Question
4.1.2 Calculate the following using the Long Division Method. \( 754 \div 58 \)
Ask by Stewart Carroll. in South Africa
Mar 16,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The division of \(754\) by \(58\) using the Long Division Method results in \(13\).
Solution
1. Write the division as:
\[
754 \div 58
\]
2. Determine how many times \(58\) goes into the first part of \(754\). Since the first digit \(7\) is too small, consider the first two digits \(75\). Compute:
\[
\left\lfloor \frac{75}{58} \right\rfloor = 1,\quad \text{because } 1 \times 58 = 58.
\]
3. Subtract to find the remainder:
\[
75 - 58 = 17.
\]
4. Bring down the next digit from \(754\) (which is \(4\)) to make \(174\).
5. Determine how many times \(58\) fits into \(174\). Calculate:
\[
\left\lfloor \frac{174}{58} \right\rfloor = 3,\quad \text{since } 58 \times 3 = 174.
\]
6. Subtract:
\[
174 - 174 = 0.
\]
7. Combine the results from each stage. The first digit of the quotient is \(1\) and the second digit is \(3\), so the complete quotient is:
\[
13.
\]
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Simplify this solution Extra Insights
To calculate \( 754 \div 58 \) using the Long Division Method, follow these steps: 1. **Divide**: Determine how many times 58 goes into the first part of 754. It goes in 12 times since \( 58 \times 12 = 696 \). 2. **Multiply**: Multiply 12 by 58 to get 696. 3. **Subtract**: Subtract 696 from 754, which gives you \( 754 - 696 = 58 \). 4. **Bring down**: Since there are no more digits to bring down, we're ready to find the remainder. 5. **Conclusion**: Since 58 fits into 58 exactly once, we write a 1 next to the 12 in the quotient. Therefore, \( 754 \div 58 = 12 R 0 \), meaning the answer is 12 and there is no remainder. The final result is \( 12 \).
