To determine which expression is represented by the given description, let's analyze it step by step.
The fractional values given in the options relate to the number line going from 0 to 1 in increments of one-eighths (which are \( \frac{1}{8}, \frac{2}{8}, \frac{3}{8}, \ldots, \frac{8}{8} \)).
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Option 1: \(\frac{7}{8} \div \frac{1}{8}\)
- This expression calculates how many eighths are in \( \frac{7}{8} \). The result of this division would be 7, since \( \frac{7}{8} \) consists of 7 eighths.
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Option 2: \(\frac{1}{8} \div \frac{7}{8}\)
- This expression calculates how much of \( \frac{7}{8} \) is in \( \frac{1}{8} \). The result would be \( \frac{1}{7} \), which is less than 1.
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Option 3: \(\frac{1}{8} \div 7\)
- This expression is equal to \( \frac{1}{56} \), which again does not relate to the action represented by the increments.
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Option 4: \(7 \div \frac{7}{8}\)
- This expression deals with how many \( \frac{7}{8} \) fit into 7. The result of this division would be 8, since there are 8 groups of \( \frac{7}{8} \) in 7 (because \( 7 \div \frac{7}{8} = 7 \times \frac{8}{7} = 8 \)).
After reviewing the options and their relations to the number line and the structure of the fractions, it appears that Option 1: \(\frac{7}{8} \div \frac{1}{8}\) best reflects the concept of dividing the number line into segments of eighths. This action determines the quantity of eighths present in the fraction \( \frac{7}{8} \), making it the most relevant choice based on the description provided.
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