To verify the quotient \( \frac{3}{2} \div \frac{1}{8} \), we can rephrase this as finding out how many \( \frac{1}{8} \) portions fit into \( \frac{3}{2} \).
First, we can convert the division into multiplication by flipping the second fraction. Thus, we have:
\[ \frac{3}{2} \div \frac{1}{8} = \frac{3}{2} \times \frac{8}{1} = \frac{3 \times 8}{2} = \frac{24}{2} = 12 \]
So, the quotient is 12, meaning that there are 12 portions of \( \frac{1}{8} \) in \( \frac{3}{2} \).
Now, we analyze the area models given:
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The first area model has 8 shaded parts. This model might represent \( \frac{1}{8} \) sections, showing that from the 12 portions found, you could visualize the total area with the \( \frac{1}{8} \) units represented.
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The second area model has 4 shaded parts and 4 unshaded parts. This likely doesn’t represent \( \frac{3}{2} \) accurately since it seems to represent a smaller quantity.
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An area model with 16 shaded parts and 8 unshaded parts. If each shaded part represents \( \frac{1}{8} \), then this adds up to 16 parts of \( \frac{1}{8} \), which indicates that \( \frac{3}{2} \) is definitely larger than this.
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An area model with 2 shaded parts and 22 unshaded parts. This would be the least relevant as it represents a much smaller quantity than \( \frac{3}{2} \).
From this analysis, the first area model with 8 shaded parts likely verifies the division \( \frac{3}{2} \div \frac{1}{8} \) by showing appropriate portions of \( \frac{1}{8} \). However, since our answer is 12, the area model representing \( \frac{1}{8} \) units should ideally present a total of 12 throughout its whole representation.
Thus, it's crucial to note the models, if accurately scaled for comparison, should appropriately delineate 12 \( \frac{1}{8} \) units found in \( \frac{3}{2} \). The first area model can be considered closest depending on its representation method despite not directly having 12 portions shown.
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