = ?

40 × 2727 = 109,080
4 × 2727 = 10,908
Total = 109,080 + 10,908 = 119,988

Now, since 4.4 has 1 decimal, 2.727 has 3 → total 4 decimals → so 11.9988

Yes.

Answer: 11.9988

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11) 20.97 + 85.62

Align:

20.97
+85.62
______
106.59

Because:

7+2=9
9+6=15 → write 5, carry 1
0+5+1=6
2+8=10 → write 0, carry 1 → but 20 + 85 = 105, plus carries? Wait:

Actually:

Hundredths: 7+2=9
Tenths: 9+6=15 → write 5, carry 1 to units
Units: 0+5+1=6
Tens: 2+8=10 → write 0, carry 1 to hundreds → so 106.59

Yes.

Answer: 106.59

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12) 48 + 58.1

48.0 + 58.1 = 106.1

Because:

0 + 1 = 1 (tenths)
8 + 8 = 16 → write 6, carry 1
4 + 5 + 1 = 10 → write 0, carry 1 → 106.1

Answer: 106.1

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Now, compiling all answers:

1) 33.422
2) 0.37
3) 34.034567
4) 19.501
5) 38.07
6) 51.02
7) 65.38
8) 0.072
9) 0.384
10) 11.9988
11) 106.59
12) 106.1

I double-checked each calculation. All seem correct.

Final Answer:
1) 33.422
2) 0.37
3) 34.034567
4) 19.501
5) 38.07
6) 51.02
7) 65.38
8) 0.072
9) 0.384
10) 11.9988
11) 106.59
12) 106.1