Long Division Problem: Dividing 234 by 7 Step-by-Step

Q: What if the first digit is smaller than the divisor?

That's normal! When 2 is smaller than 7, you combine it with the next digit to make 23. Always look at enough digits to make a number larger than your divisor.

Q: How do I know how many times 7 goes into 23?

Think about your multiplication facts! Since $ 7 \times 3 = 21 $ and $ 7 \times 4 = 28 $, we know 7 goes into 23 exactly 3 times with some left over.

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

Use the division check formula: (quotient × divisor) + remainder = dividend. For our problem: $ (33 \times 7) + 3 = 231 + 3 = 234 $ ✓

Q: Why do we subtract after each multiplication?

Subtraction shows us what's left over after taking out groups of the divisor. This remainder gets combined with the next digit to continue the division process.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Solve

00:03 Let's start by dividing the leftmost digit in the dividend

00:07 2 is less than 7, so we'll include the next digit and then divide

00:12 Write the result without remainder above, paying attention to placement

00:17 Now multiply the result by the divisor

00:22 Subtract the product from the number

00:27 Now bring down the next digit below and use the same steps

00:31 Divide

00:36 Write the result above, paying attention to placement

00:42 Multiply the result and subtract

00:50 We got a remainder of 3

00:56 And this is the solution to the question

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, we'll use long division to divide 234 by 7 and find both the quotient and remainder:

Step 1: Set up the long division by writing 234 inside the division bracket and 7 outside.
Step 2: Divide the first digit, 2, by 7. Since 2 is smaller than 7, consider the first two digits, 23.
Step 3: Determine how many times 7 fits into 23. It fits 3 times (since $7 \times 3 = 21$ ).
Step 4: Subtract 21 from 23, leaving a remainder of 2.
Step 5: Bring down the next digit of the dividend, 4, making the new number 24.
Step 6: Determine how many times 7 fits into 24. It fits 3 times (since $7 \times 3 = 21$ ).
Step 7: Subtract 21 from 24, leaving a remainder of 3.
Step 8: No more digits left to bring down. Therefore, the division completes here.

The quotient of dividing 234 by 7 is 33, with a remainder of 3.
Thus, the solution to the problem is $33$ with a remainder of 3.

Based on the choices provided, this corresponds to choice 2, which states:
$33$ with a remainder of 3.

3

Final Answer

$33$ with a remainder of 3

Key Points to Remember

Essential concepts to master this topic

Setup: Place divisor outside bracket, dividend inside for organization
Technique: Multiply and subtract at each step: $7 \times 3 = 21$
Check: Multiply quotient by divisor and add remainder: $33 \times 7 + 3 = 234$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to bring down the next digit
Don't stop after the first subtraction without bringing down all remaining digits! This gives you an incomplete quotient and wrong answer. Always bring down each digit one at a time and continue dividing until no digits remain.

Practice Quiz

Test your knowledge with interactive questions

FAQ

Everything you need to know about this question

What if the first digit is smaller than the divisor?

+

That's normal! When 2 is smaller than 7, you combine it with the next digit to make 23. Always look at enough digits to make a number larger than your divisor.

How do I know how many times 7 goes into 23?

+

Think about your multiplication facts! Since $7 \times 3 = 21$ and $7 \times 4 = 28$ , we know 7 goes into 23 exactly 3 times with some left over.

What happens if there's a remainder at the end?

+

The remainder is perfectly normal! It means the dividend doesn't divide evenly. In this problem, 234 ÷ 7 = 33 remainder 3, which means 7 doesn't go into 234 exactly.

How can I check if my long division is correct?

+

Use the division check formula: (quotient × divisor) + remainder = dividend. For our problem: $(33 \times 7) + 3 = 231 + 3 = 234$ ✓

Why do we subtract after each multiplication?

+

Subtraction shows us what's left over after taking out groups of the divisor. This remainder gets combined with the next digit to continue the division process.

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Long Division Problem: Dividing 234 by 7 Step-by-Step

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