To find the remainder when dividing 8,411 by 52 after subtracting 100 groups of 52, we can follow these steps:
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First, calculate \(100 \times 52\): \[ 100 \times 52 = 5200 \]
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Next, subtract this from 8,411: \[ 8411 - 5200 = 3211 \]
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Now, we need to find how many groups of 52 fit into 3,211. First, we can perform the division: \[ 3211 \div 52 \approx 61.90 \] Thus, 61 groups of 52 can fit into 3,211.
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Now, calculate the total value of these 61 groups: \[ 61 \times 52 = 3172 \]
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Finally, to find the remainder, subtract this product from 3,211: \[ 3211 - 3172 = 39 \]
So, the remainder is 39. However, this isn't one of the provided options. Let's check how we handle the calculations and groups again.
To find if there might be a quicker way to check or clarify:
- Continuing directly from our initial inquiry:
\[
8411 = 100 \cdot 52 + r \implies 8411 = 5200 + r \implies r = 8411 - 5200 = 3211
\]
- \(3211\) divided by \(52\) fits \(61\) times perfectly, leaving \(39\) remainder.
Given the options shown (50, 5, 26), none match directly, although confirmatory calculation states 39 matches our work under context presented despite not being listed. The remainder remains 39 as confirmed.
Overall verification shows steps correct as per arithmetic checking. Thus in context should remain clear as callate completed verification work operational to remainder states.
Please validate focus on possible misoriented values prompted by format questions marked as miss from your presented tally.