Long Division interactive worksheet for 4 - Free Printable

Let’s solve each division problem step by step using the long division method: Divide, Multiply, Subtract, Bring Down.

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Problem a: 81 ÷ 4

Step 1: How many times does 4 go into 8? → 2
Write 2 above the 8.
Multiply: 2 × 4 = 8
Subtract: 8 - 8 = 0
Bring down the 1 → now we have 1

Step 2: How many times does 4 go into 1? → 0 (since 4 > 1)
Write 0 above the 1.
Multiply: 0 × 4 = 0
Subtract: 1 - 0 = 1
No more digits to bring down → remainder is 1

So quotient is 20, remainder 1

But since the worksheet shows 3 boxes for the quotient, maybe they expect decimal or just fill in what fits. But looking at layout — it's likely expecting whole number with remainder shown below.

Actually, let’s check again — perhaps I misread the box structure.

Looking at problem a:

It has:
- 3 boxes on top → so maybe they want 3-digit answer? But 81 ÷ 4 is only 20.something.

Wait — actually, looking carefully at the layout:

In problem a:
Divisor: 4
Dividend: 81
Top row: 3 empty boxes → probably meant for quotient digits as you go.

Standard way:

_2_0_
4)8 1
-8
--
0 1
-0
--
1 ← remainder

So quotient is 20, remainder 1.

But the top has 3 boxes — maybe they expect “020” or something? No, that doesn’t make sense.

Alternatively, perhaps the first box is for tens place, second for ones, third for remainder? But usually remainder goes below.

Looking at other problems:

Problem b: 85 ÷ 5 → should be 17, and top has 2 boxes → matches.

Problem c: 182 ÷ 2 → 91, top has 2 boxes → but 91 is two digits, okay.

Problem d: 771 ÷ 6 → 128.5? Wait, 6×128=768, remainder 3 → so quotient 128, which is 3 digits, and top has 4 boxes? Hmm.

Wait — problem d dividend is 771, divisor 6.

Let me recalculate all properly.

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a. 81 ÷ 4

4 into 8 → 2
2 × 4 = 8
8 - 8 = 0
Bring down 1 → 1
4 into 1 → 0
0 × 4 = 0
1 - 0 = 1 → remainder

Quotient: 20, remainder 1

But the top has 3 boxes — perhaps they want us to write 2, then 0, and leave last blank? Or maybe it's a typo. In standard long division, we don't pad with leading zeros.

Perhaps the third box is for the remainder? But usually remainder is written below.

Looking at the diagram:

After subtracting, there’s a line, then another subtraction, then final box at bottom — that’s likely the remainder.

And top boxes are for quotient digits.

For 81 ÷ 4:

First digit: 2 (above 8)
Second digit: 0 (above 1)
Third box? Maybe not used? Or perhaps they expect decimal?

But no decimals indicated.

I think for this level, they might accept quotient as 20, and remainder 1.

But let’s see how the boxes are arranged.

In problem a:

Top: [ ][ ][ ] → three boxes over 81? That would imply quotient up to hundreds, but 81 is less than 100.

Perhaps it's a mistake in the worksheet design. We’ll proceed with correct math.

Similarly, problem b: 85 ÷ 5

5 into 8 → 1
1 × 5 = 5
8 - 5 = 3
Bring down 5 → 35
5 into 35 → 7
7 × 5 = 35
35 - 35 = 0

Quotient: 17, remainder 0

Top has 2 boxes → perfect.

Problem c: 182 ÷ 2

2 into 1 → 0? But we don’t write leading zero. Actually, 2 into 18 → 9

Better:

2 into 1 → can’t, so take 18
2 into 18 → 9
9 × 2 = 18
18 - 18 = 0
Bring down 2 → 2
2 into 2 → 1
1 × 2 = 2
2 - 2 = 0

Quotient: 91, remainder 0

Top has 2 boxes → good.

Problem d: 771 ÷ 6

6 into 7 → 1
1 × 6 = 6
7 - 6 = 1
Bring down 7 → 17
6 into 17 → 2
2 × 6 = 12
17 - 12 = 5
Bring down 1 → 51
6 into 51 → 8
8 × 6 = 48
51 - 48 = 3

Quotient: 128, remainder 3

Top has 4 boxes — but 128 is 3 digits. Perhaps the fourth box is unused or for decimal? But no indication.

Maybe they expect to write 0128? Unlikely.

Perhaps the first box is for hundreds, etc., and we start from left.

In any case, mathematically:

a. 81 ÷ 4 = 20 R1
b. 85 ÷ 5 = 17 R0
c. 182 ÷ 2 = 91 R0
d. 771 ÷ 6 = 128 R3

Now, to fill the boxes as per diagram:

For a:

Top: first box: 2, second box: 0, third box: ? (probably leave blank or put nothing, but since it's there, maybe they expect remainder? But remainder is at bottom)

Looking at the diagram structure:

In a:

After first subtraction, there’s a box under the 8, then arrow down to next line, then two boxes, then minus, then one box, then line, then one box at bottom.

Standard long division format:

q1 q2
-------
d ) n1 n2
-m1
----
r1 n3
-m2
----
r2

For a: 4 ) 8 1

Step 1: 4 into 8 → 2, write 2 above 8
Multiply: 2*4=8, write under 8
Subtract: 8-8=0
Bring down 1 → now 01 or just 1

Step 2: 4 into 1 → 0, write 0 above 1
Multiply: 0*4=0, write under 1
Subtract: 1-0=1 → remainder

So the boxes:

Top: [2] [0] [ ] → but there are three boxes. Perhaps the third is not used, or maybe they want the remainder in the last top box? Unconventional.

Perhaps for single-digit dividends after bring down, they still use a box.

Another possibility: in some formats, they include the remainder in the quotient area, but I doubt it.

Let’s look at problem d: 771 ÷ 6, top has 4 boxes.

771 ÷ 6 = 128.5? But 6*128=768, 771-768=3, so 128 R3.

If they expect decimal, 128.5, but 0.5 is 3/6, so yes, but usually not unless specified.

The worksheet says "find the quotient", and in elementary math, quotient often means integer part with remainder.

Moreover, the bottom box is likely for remainder.

In problem a, bottom box is after last subtraction, so remainder.

Similarly for others.

So for a:

Quotient digits: 2 and 0 → so first two top boxes: 2, 0; third box might be extra or for something else. Perhaps it's a mistake, or perhaps they want us to write the remainder in the last top box? But that would be confusing.

Maybe for consistency, since 81 is two digits, quotient is two digits, so third box is unused.

But in the diagram, for a, there are three top boxes, for b two, for c two, for d four — so it varies based on expected quotient length.

For 81÷4, quotient is 20, two digits, so perhaps only first two boxes used, third left blank.

Similarly, for d, 128 is three digits, but four boxes — maybe they expect 0128 or something? No.

771 ÷ 6: let's calculate again.

6 into 7 → 1 (hundreds place)
1*6=6, subtract from 7 → 1
Bring down 7 → 17
6 into 17 → 2 (tens place)
2*6=12, subtract → 5
Bring down 1 → 51
6 into 51 → 8 (ones place)
8*6=48, subtract → 3

So quotient is 128, three digits. Top has four boxes — perhaps the first box is for thousands, which is 0, but we don't write it.

I think it's safe to assume that we fill the quotient digits from left to right, and if there are extra boxes, leave them blank or ignore.

But to match the diagram, let's fill as per calculation.

Perhaps for a, since 81 is two digits, and divisor 4, quotient is two digits, so use first two boxes.

Similarly for others.

Let's do each one with filled boxes.

a. 81 ÷ 4

Top boxes: [2] [0] [ ] (third box empty or not used)

Under 8: [8] (from 2*4)

Then after bring down, we have 1, so next line: [0] [1] ? Let's see the diagram.

In the diagram for a:

After first subtraction, there's a box under the 8, then an arrow down to the next line, which has two boxes, then a minus sign, then one box, then line, then one box at bottom.

Standard:

2 0
-----
4 ) 8 1
-8
---
0 1
-0
---
1

So:

- First top box: 2 (above 8)
- Second top box: 0 (above 1)
- Third top box: ? perhaps not used, or maybe they have an extra box by mistake.

In the subtraction part:

Under 8: box with 8

Then below that, after bring down, we have "0 1" — so two boxes: first is 0 (from the subtraction result), second is 1 (brought down)

Then minus, then under that, a box with 0 (from 0*4)

Then line, then bottom box with 1 (remainder)

So for a:

Top: [2] [0] [ ] — but there are three boxes. Perhaps the third is for the remainder? But usually not.

Maybe in this worksheet, the top boxes include the remainder position, but that would be unusual.

Another idea: perhaps for the quotient, they want all digits including leading zero if necessary, but 81÷4 is 20, not 020.

I think it's best to proceed with correct values and fill the boxes as per standard long division.

Let's list the answers clearly.

Final Answers:

a. Quotient: 20, Remainder: 1
b. Quotient: 17, Remainder: 0
c. Quotient: 91, Remainder: 0
d. Quotient: 128, Remainder: 3

Now, to present in the boxed format as per the worksheet.

Since the user asked to solve the problem, and the problem is to find the quotient, and in context, quotient may include remainder or not, but typically in such worksheets, they expect the full division result.

But the instruction is "find the quotient", and in mathematics, quotient can mean the integer part, with remainder separate.

Given that, and the diagrams have space for remainder at bottom, I'll provide quotient and remainder for each.

For the response, since no explanation is requested (ExplainAnswer=false), I'll just give the final answers.

But the rules say: "Complete ALL reasoning and explanations BEFORE writing the Final Answer." and "If ExplainAnswer is false, completely omit that section."

Also, "Final Answer: [Provide only the final correct answer]"

So I need to output only the final answer, but after reasoning in my mind.

The final answer should be the solutions to a,b,c,d.

Perhaps list them as:

a. 20 R1
b. 17 R0
c. 91 R0
d. 128 R3

Or since the worksheet has boxes, maybe just the numbers.

But for clarity, I'll state the quotient and remainder.

Since the problem says "find the quotient", and in some contexts quotient includes the remainder, but usually not.

In long division, the quotient is the result of division, which can be expressed as mixed number, but here likely integer quotient with remainder.

I think for this level, they expect the integer quotient and the remainder.

So for the final answer, I'll provide:

a. Quotient: 20, Remainder: 1
b. Quotient: 17, Remainder: 0
c. Quotient: 91, Remainder: 0
d. Quotient: 128, Remainder: 3

To match the box-filling, perhaps just the numbers.

But since the user didn't specify, I'll go with clear statements.

In the final answer section, I can write:

a. 20 R1
b. 17
c. 91
d. 128 R3

But for b and c, remainder 0, so sometimes omitted.

To be consistent, include remainder.

Another way: in the worksheet, the bottom box is for remainder, so for b and c, it should be 0.

So for final answer, I'll list the quotient and remainder for each.

Let's confirm calculations once more.

a. 4 * 20 = 80, 81 - 80 = 1 → correct.

b. 5 * 17 = 85, 85 - 85 = 0 → correct.

c. 2 * 91 = 182, 182 - 182 = 0 → correct.

d. 6 * 128 = 768, 771 - 768 = 3 → correct.

All good.

So Final Answer:

a. Quotient: 20, Remainder: 1
b. Quotient: 17, Remainder: 0
c. Quotient: 91, Remainder: 0
d. Quotient: 128, Remainder: 3

But to make it concise, perhaps:

a. 20 R1
b. 17 R0
c. 91 R0
d. 128 R3

Yes.

Since the worksheet might expect only the quotient number, but given the remainder boxes, I think including remainder is fine.

For the response, I'll box the answers as per the problems.

Final Answer:
a. 20 R1
b. 17 R0
c. 91 R0
d. 128 R3