$ 125 $ with a remainder of 4

$ 135\text{ } $ with a remainder of 2

$ 143 $ with a remainder of 2

Long Division Problem: Divide 974 by 8

Q: What do I do when a digit is smaller than the divisor?

If the digit is smaller than the divisor (like 9 0 in the quotient and bring down the next digit to make a larger number.

Q: How do I know when to stop dividing?

Stop when you've brought down all the digits from the dividend. The number left over (if any) is your remainder.

Q: What if my remainder is bigger than the divisor?

If your remainder is equal to or larger than the divisor, you made an error! Go back and check - you can probably divide one more time.

Q: Why do we write the quotient above the dividend?

Each digit of the quotient goes directly above the corresponding digit in the dividend. This helps you keep track of place values (hundreds, tens, ones).

Q: How can I check if my long division is correct?

Use this formula: $ \text{Quotient} \times \text{Divisor} + \text{Remainder} = \text{Dividend} $. For our problem: $ 121 \times 8 + 6 = 974 $ ✓

Long Division with Three-Digit Dividends

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's get started with solving this problem.

00:08 First, divide the leftmost digit of the dividend by the divisor.

00:13 Write the result above, without including the remainder.

00:17 Now, multiply that result by the divisor.

00:20 Subtract this product from the number we started with.

00:24 Next, bring down the next digit and repeat these steps.

00:28 Let's divide again.

00:31 Write your answer above, and don't include the remainder.

00:35 Multiply this result, subtract to see what's left.

00:42 Bring down the next digit and keep repeating.

00:49 Divide once more.

00:52 Place the result above, without the leftover part.

00:56 Multiply again and subtract it.

00:59 We have a remainder of six.

01:04 And that's how we solve this 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 perform long division of 974 by 8. Here are the detailed steps:

Step 1: Set up the division
Write 974 under the division bar and 8 outside.
Step 2: Divide
Start with the leftmost digit, which is 9.
8 goes into 9 one time ( $8 \times 1 = 8$ ).
Subtract 8 from 9 to get a remainder of 1.
Step 3: Bring down the next digit
Bring down 7, the next digit of 974, to make it 17.
8 goes into 17 two times ( $8 \times 2 = 16$ ).
Subtract 16 from 17 to get a remainder of 1.
Step 4: Bring down the last digit
Bring down the last digit, which is 4, making it 14.
8 goes into 14 one time ( $8 \times 1 = 8$ ).
Subtract 8 from 14 to get a remainder of 6.

Putting it all together, the quotient is 121, and the final remainder is 6.

Therefore, the solution to the problem is $121$ with a remainder of 6.

Among the choices given, the correct one is choice 4: $121$ with a remainder of 6.

Final Answer

$121$ with a remainder of 6

Key Points to Remember

Essential concepts to master this topic

Setup: Place divisor outside and dividend inside the division bracket
Technique: Divide digit by digit: 9÷8=1, bring down 7 to make 17
Check: Multiply quotient by divisor and add remainder: $121 \times 8 + 6 = 974$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to bring down the next digit
Don't work with single digits when the remainder is larger than the divisor = wrong quotient! This happens when you forget to bring down the next digit from the dividend. Always bring down the next digit after each division step to continue the process.

Practice Quiz

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FAQ

Everything you need to know about this question

What do I do when a digit is smaller than the divisor?

If the digit is smaller than the divisor (like 9 < something), you can't divide it evenly. Write 0 in the quotient and bring down the next digit to make a larger number.

How do I know when to stop dividing?

Stop when you've brought down all the digits from the dividend. The number left over (if any) is your remainder.

What if my remainder is bigger than the divisor?

If your remainder is equal to or larger than the divisor, you made an error! Go back and check - you can probably divide one more time.

Why do we write the quotient above the dividend?

Each digit of the quotient goes directly above the corresponding digit in the dividend. This helps you keep track of place values (hundreds, tens, ones).

How can I check if my long division is correct?

Use this formula: $\text{Quotient} \times \text{Divisor} + \text{Remainder} = \text{Dividend}$ . For our problem: $121 \times 8 + 6 = 974$ ✓

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