$ 566 $ with a remainder of 1

$ 362 $ with a remainder of 8

$ 724 $ with a remainder of 3

Long Division Problem: Dividing 5111 by 11 Step-by-Step

Q: Why do I start with 51 instead of just 5?

Since 5 is smaller than 11, we can't divide it evenly. We need to look at the first two digits (51) to get a number that's greater than or equal to our divisor!

Q: How do I know what number to multiply 11 by?

Ask yourself: "What's the largest number I can multiply 11 by without going over my target?" For 71, that's 6 because $ 6 \times 11 = 66 $ but $ 7 \times 11 = 77 $ is too big.

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

Use this formula: Dividend = (Quotient × Divisor) + RemainderFor our problem: $ 5111 = (464 \times 11) + 7 = 5104 + 7 = 5111 $ ✓

Q: Why is my remainder 7 and not something else?

The remainder must always be smaller than the divisor! Since we're dividing by 11, any remainder must be between 0 and 10. A remainder of 7 means we have 7 left over that can't be divided by 11.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's solve a division problem.

00:08 First, look at the leftmost digit of the dividend.

00:12 Five is less than eleven. So, add the next digit and divide.

00:18 Write the result above. Make sure it's in the right place.

00:23 Next, multiply this result by the divisor.

00:27 Now, subtract that product from the number.

00:33 Bring down the next digit.

00:36 Repeat the division steps.

00:42 Write the new result on top without any remainder.

00:46 Multiply and then subtract again.

00:52 Bring down the next digit just like before.

00:56 Repeat the division process.

01:02 Place the result on top without remainder.

01:06 Multiply, then subtract. Almost done!

01:10 There is a remainder of seven.

01:17 Great job! That's the solution.

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 this problem using long division, we will follow these steps:

Step 1: Set up the division of 5111 by 11.
Step 2: Divide the first few digits until you have a number greater than or equal to 11.
Step 3: Subtract the result and bring down the next digit.
Step 4: Repeat the process until all digits are used.

Let's perform the division:

Step 1: Take the first digit of 5111, which is 5. Since 5 is less than 11, look at the first two digits, 51.

Step 2: Divide 51 by 11. The result is 4 (since $4 \times 11 = 44$ ), with a remainder of 7.

Subtract 44 from 51, we get 7. Bring down the next digit, 1, making the number 71.

Step 3: Divide 71 by 11, which is 6 (since $6 \times 11 = 66$ ), with a remainder of 5.

Subtract 66 from 71, we get 5. Bring down the next digit, 1, making the number 51.

Step 4: Divide 51 by 11, which is 4 again, with a remainder of 7 (since $4 \times 11 = 44$ ). There are no more digits to bring down.

The quotient from dividing 5111 by 11 is therefore 464 with a remainder of 7.

Therefore, the solution to the problem is $464$ with a remainder of 7.

3

Final Answer

$464$ with a remainder of 7

Key Points to Remember

Essential concepts to master this topic

Setup: Start with largest place value that contains the divisor
Technique: Multiply back and subtract: $6 \times 11 = 66$ , then $71 - 66 = 5$
Check: Multiply quotient by divisor and add remainder: $464 \times 11 + 7 = 5111$ ✓

Common Mistakes

Avoid these frequent errors

Not properly handling remainders when bringing down digits
Don't forget the remainder when bringing down the next digit = wrong calculations throughout! The remainder becomes the tens digit of your new number. Always combine the remainder with the brought-down digit to form the next number to divide.

Practice Quiz

Test your knowledge with interactive questions

FAQ

Everything you need to know about this question

Why do I start with 51 instead of just 5?

+

Since 5 is smaller than 11, we can't divide it evenly. We need to look at the first two digits (51) to get a number that's greater than or equal to our divisor!

How do I know what number to multiply 11 by?

+

Ask yourself: "What's the largest number I can multiply 11 by without going over my target?" For 71, that's 6 because $6 \times 11 = 66$ but $7 \times 11 = 77$ is too big.

What if I get confused with the remainders?

+

Write down each step clearly! When you subtract and get a remainder, that remainder becomes the first digit of your next number when you bring down the next digit.

How can I check if my long division is correct?

+

Use this formula: Dividend = (Quotient × Divisor) + Remainder
For our problem: $5111 = (464 \times 11) + 7 = 5104 + 7 = 5111$ ✓

Why is my remainder 7 and not something else?

+

The remainder must always be smaller than the divisor! Since we're dividing by 11, any remainder must be between 0 and 10. A remainder of 7 means we have 7 left over that can't be divided by 11.

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Long Division Problem: Dividing 5111 by 11 Step-by-Step

Long Division with Multi-Digit Remainders

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