$ 299 $ with a remainder of 1

$ 285 $ with a remainder of 12

$ 321 $ with a remainder of 13

Long Division Problem: Dividing 7235 by 28 Step-by-Step

Q: How do I know which multiple of 28 to use for each step?

Find the largest multiple that doesn't exceed your current number. For example, when dividing 235 by 28, calculate: $ 28 \times 8 = 224 $ (fits) and $ 28 \times 9 = 252 $ (too big), so use 8.

Q: What if I make an error in one step?

No worries! Check each step by multiplying your quotient digit by the divisor. If the result is larger than what you're dividing into, go back and try a smaller digit.

Q: Why do I need to bring down digits one at a time?

Bringing down digits one at a time keeps the numbers manageable and prevents errors. It's like solving several smaller division problems instead of one huge one!

Q: How can I check if my final answer is correct?

Use the division check formula: quotient × divisor + remainder = dividend. For this problem: $ 258 \times 28 + 11 = 7224 + 11 = 7235 $ ✓

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

If your remainder is larger than or equal to the divisor, you made an error! The remainder must always be smaller than what you're dividing by. Go back and check your quotient digit.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:05 Let's solve this problem step by step.

00:09 First, divide the leftmost digit of the dividend.

00:13 Since seven is less than twenty-eight, we'll add the next digit, then divide.

00:20 Write the result above, with no remainder; keep it aligned.

00:25 Next, multiply the result by the divisor.

00:29 Subtract that product from your number.

00:34 Bring down the next digit. Use the same steps.

00:42 Okay, divide again.

00:47 Write the result above, without any remainder; keep it aligned.

00:54 Multiply your result and subtract again.

01:03 Now, bring down the next digit and repeat.

01:07 Let's divide one more time.

01:13 Write the result, again without any remainder; make sure it's aligned.

01:18 Multiply and subtract once more.

01:27 We have a remainder of eleven.

01:34 And that's how you solve this 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 division of 7235 by 28, we will use the long division method:

Step 1: Determine how many times 28 can go into the first part of the number, 72. Since $28 \times 2 = 56$ and $28 \times 3 = 84$ , 28 fits into 72 twice. Write 2 on top.
Step 2: Subtract $56$ from $72$ to get $16$ . Bring down the next digit, which is 3, making it 163.
Step 3: Determine how many times 28 fits into 163. Since $28 \times 5 = 140$ and $28 \times 6 = 168$ , 28 fits in 163 five times. Write 5 on top next to 2.
Step 4: Subtract $140$ from $163$ to get $23$ . Bring down the final digit, 5, making it 235.
Step 5: Determine how many times 28 fits into 235. Since $28 \times 8 = 224$ and $28 \times 9 = 252$ , 28 fits into 235 eight times. Write 8 on top next to the 25, making our partial quotient 258.
Step 6: Subtract $224$ from $235$ to get a remainder of $11$ .

Therefore, when dividing 7235 by 28, the quotient is $258$ with a remainder of $11$ .

The correct answer to the multiple-choice question is $\text{Option 2:}$ $258$ with a remainder of $11$ .

3

Final Answer

$258$ with a remainder of 11

Key Points to Remember

Essential concepts to master this topic

Process: Divide step-by-step, bringing down one digit at a time
Technique: Find largest multiple: $28 \times 8 = 224$ fits into 235
Check: Verify $258 \times 28 + 11 = 7235$ ✓

Common Mistakes

Avoid these frequent errors

Guessing quotient digits without calculating multiples
Don't just guess that 28 goes into 235 nine times = 252 which is too big! This creates negative remainders and wrong answers. Always calculate the exact multiples like $28 \times 8 = 224$ to find the largest that fits.

Practice Quiz

Test your knowledge with interactive questions

FAQ

Everything you need to know about this question

How do I know which multiple of 28 to use for each step?

+

Find the largest multiple that doesn't exceed your current number. For example, when dividing 235 by 28, calculate: $28 \times 8 = 224$ (fits) and $28 \times 9 = 252$ (too big), so use 8.

What if I make an error in one step?

+

No worries! Check each step by multiplying your quotient digit by the divisor. If the result is larger than what you're dividing into, go back and try a smaller digit.

Why do I need to bring down digits one at a time?

+

Bringing down digits one at a time keeps the numbers manageable and prevents errors. It's like solving several smaller division problems instead of one huge one!

How can I check if my final answer is correct?

+

Use the division check formula: quotient × divisor + remainder = dividend. For this problem: $258 \times 28 + 11 = 7224 + 11 = 7235$ ✓

What happens if my remainder is bigger than the divisor?

+

If your remainder is larger than or equal to the divisor, you made an error! The remainder must always be smaller than what you're dividing by. Go back and check your quotient digit.

Is there a faster way to do long division?

+

Long division is already the most reliable method for multi-digit division. Focus on accuracy over speed - getting the right answer is more important than going fast!

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Long Division Problem: Dividing 7235 by 28 Step-by-Step

Long Division with Multi-Digit Remainders

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