To analyze the situation described, we need to interpret the area model provided. It has 4 shaded parts, and these represent \(\frac{4}{5}\) of the whole. That implies the unshaded part represents \(\frac{1}{5}\), since \(1 - \frac{4}{5} = \frac{1}{5}\).
In this case, we need to determine the expression that corresponds to the fraction of shaded parts.
The 4 shaded parts representing \(\frac{4}{5}\) suggests that if 'whole' is considered to be broken down into parts, the respective operation involved might relate one quantity to another.
Now let’s analyze the options:
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4 divided by one-fifth: This would yield \(4 \div \frac{1}{5} = 4 \times 5 = 20\). This does not relate to the area model directly in terms of fractions and shaded/ unshaded parts.
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4 divided by \(\frac{4}{5}\): This implies calculating how many times \(\frac{4}{5}\) fits into 4, which is equal to \(4 \div \frac{4}{5} = 4 \times \frac{5}{4} = 5\). This is a valid division concerning the given area model.
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\(\frac{4}{5}\) divided by one-fifth: This calculates how many times \(\frac{1}{5}\) fits into \(\frac{4}{5}\) yielding \(\frac{4}{5} \div \frac{1}{5} = \frac{4}{5} \times 5 = 4\). This could relate in terms of portions but doesn't reflect what the area model initially showcases.
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One-fifth divided by \(\frac{4}{5}\): This would give \(\frac{1}{5} \div \frac{4}{5} = \frac{1}{5} \times \frac{5}{4} = \frac{1}{4}\). This doesn't match the shaded section as well.
From this analysis, the most appropriate expression that could be modeled using the given area model with 4 shaded parts and 1 unshaded part labeled as \(\frac{4}{5}\) is:
4 divided by \(\frac{4}{5}\).
1 answer