Question
Using partial quotients, which would be the best choice for the first number to subtract in the division problem 5,166
42?
4,200
5,000
420
840
42?
4,200
5,000
420
840
Answers
GPT-4o mini
To solve the division problem \( 5,166 \div 42 \) using partial quotients, we want to choose a number that is a multiple of \( 42 \) and is somewhat close to \( 5,166 \) to make the subtraction manageable.
Let's evaluate each option:
1. **4,200**: This is \( 42 \times 100 = 4,200 \). This is a reasonable option since it's a straightforward multiple of \( 42 \).
2. **5,000**: This is not a multiple of \( 42 \), but it's close to \( 5,166 \). However, the subtraction would require us to calculate the exact value of how many \( 42's \) fit into \( 5,000 \). It's not the most efficient.
3. **420**: This is \( 42 \times 10 = 420 \). While it is a reasonable option, it is much less than \( 5,166 \) and will require more iterations to get to the final answer.
4. **840**: This is \( 42 \times 20 = 840 \). This number is a bit more manageable than \( 420 \), but it is still significantly less than \( 5,166 \).
Among these, **4,200** is likely the best starting point, as it allows for a significant reduction from \( 5,166 \), and it is a round multiple of \( 42 \).
So, the best choice for the first number to subtract in the division problem \( 5,166 \div 42 \) is **4,200**.
Let's evaluate each option:
1. **4,200**: This is \( 42 \times 100 = 4,200 \). This is a reasonable option since it's a straightforward multiple of \( 42 \).
2. **5,000**: This is not a multiple of \( 42 \), but it's close to \( 5,166 \). However, the subtraction would require us to calculate the exact value of how many \( 42's \) fit into \( 5,000 \). It's not the most efficient.
3. **420**: This is \( 42 \times 10 = 420 \). While it is a reasonable option, it is much less than \( 5,166 \) and will require more iterations to get to the final answer.
4. **840**: This is \( 42 \times 20 = 840 \). This number is a bit more manageable than \( 420 \), but it is still significantly less than \( 5,166 \).
Among these, **4,200** is likely the best starting point, as it allows for a significant reduction from \( 5,166 \), and it is a round multiple of \( 42 \).
So, the best choice for the first number to subtract in the division problem \( 5,166 \div 42 \) is **4,200**.