$ 71214 $ with a remainder of 3

$ 63121 $ with a remainder of 5

$ 32144 $ with a remainder of 8

Long Division Problem: Dividing 83214 by 7 Step-by-Step

Q: How do I know when I'm done with long division?

You're done when you've brought down all digits from the dividend. The final remainder (if any) should be smaller than the divisor.

Q: What does the remainder really mean?

The remainder is what's left over after dividing. In this problem, remainder 5 means we have 5 units that can't be divided evenly by 7.

Q: Can I check my answer without doing the whole multiplication?

Yes! Use estimation: $ 11887 \times 7 $ should be close to $ 12000 \times 7 = 84000 $, which matches our dividend 83214.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:06 Alright, let's solve this problem step by step.

00:10 First, take the leftmost digit of the dividend. Divide it by the divisor.

00:15 Write the quotient on top. Be careful with placement!

00:19 Next, multiply this quotient by the divisor.

00:23 Then, subtract that product from your current number.

00:27 Bring down the next digit from the dividend.

00:30 Now, divide the new number just like before.

00:33 Write the new result above.

00:36 Multiply, then subtract like last time.

00:40 Again, bring down the next digit.

00:43 Divide the new number we created.

00:46 Place the new quotient carefully on top.

00:49 Multiply the quotient and subtract again.

00:56 Bring down another digit.

01:01 Now, divide the number as we've practiced.

01:06 Write this quotient above without remainder.

01:10 Multiply, subtract, and repeat!

01:15 One more time, bring down the next digit.

01:19 Divide it, just like before.

01:23 Write down this result with no remainder.

01:28 Multiply and subtract from the current number.

01:34 Notice, we have a remainder of 5.

01:40 And that's how we solve the problem. Great job!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

2

Step-by-step solution

To solve the problem of dividing 83214 by 7 using long division, follow these steps:

Step 1: Start with the first digit of the dividend. Divide 8 by 7. The result is 1.
Step 2: Write 1 as part of the quotient. Multiply 1 by 7 to get 7. Subtract 7 from 8, leaving a remainder of 1.
Step 3: Bring down the next digit of the dividend, which is 3, making it 13.
Step 4: Divide 13 by 7 to get 1. Write 1 as the next digit of the quotient. Multiply 1 by 7 to get 7 and subtract from 13, leaving 6.
Step 5: Bring down the next dividend digit, which is 2, making it 62.
Step 6: Divide 62 by 7 to get 8. Write down 8 in the quotient. Multiply 8 by 7 to obtain 56 and subtract from 62, resulting in 6.
Step 7: Bring down the next digit, which is 1, leading to 61.
Step 8: Divide 61 by 7 to get 8. Write down 8 in the quotient. Multiply 8 by 7 to get 56 and subtract from 61, leaving 5.
Step 9: Bring down the last digit, which is 4, resulting in 54.
Step 10: Divide 54 by 7 to get 7. Write down 7 in the quotient. Multiply 7 by 7 to get 49, subtract from 54, leaving a remainder of 5.

Thus, after dividing 83214 by 7 using long division, the quotient is $11887$ with a remainder of 5.

3

Final Answer

$11887$ with a remainder of 5

Key Points to Remember

Essential concepts to master this topic

Process: Divide, multiply, subtract, bring down each digit systematically
Technique: 83 ÷ 7 = 11 remainder 6, then continue with 62
Check: Multiply quotient by divisor: 11887 × 7 + 5 = 83214 ✓

Common Mistakes

Avoid these frequent errors

Skipping steps or bringing down multiple digits
Don't rush by bringing down 2 or 3 digits at once = wrong quotient digits! This throws off the entire division pattern and leads to incorrect answers. Always bring down exactly one digit at a time after each division step.

Practice Quiz

Test your knowledge with interactive questions

FAQ

Everything you need to know about this question

What if the dividend digit is smaller than the divisor?

+

If you can't divide (like 3 ÷ 7), write 0 in the quotient and bring down the next digit. For example, 3 becomes 32 when you bring down the next digit.

How do I know when I'm done with long division?

+

You're done when you've brought down all digits from the dividend. The final remainder (if any) should be smaller than the divisor.

What does the remainder really mean?

+

The remainder is what's left over after dividing. In this problem, remainder 5 means we have 5 units that can't be divided evenly by 7.

Why do we multiply and subtract in each step?

+

Multiplying checks how much we've used up, and subtracting shows what's left. This systematic approach ensures we account for every digit correctly!

Can I check my answer without doing the whole multiplication?

+

Yes! Use estimation: $11887 \times 7$ should be close to $12000 \times 7 = 84000$ , which matches our dividend 83214.

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Long Division Problem: Dividing 83214 by 7 Step-by-Step

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