Compute using long division: 1,234÷68

Compute using long division: 1,234÷68

The Correct Answer and Explanation is:

To divide 1,234 by 68 using long division, follow these steps:

Step 1: Set up the long division

Write 1,234 (the dividend) inside the long division symbol and 68 (the divisor) outside of it.

[
\begin{array}{r}
68 \, \big| \, 1234
\end{array}
]

Step 2: Divide the first two digits

Look at the first two digits of the dividend, which are 12. We need to determine how many times 68 can fit into 12. Since 68 is larger than 12, we move on to the next digit, 123.

Step 3: Divide 123 by 68

Now, consider how many times 68 fits into 123. We know that 68 fits into 123 once. Write 1 above the division bar.

[
1 \quad \text{(write above the 3)}
]

Now, multiply 68 by 1, which equals 68. Subtract 68 from 123 to get the remainder:

[
123 – 68 = 55
]

Step 4: Bring down the next digit

Next, bring down the next digit of the dividend, which is 4, making the new number 554.

Step 5: Divide 554 by 68

Now, divide 554 by 68. 68 fits into 554 8 times, as 68 × 8 = 544. Write 8 above the division bar next to 1.

[
18 \quad \text{(write above the 4)}
]

Now, subtract 544 from 554 to get the remainder:

[
554 – 544 = 10
]

Step 6: Final result

At this point, there are no more digits to bring down, and the remainder is 10. So, the division of 1,234 by 68 is:

[
1,234 \div 68 = 18 \text{ remainder } 10
]

This means:

[
1,234 \div 68 = 18 \, \text{with a remainder of} \, 10.
]

Explanation:

In this division process, we break down the dividend step-by-step and divide using the closest approximations possible. At each step, we determine how many times the divisor can fit into the current portion of the dividend, multiply to get a product, and subtract that product from the portion of the dividend we are working with. This continues until there are no more digits to bring down, at which point we have our quotient (18) and remainder (10).