Math worksheet focused on long division, featuring four problems with step-by-step instructions and a reminder of the division steps: Divide, Multiply, Subtract, Bring Down.
Division worksheet for students to practice long division with step-by-step guidance and examples.
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Step-by-step solution for: Long Division interactive activity for 4
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Show Answer Key & Explanations
Step-by-step solution for: Long Division interactive activity for 4
Let’s solve each long division problem step by step.
---
Problem a: 67 ÷ 3
Step 1: Divide
How many times does 3 go into 6? → 2 times (because 3 × 2 = 6)
Write 2 above the 6.
Step 2: Multiply
3 × 2 = 6 → write 6 under the 6 in 67.
Step 3: Subtract
6 - 6 = 0
Step 4: Bring Down
Bring down the 7 → now we have 07, which is just 7.
Now repeat:
Step 5: Divide
How many times does 3 go into 7? → 2 times (3 × 2 = 6)
Write 2 next to the first 2 → so quotient is 22 so far.
Step 6: Multiply
3 × 2 = 6 → write under the 7.
Step 7: Subtract
7 - 6 = 1
No more digits to bring down → remainder is 1.
✔ So, 67 ÷ 3 = 22 R1
But since the worksheet has 3 boxes for the quotient, and no remainder box shown, maybe they want only the whole number part? Let’s check others — all are set up with 3-digit quotients, but some dividends are 2-digit. Probably, leading zeros are allowed or it's just formatting.
Actually, looking at the setup:
For 67 ÷ 3:
- First digit of quotient goes over the 6 → that’s tens place.
- Second digit goes over the 7 → ones place.
- Third box? Maybe for decimal? But this is likely integer division with remainder.
Wait — let’s look at the structure again. The quotient has 3 blank boxes above the dividend. For 67 (2-digit), probably the first box is empty or zero? But standard long division doesn’t pad with leading zeros.
Alternatively, perhaps the third box is for the remainder? No, remainder is written below.
Looking at problem c and d — they have 3-digit dividends, so 3-digit quotients make sense.
For 2-digit dividends like 67 and 88, the quotient will be 2-digit, so maybe the first box is left blank? Or perhaps it’s a typo? But let’s proceed with correct math.
Actually, in long division layout, you write the quotient digits directly above the corresponding digits of the dividend.
So for 67 ÷ 3:
__22__
3 ) 67
6
--
7
6
--
1
Quotient is 22, remainder 1.
But the template has 3 boxes. Maybe for consistency, we can write it as 022? That would be unusual.
Wait — let’s do problem b similarly.
---
Problem b: 88 ÷ 7
Step 1: 7 into 8 → 1 time (7×1=7)
Write 1 above the first 8.
Step 2: 7×1=7 → subtract from 8 → 1
Step 3: Bring down the second 8 → makes 18
Step 4: 7 into 18 → 2 times (7×2=14)
Write 2 above the second 8.
Step 5: 18 - 14 = 4 → remainder 4
So quotient is 12, remainder 4.
Again, 2-digit quotient.
---
Problem c: 423 ÷ 3
This is 3-digit, so 3-digit quotient expected.
Step 1: 3 into 4 → 1 time (3×1=3)
Write 1 above 4.
Subtract: 4 - 3 = 1
Bring down 2 → makes 12
Step 2: 3 into 12 → 4 times (3×4=12)
Write 4 above 2.
Subtract: 12 - 12 = 0
Bring down 3 → makes 03 or just 3
Step 3: 3 into 3 → 1 time (3×1=3)
Write 1 above 3.
Subtract: 3 - 3 = 0
✔ Quotient: 141, remainder 0.
Perfect — fits 3 boxes.
---
Problem d: 640 ÷ 5
Step 1: 5 into 6 → 1 time (5×1=5)
Write 1 above 6.
Subtract: 6 - 5 = 1
Bring down 4 → makes 14
Step 2: 5 into 14 → 2 times (5×2=10)
Write 2 above 4.
Subtract: 14 - 10 = 4
Bring down 0 → makes 40
Step 3: 5 into 40 → 8 times (5×8=40)
Write 8 above 0.
Subtract: 40 - 40 = 0
✔ Quotient: 128, remainder 0.
---
Now back to problems a and b — they have 2-digit dividends but 3-box quotient templates. In educational worksheets, sometimes they include an extra box for alignment or future use, but mathematically, the quotient is 2-digit.
However, looking at the arrow placements and subtraction steps, for problem a:
After bringing down 7, we get 7, divide by 3 → 2, multiply 6, subtract → 1. So final answer should be 22 with remainder 1.
Similarly for b: 12 with remainder 4.
But the worksheet says “Find the quotient.” — which usually means the whole number part, ignoring remainder unless specified.
Also, note that in problem c and d, remainders are 0, so no issue.
Perhaps for a and b, we should write the quotient as 2-digit, leaving the first box blank? But the instruction doesn't say.
Another thought: maybe the third box is for the remainder? But in the diagram, the remainder is written at the bottom after last subtraction.
Looking at the structure:
In problem a:
[ ][ ][ ] ← quotient
3 ) 6 7
[ ] ← 3×first digit
----
[ ][ ] ← result after bring down
- [ ] ← 3×second digit
----
[ ] ← remainder
So the quotient has three boxes, but for 67÷3, only two digits are used. Probably, the first box is not used, or perhaps it's a mistake. But to match the format, maybe we put 0 in the first box? That would be incorrect mathematically.
I think the best approach is to provide the correct mathematical quotient, and if the template has extra boxes, leave them blank or assume it's for alignment.
But since the user expects answers to fill in, and for c and d we have 3-digit quotients, for a and b, perhaps they expect 2-digit with leading space.
Wait — let's calculate numerically:
a. 67 ÷ 3 = 22.333... → integer quotient 22
b. 88 ÷ 7 = 12.571... → integer quotient 12
c. 423 ÷ 3 = 141
d. 640 ÷ 5 = 128
And in long division, we write the quotient digits above the dividend digits.
For 67:
- Above 6: 2
- Above 7: 2
- No third digit, so third box might be empty.
But the problem says "find the quotient", and in context, likely the whole number part.
Moreover, in the initial reminder, it says "Divide, Multiply, Subtract, Bring Down" — which is for integer division with possible remainder.
So I'll go with:
a. 22 (remainder 1)
b. 12 (remainder 4)
c. 141
d. 128
But to fit the 3-box format, perhaps for a and b, we write 022 and 012? That seems forced.
Another idea: maybe the third box is for the remainder? But in the diagram, the remainder is clearly at the bottom.
Looking at problem a's diagram:
After last subtraction, there's one box at the bottom — that's the remainder.
The quotient is above, with three boxes.
Perhaps for 2-digit dividends, the first quotient box is for hundreds place, which is 0.
In some curricula, they teach to consider the dividend as having leading zeros if needed, but that's advanced.
I think for simplicity and correctness, I'll provide the actual quotient values, and assume the student writes them in the appropriate boxes.
Since the worksheet is titled "Division" and uses long division steps, and for c and d it works perfectly, for a and b, the quotient is 2-digit, so likely the first box is left blank or not used.
But to give a concrete answer, I'll state the numerical quotient.
Final decision:
a. 22
b. 12
c. 141
d. 128
And ignore the extra box for a and b, or consider it as 022 etc., but that's not standard.
Upon second thought, in the diagram for problem a, the first subtraction is under the 6, then bring down 7, then subtract under the 7, so the quotient has two digits: one over 6, one over 7. The third box might be a red herring or for decimal, but since no decimal point, probably not.
I think it's safe to provide the correct quotients.
So:
a. 67 ÷ 3 = 22 R1 → quotient is 22
b. 88 ÷ 7 = 12 R4 → quotient is 12
c. 423 ÷ 3 = 141
d. 640 ÷ 5 = 128
Now, to confirm calculations:
a. 3 * 22 = 66, 67 - 66 = 1 → correct
b. 7 * 12 = 84, 88 - 84 = 4 → correct
c. 3 * 141 = 423 → correct
d. 5 * 128 = 640 → correct
All good.
Final Answer:
a. 22
b. 12
c. 141
d. 128
---
Problem a: 67 ÷ 3
Step 1: Divide
How many times does 3 go into 6? → 2 times (because 3 × 2 = 6)
Write 2 above the 6.
Step 2: Multiply
3 × 2 = 6 → write 6 under the 6 in 67.
Step 3: Subtract
6 - 6 = 0
Step 4: Bring Down
Bring down the 7 → now we have 07, which is just 7.
Now repeat:
Step 5: Divide
How many times does 3 go into 7? → 2 times (3 × 2 = 6)
Write 2 next to the first 2 → so quotient is 22 so far.
Step 6: Multiply
3 × 2 = 6 → write under the 7.
Step 7: Subtract
7 - 6 = 1
No more digits to bring down → remainder is 1.
✔ So, 67 ÷ 3 = 22 R1
But since the worksheet has 3 boxes for the quotient, and no remainder box shown, maybe they want only the whole number part? Let’s check others — all are set up with 3-digit quotients, but some dividends are 2-digit. Probably, leading zeros are allowed or it's just formatting.
Actually, looking at the setup:
For 67 ÷ 3:
- First digit of quotient goes over the 6 → that’s tens place.
- Second digit goes over the 7 → ones place.
- Third box? Maybe for decimal? But this is likely integer division with remainder.
Wait — let’s look at the structure again. The quotient has 3 blank boxes above the dividend. For 67 (2-digit), probably the first box is empty or zero? But standard long division doesn’t pad with leading zeros.
Alternatively, perhaps the third box is for the remainder? No, remainder is written below.
Looking at problem c and d — they have 3-digit dividends, so 3-digit quotients make sense.
For 2-digit dividends like 67 and 88, the quotient will be 2-digit, so maybe the first box is left blank? Or perhaps it’s a typo? But let’s proceed with correct math.
Actually, in long division layout, you write the quotient digits directly above the corresponding digits of the dividend.
So for 67 ÷ 3:
__22__
3 ) 67
6
--
7
6
--
1
Quotient is 22, remainder 1.
But the template has 3 boxes. Maybe for consistency, we can write it as 022? That would be unusual.
Wait — let’s do problem b similarly.
---
Problem b: 88 ÷ 7
Step 1: 7 into 8 → 1 time (7×1=7)
Write 1 above the first 8.
Step 2: 7×1=7 → subtract from 8 → 1
Step 3: Bring down the second 8 → makes 18
Step 4: 7 into 18 → 2 times (7×2=14)
Write 2 above the second 8.
Step 5: 18 - 14 = 4 → remainder 4
So quotient is 12, remainder 4.
Again, 2-digit quotient.
---
Problem c: 423 ÷ 3
This is 3-digit, so 3-digit quotient expected.
Step 1: 3 into 4 → 1 time (3×1=3)
Write 1 above 4.
Subtract: 4 - 3 = 1
Bring down 2 → makes 12
Step 2: 3 into 12 → 4 times (3×4=12)
Write 4 above 2.
Subtract: 12 - 12 = 0
Bring down 3 → makes 03 or just 3
Step 3: 3 into 3 → 1 time (3×1=3)
Write 1 above 3.
Subtract: 3 - 3 = 0
✔ Quotient: 141, remainder 0.
Perfect — fits 3 boxes.
---
Problem d: 640 ÷ 5
Step 1: 5 into 6 → 1 time (5×1=5)
Write 1 above 6.
Subtract: 6 - 5 = 1
Bring down 4 → makes 14
Step 2: 5 into 14 → 2 times (5×2=10)
Write 2 above 4.
Subtract: 14 - 10 = 4
Bring down 0 → makes 40
Step 3: 5 into 40 → 8 times (5×8=40)
Write 8 above 0.
Subtract: 40 - 40 = 0
✔ Quotient: 128, remainder 0.
---
Now back to problems a and b — they have 2-digit dividends but 3-box quotient templates. In educational worksheets, sometimes they include an extra box for alignment or future use, but mathematically, the quotient is 2-digit.
However, looking at the arrow placements and subtraction steps, for problem a:
After bringing down 7, we get 7, divide by 3 → 2, multiply 6, subtract → 1. So final answer should be 22 with remainder 1.
Similarly for b: 12 with remainder 4.
But the worksheet says “Find the quotient.” — which usually means the whole number part, ignoring remainder unless specified.
Also, note that in problem c and d, remainders are 0, so no issue.
Perhaps for a and b, we should write the quotient as 2-digit, leaving the first box blank? But the instruction doesn't say.
Another thought: maybe the third box is for the remainder? But in the diagram, the remainder is written at the bottom after last subtraction.
Looking at the structure:
In problem a:
[ ][ ][ ] ← quotient
3 ) 6 7
[ ] ← 3×first digit
----
[ ][ ] ← result after bring down
- [ ] ← 3×second digit
----
[ ] ← remainder
So the quotient has three boxes, but for 67÷3, only two digits are used. Probably, the first box is not used, or perhaps it's a mistake. But to match the format, maybe we put 0 in the first box? That would be incorrect mathematically.
I think the best approach is to provide the correct mathematical quotient, and if the template has extra boxes, leave them blank or assume it's for alignment.
But since the user expects answers to fill in, and for c and d we have 3-digit quotients, for a and b, perhaps they expect 2-digit with leading space.
Wait — let's calculate numerically:
a. 67 ÷ 3 = 22.333... → integer quotient 22
b. 88 ÷ 7 = 12.571... → integer quotient 12
c. 423 ÷ 3 = 141
d. 640 ÷ 5 = 128
And in long division, we write the quotient digits above the dividend digits.
For 67:
- Above 6: 2
- Above 7: 2
- No third digit, so third box might be empty.
But the problem says "find the quotient", and in context, likely the whole number part.
Moreover, in the initial reminder, it says "Divide, Multiply, Subtract, Bring Down" — which is for integer division with possible remainder.
So I'll go with:
a. 22 (remainder 1)
b. 12 (remainder 4)
c. 141
d. 128
But to fit the 3-box format, perhaps for a and b, we write 022 and 012? That seems forced.
Another idea: maybe the third box is for the remainder? But in the diagram, the remainder is clearly at the bottom.
Looking at problem a's diagram:
After last subtraction, there's one box at the bottom — that's the remainder.
The quotient is above, with three boxes.
Perhaps for 2-digit dividends, the first quotient box is for hundreds place, which is 0.
In some curricula, they teach to consider the dividend as having leading zeros if needed, but that's advanced.
I think for simplicity and correctness, I'll provide the actual quotient values, and assume the student writes them in the appropriate boxes.
Since the worksheet is titled "Division" and uses long division steps, and for c and d it works perfectly, for a and b, the quotient is 2-digit, so likely the first box is left blank or not used.
But to give a concrete answer, I'll state the numerical quotient.
Final decision:
a. 22
b. 12
c. 141
d. 128
And ignore the extra box for a and b, or consider it as 022 etc., but that's not standard.
Upon second thought, in the diagram for problem a, the first subtraction is under the 6, then bring down 7, then subtract under the 7, so the quotient has two digits: one over 6, one over 7. The third box might be a red herring or for decimal, but since no decimal point, probably not.
I think it's safe to provide the correct quotients.
So:
a. 67 ÷ 3 = 22 R1 → quotient is 22
b. 88 ÷ 7 = 12 R4 → quotient is 12
c. 423 ÷ 3 = 141
d. 640 ÷ 5 = 128
Now, to confirm calculations:
a. 3 * 22 = 66, 67 - 66 = 1 → correct
b. 7 * 12 = 84, 88 - 84 = 4 → correct
c. 3 * 141 = 423 → correct
d. 5 * 128 = 640 → correct
All good.
Final Answer:
a. 22
b. 12
c. 141
d. 128
Parent Tip: Review the logic above to help your child master the concept of worksheet for long division.