$ 3212 $ with a remainder of 1

$ 2135 $ with a remainder of 1

$ 3211 $ with a remainder of 2

Long Division Problem: Dividing 8422 by 3 Step-by-Step

Q: How do I know if I can divide a number by 3?

Ask yourself: How many times does 3 fit into this number? Try multiplying 3 by different numbers until you get close but don't go over.

Q: What if I get confused with the remainders?

Always subtract your multiplication result from the current number. The difference is your remainder, which you carry to the next step.

Q: Why do we check by multiplying the quotient back?

This verifies our work! If $ quotient \times divisor + remainder = original \, number $, then our division is correct.

Q: Can the remainder ever be bigger than the divisor?

No! If your remainder is 3 or bigger when dividing by 3, you made an error. The remainder must always be smaller than the divisor.

Long Division with Four-Digit Numbers

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve this division problem together.

00:08 First, look at the leftmost digit of the number being divided.

00:14 Write the result above, but don't include any remainder yet.

00:21 Next, multiply this result by the number you're dividing by.

00:25 Subtract what you got from the previous step.

00:28 Now, bring down the next digit and repeat the process.

00:33 Time to divide the new number.

00:36 Write that result above, keeping track of its place.

00:41 Multiply the result again, then subtract.

00:47 Bring down another digit, and keep going.

00:54 Let's divide once more.

00:58 Add the result above and watch its position.

01:01 Multiply and subtract again.

01:04 And bring down the next number to continue.

01:07 Another round of division.

01:12 Place the new result without the remainder.

01:16 Multiply and subtract one last time.

01:21 We have a remainder of 1.

01:25 And that's how we solve this division problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Step-by-step solution

To solve this problem, we'll execute a long division of 8422 by 3 as follows:

First, divide the first digit, 8, by 3. 3 goes into 8 two times, since $3 \times 2 = 6$ . The remainder is 8 - 6 = 2.
Bring down the next digit, 4, to the remainder, making it 24. Now, divide 24 by 3. 3 goes into 24 eight times, since $3 \times 8 = 24$ . The remainder is 24 - 24 = 0.
Bring down the next digit, 2, making it 2. Divide 2 by 3. 3 cannot go into 2, so the quotient is 0 and the remainder remains 2.
Bring down the final digit, 2, making it 22. Divide 22 by 3. 3 goes into 22 seven times, since $3 \times 7 = 21$ . The remainder is 22 - 21 = 1.

Following the division steps leads us to a quotient of 2807 with a remainder of 1.

Therefore, the solution to the problem is $2807$ with a remainder of 1.

Final Answer

$2807$ with a remainder of 1

Key Points to Remember

Essential concepts to master this topic

Process: Divide digit by digit, bringing down next digit each step
Technique: Check if 3 goes into 8: $3 \times 2 = 6$ , remainder 2
Check: Multiply quotient by divisor: $2807 \times 3 + 1 = 8422$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to bring down digits after getting zero remainder
Don't stop dividing when you get remainder 0 in middle steps = incomplete quotient! You must continue through all digits even after getting zero. Always bring down every remaining digit and complete the entire division process.

Practice Quiz

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FAQ

Everything you need to know about this question

What do I do when the divisor doesn't go into a digit?

Write 0 in the quotient and bring down the next digit! For example, 3 doesn't go into 2, so write 0 and make it 22 with the next digit.

How do I know if I can divide a number by 3?

Ask yourself: How many times does 3 fit into this number? Try multiplying 3 by different numbers until you get close but don't go over.

What if I get confused with the remainders?

Always subtract your multiplication result from the current number. The difference is your remainder, which you carry to the next step.

Why do we check by multiplying the quotient back?

This verifies our work! If $quotient \times divisor + remainder = original \, number$ , then our division is correct.

Can the remainder ever be bigger than the divisor?

No! If your remainder is 3 or bigger when dividing by 3, you made an error. The remainder must always be smaller than the divisor.

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