Worksheet for practicing long division using a grid format.
Long division problems with grid lines for students to solve, labeled "Long Division with a Grid (A)".
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Step-by-step solution for: 4-Digit by 1-Digit Long Division with Remainders with Grid ...
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Show Answer Key & Explanations
Step-by-step solution for: 4-Digit by 1-Digit Long Division with Remainders with Grid ...
Let’s solve each long division problem step by step. We’ll go one at a time, carefully checking our work.
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Problem 1: 7565 ÷ 4
We divide 7565 by 4 using long division with grid (we’ll do it mentally but show steps clearly).
- 4 goes into 7 → 1 time (1 × 4 = 4), subtract: 7 - 4 = 3
- Bring down 5 → 35
- 4 goes into 35 → 8 times (8 × 4 = 32), subtract: 35 - 32 = 3
- Bring down 6 → 36
- 4 goes into 36 → 9 times (9 × 4 = 36), subtract: 0
- Bring down 5 → 5
- 4 goes into 5 → 1 time (1 × 4 = 4), subtract: 1
So quotient is 1891, remainder 1
But since the worksheet says “calculate each quotient”, and doesn’t mention remainders, we assume they want exact division or just the whole number part? Let’s check if any are not divisible.
Wait — let’s double-check:
Actually, 4 × 1891 = 7564 → so 7565 - 7564 = 1 → yes, remainder 1.
But maybe the problems are designed to be exact? Let’s check others.
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Problem 2: 7244 ÷ 3
- 3 into 7 → 2 (2×3=6), rem 1
- Bring down 2 → 12
- 3 into 12 → 4 (4×3=12), rem 0
- Bring down 4 → 4
- 3 into 4 → 1 (1×3=3), rem 1
- Bring down 4 → 14
- 3 into 14 → 4 (4×3=12), rem 2
Quotient: 2414, remainder 2 → Not exact.
Hmm. Maybe we’re supposed to write the full quotient including decimal? But the grid suggests integer division.
Wait — perhaps I made a mistake. Let me recalculate 7244 ÷ 3.
3 × 2414 = 7242 → 7244 - 7242 = 2 → yes, remainder 2.
But let’s look at Problem 3: 3447 ÷ 2
That should be easy: 3447 is odd → divided by 2 will have remainder 1.
This suggests that maybe the worksheet expects us to compute the quotient as a whole number and ignore remainder? Or perhaps include remainder?
Looking back at title: “Calculate each quotient.” In math, quotient can mean the result of division, which may include remainder or decimal.
But in elementary school context, especially with grids, often they expect the whole number quotient and possibly remainder written separately.
However, looking at the layout — there’s no space for remainder. The grid is under the dividend, suggesting we fill in digits of quotient above.
In standard long division format shown here, the quotient is written on top, and you stop when you’ve used all digits.
So likely, they want the integer quotient (ignoring remainder) OR perhaps these ARE all divisible?
Wait — let me recheck Problem 1: 7565 ÷ 4
Is 7565 divisible by 4? Last two digits: 65 → 65 ÷ 4 = 16.25 → not divisible. So remainder exists.
Same for others.
Perhaps the instruction means to perform the division and write the quotient (whole number part) and that’s it.
Alternatively, maybe I misread the numbers?
Let me verify each problem again carefully.
---
Actually, let’s try solving them properly with long division steps and see what quotients we get.
I think the best approach is to compute each one accurately and report the quotient (integer part) unless specified otherwise.
But to be safe, let’s do exact division where possible.
Wait — perhaps some ARE divisible.
Let me test:
Problem 1: 7565 ÷ 4
As before: 4 × 1891 = 7564 → remainder 1 → quotient = 1891 R1
But maybe they want decimal? Unlikely with grid.
Another idea: perhaps the grid is for writing intermediate steps, and quotient is written above.
In that case, we write the quotient digit by digit.
For example, for 7565 ÷ 4:
Write 4 outside, 7565 inside.
Step 1: 4 into 7 → 1, write 1 above 7, multiply 1×4=4, subtract from 7 → 3
Bring down 5 → 35
4 into 35 → 8, write 8 above 5, 8×4=32, subtract → 3
Bring down 6 → 36
4 into 36 → 9, write 9 above 6, 9×4=36, subtract → 0
Bring down 5 → 5
4 into 5 → 1, write 1 above 5, 1×4=4, subtract → 1
So quotient written above is 1891, and remainder 1.
Similarly for others.
Since the worksheet says "calculate each quotient", and in many curricula, "quotient" refers to the integer result before remainder, I'll proceed with that.
But let's confirm with another problem.
Problem 2: 7244 ÷ 3
3 into 7 → 2, 2×3=6, sub → 1
Bring down 2 → 12
3 into 12 → 4, 4×3=12, sub → 0
Bring down 4 → 4
3 into 4 → 1, 1×3=3, sub → 1
Bring down 4 → 14
3 into 14 → 4, 4×3=12, sub → 2
Quotient: 2414, remainder 2
Problem 3: 3447 ÷ 2
2 into 3 → 1, 1×2=2, sub → 1
Bring down 4 → 14
2 into 14 → 7, 7×2=14, sub → 0
Bring down 4 → 4
2 into 4 → 2, 2×2=4, sub → 0
Bring down 7 → 7
2 into 7 → 3, 3×2=6, sub → 1
Quotient: 1723, remainder 1
Problem 4: 4544 ÷ 3
3 into 4 → 1, 1×3=3, sub → 1
Bring down 5 → 15
3 into 15 → 5, 5×3=15, sub → 0
Bring down 4 → 4
3 into 4 → 1, 1×3=3, sub → 1
Bring down 4 → 14
3 into 14 → 4, 4×3=12, sub → 2
Quotient: 1514, remainder 2
Problem 5: 6131 ÷ 4
4 into 6 → 1, 1×4=4, sub → 2
Bring down 1 → 21
4 into 21 → 5, 5×4=20, sub → 1
Bring down 3 → 13
4 into 13 → 3, 3×4=12, sub → 1
Bring down 1 → 11
4 into 11 → 2, 2×4=8, sub → 3
Quotient: 1532, remainder 3
Problem 6: 6131 ÷ 7
7 into 6 → 0, so consider 61
7 into 61 → 8, 8×7=56, sub → 5
Bring down 3 → 53
7 into 53 → 7, 7×7=49, sub → 4
Bring down 1 → 41
7 into 41 → 5, 5×7=35, sub → 6
Quotient: 875, remainder 6
All have remainders. But perhaps the worksheet still wants the quotient as the integer part.
Maybe I should present the answers as quotients with remainders, but the format doesn't allow it.
Another thought: perhaps "quotient" here means the complete result, but since it's grid-based, likely integer quotient.
To resolve this, let's assume that for this level, they want the whole number quotient (the number you write on top during long division), and we'll provide that.
So final quotients are:
1. 7565 ÷ 4 = 1891
2. 7244 ÷ 3 = 2414
3. 3447 ÷ 2 = 1723
4. 4544 ÷ 3 = 1514
5. 6131 ÷ 4 = 1532
6. 6131 ÷ 7 = 875
But wait — for problem 6, 6131 ÷ 7: let me verify 7 × 875 = ?
7 × 800 = 5600
7 × 75 = 525
Total = 5600 + 525 = 6125
6131 - 6125 = 6 → yes, remainder 6, so quotient 875 is correct.
Now, to ensure accuracy, let's list them clearly.
Final Answer:
The quotients for each division problem are:
- 7565 ÷ 4 = 1891
- 7244 ÷ 3 = 2414
- 3447 ÷ 2 = 1723
- 4544 ÷ 3 = 1514
- 6131 ÷ 4 = 1532
- 6131 ÷ 7 = 875
Note: All divisions have remainders, but since the task asks for "quotient", we provide the integer part obtained from long division.
Final Answer:
1891, 2414, 1723, 1514, 1532, 875
---
Problem 1: 7565 ÷ 4
We divide 7565 by 4 using long division with grid (we’ll do it mentally but show steps clearly).
- 4 goes into 7 → 1 time (1 × 4 = 4), subtract: 7 - 4 = 3
- Bring down 5 → 35
- 4 goes into 35 → 8 times (8 × 4 = 32), subtract: 35 - 32 = 3
- Bring down 6 → 36
- 4 goes into 36 → 9 times (9 × 4 = 36), subtract: 0
- Bring down 5 → 5
- 4 goes into 5 → 1 time (1 × 4 = 4), subtract: 1
So quotient is 1891, remainder 1
But since the worksheet says “calculate each quotient”, and doesn’t mention remainders, we assume they want exact division or just the whole number part? Let’s check if any are not divisible.
Wait — let’s double-check:
Actually, 4 × 1891 = 7564 → so 7565 - 7564 = 1 → yes, remainder 1.
But maybe the problems are designed to be exact? Let’s check others.
---
Problem 2: 7244 ÷ 3
- 3 into 7 → 2 (2×3=6), rem 1
- Bring down 2 → 12
- 3 into 12 → 4 (4×3=12), rem 0
- Bring down 4 → 4
- 3 into 4 → 1 (1×3=3), rem 1
- Bring down 4 → 14
- 3 into 14 → 4 (4×3=12), rem 2
Quotient: 2414, remainder 2 → Not exact.
Hmm. Maybe we’re supposed to write the full quotient including decimal? But the grid suggests integer division.
Wait — perhaps I made a mistake. Let me recalculate 7244 ÷ 3.
3 × 2414 = 7242 → 7244 - 7242 = 2 → yes, remainder 2.
But let’s look at Problem 3: 3447 ÷ 2
That should be easy: 3447 is odd → divided by 2 will have remainder 1.
This suggests that maybe the worksheet expects us to compute the quotient as a whole number and ignore remainder? Or perhaps include remainder?
Looking back at title: “Calculate each quotient.” In math, quotient can mean the result of division, which may include remainder or decimal.
But in elementary school context, especially with grids, often they expect the whole number quotient and possibly remainder written separately.
However, looking at the layout — there’s no space for remainder. The grid is under the dividend, suggesting we fill in digits of quotient above.
In standard long division format shown here, the quotient is written on top, and you stop when you’ve used all digits.
So likely, they want the integer quotient (ignoring remainder) OR perhaps these ARE all divisible?
Wait — let me recheck Problem 1: 7565 ÷ 4
Is 7565 divisible by 4? Last two digits: 65 → 65 ÷ 4 = 16.25 → not divisible. So remainder exists.
Same for others.
Perhaps the instruction means to perform the division and write the quotient (whole number part) and that’s it.
Alternatively, maybe I misread the numbers?
Let me verify each problem again carefully.
---
Actually, let’s try solving them properly with long division steps and see what quotients we get.
I think the best approach is to compute each one accurately and report the quotient (integer part) unless specified otherwise.
But to be safe, let’s do exact division where possible.
Wait — perhaps some ARE divisible.
Let me test:
Problem 1: 7565 ÷ 4
As before: 4 × 1891 = 7564 → remainder 1 → quotient = 1891 R1
But maybe they want decimal? Unlikely with grid.
Another idea: perhaps the grid is for writing intermediate steps, and quotient is written above.
In that case, we write the quotient digit by digit.
For example, for 7565 ÷ 4:
Write 4 outside, 7565 inside.
Step 1: 4 into 7 → 1, write 1 above 7, multiply 1×4=4, subtract from 7 → 3
Bring down 5 → 35
4 into 35 → 8, write 8 above 5, 8×4=32, subtract → 3
Bring down 6 → 36
4 into 36 → 9, write 9 above 6, 9×4=36, subtract → 0
Bring down 5 → 5
4 into 5 → 1, write 1 above 5, 1×4=4, subtract → 1
So quotient written above is 1891, and remainder 1.
Similarly for others.
Since the worksheet says "calculate each quotient", and in many curricula, "quotient" refers to the integer result before remainder, I'll proceed with that.
But let's confirm with another problem.
Problem 2: 7244 ÷ 3
3 into 7 → 2, 2×3=6, sub → 1
Bring down 2 → 12
3 into 12 → 4, 4×3=12, sub → 0
Bring down 4 → 4
3 into 4 → 1, 1×3=3, sub → 1
Bring down 4 → 14
3 into 14 → 4, 4×3=12, sub → 2
Quotient: 2414, remainder 2
Problem 3: 3447 ÷ 2
2 into 3 → 1, 1×2=2, sub → 1
Bring down 4 → 14
2 into 14 → 7, 7×2=14, sub → 0
Bring down 4 → 4
2 into 4 → 2, 2×2=4, sub → 0
Bring down 7 → 7
2 into 7 → 3, 3×2=6, sub → 1
Quotient: 1723, remainder 1
Problem 4: 4544 ÷ 3
3 into 4 → 1, 1×3=3, sub → 1
Bring down 5 → 15
3 into 15 → 5, 5×3=15, sub → 0
Bring down 4 → 4
3 into 4 → 1, 1×3=3, sub → 1
Bring down 4 → 14
3 into 14 → 4, 4×3=12, sub → 2
Quotient: 1514, remainder 2
Problem 5: 6131 ÷ 4
4 into 6 → 1, 1×4=4, sub → 2
Bring down 1 → 21
4 into 21 → 5, 5×4=20, sub → 1
Bring down 3 → 13
4 into 13 → 3, 3×4=12, sub → 1
Bring down 1 → 11
4 into 11 → 2, 2×4=8, sub → 3
Quotient: 1532, remainder 3
Problem 6: 6131 ÷ 7
7 into 6 → 0, so consider 61
7 into 61 → 8, 8×7=56, sub → 5
Bring down 3 → 53
7 into 53 → 7, 7×7=49, sub → 4
Bring down 1 → 41
7 into 41 → 5, 5×7=35, sub → 6
Quotient: 875, remainder 6
All have remainders. But perhaps the worksheet still wants the quotient as the integer part.
Maybe I should present the answers as quotients with remainders, but the format doesn't allow it.
Another thought: perhaps "quotient" here means the complete result, but since it's grid-based, likely integer quotient.
To resolve this, let's assume that for this level, they want the whole number quotient (the number you write on top during long division), and we'll provide that.
So final quotients are:
1. 7565 ÷ 4 = 1891
2. 7244 ÷ 3 = 2414
3. 3447 ÷ 2 = 1723
4. 4544 ÷ 3 = 1514
5. 6131 ÷ 4 = 1532
6. 6131 ÷ 7 = 875
But wait — for problem 6, 6131 ÷ 7: let me verify 7 × 875 = ?
7 × 800 = 5600
7 × 75 = 525
Total = 5600 + 525 = 6125
6131 - 6125 = 6 → yes, remainder 6, so quotient 875 is correct.
Now, to ensure accuracy, let's list them clearly.
Final Answer:
The quotients for each division problem are:
- 7565 ÷ 4 = 1891
- 7244 ÷ 3 = 2414
- 3447 ÷ 2 = 1723
- 4544 ÷ 3 = 1514
- 6131 ÷ 4 = 1532
- 6131 ÷ 7 = 875
Note: All divisions have remainders, but since the task asks for "quotient", we provide the integer part obtained from long division.
Final Answer:
1891, 2414, 1723, 1514, 1532, 875
Parent Tip: Review the logic above to help your child master the concept of long division worksheet with grid.