Long Division Problem: Dividing 648 by 12 Step-by-Step

Q: What do I do when the divisor is bigger than the first digit?

Move to the next digit! Since 12 can't go into 6, look at 64 instead. This is completely normal in long division.

Q: How do I know if 12 goes into 64 exactly 5 times?

Try multiplying: $ 12 \times 5 = 60 $ and $ 12 \times 6 = 72 $. Since 60 ≤ 64 but 72 > 64, the answer is 5.

Q: Is there a faster way than long division?

For simple cases like this, you might recognize that $ 648 = 12 \times 54 $ from multiplication facts. But long division works for any numbers!

Q: How do I check my final answer?

Multiply your quotient by the divisor: $ 54 \times 12 $. If you get the original dividend (648), your answer is correct!

Long Division with Two-Digit Divisors

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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 6 is less than 12, so we'll bring down the next digit and then divide

00:16 Write the result without the remainder above, paying attention to position

00:21 Now multiply the result by the divisor

00:25 Subtract the product from the number

00:29 Now bring down the next digit below and use the same steps

00:34 Divide

00:38 Write the result without the remainder above, paying attention to position

00:41 Multiply the result and subtract

00:48 We got a remainder of 0

00:51 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Step-by-step solution

To solve the division problem $\frac{648}{12}$ , we'll use the long division method. Here's each step broken down:

Step 1: Begin by writing 648 under the division bar and 12 outside the bar.
Step 2: Determine how many times 12 fits into the first digit, 6. Since 12 is greater than 6, check the first two digits together, 64.
Step 3: Determine how many times 12 goes into 64. The answer is 5, because $12 \times 5 = 60$ , which is less than 64. Write 5 above the division bar.
Step 4: Subtract 60 from 64, leaving a remainder of 4. Carry down the next digit, 8, to get 48.
Step 5: Determine how many times 12 goes into 48. The answer is 4, since $12 \times 4 = 48$ .
Step 6: Subtract 48 from 48, leaving a remainder of 0.

The quotient of $\frac{648}{12}$ is, therefore, 54.

Thus, the solution to the problem is $54$ .

Final Answer

$54$

Key Points to Remember

Essential concepts to master this topic

Strategy: Use multi-digit grouping when divisor is larger than first digit
Technique: Check 12 × 5 = 60, which fits under 64
Verification: Multiply quotient by divisor: 54 × 12 = 648 ✓

Common Mistakes

Avoid these frequent errors

Trying to divide into single digits when divisor is too large
Don't try to divide 12 into just 6 = impossible division! This leads to confusion and wrong setup. Always group enough digits so the divisor fits, like using 64 instead of just 6.

Practice Quiz

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FAQ

Everything you need to know about this question

What do I do when the divisor is bigger than the first digit?

Move to the next digit! Since 12 can't go into 6, look at 64 instead. This is completely normal in long division.

How do I know if 12 goes into 64 exactly 5 times?

Try multiplying: $12 \times 5 = 60$ and $12 \times 6 = 72$ . Since 60 ≤ 64 but 72 > 64, the answer is 5.

What if I get a remainder that's not zero?

That means your division doesn't come out evenly! You can either express it as a remainder (like 54 R 0) or continue with decimal places.

Is there a faster way than long division?

For simple cases like this, you might recognize that $648 = 12 \times 54$ from multiplication facts. But long division works for any numbers!

How do I check my final answer?

Multiply your quotient by the divisor: $54 \times 12$ . If you get the original dividend (648), your answer is correct!

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