To determine which division problem the area models represent, we need to interpret the shaded and unshaded parts.
In the first model, there are 4 shaded parts, which could indicate a division where the total number (the dividend) is 7/4.
In the second model, with 3 shaded parts and 1 unshaded part, we can infer that there is a total of 4 parts (3 shaded + 1 unshaded). This suggests we are dividing the total amount into 4 equal parts.
To analyze the given options:
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StartFraction 7 Over 4 EndFraction divided by one-half = 3 and one-half:
- Dividing by 1/2 means you're determining how many half-units are in 7/4. We can calculate: \[ \frac{7/4}{1/2} = \frac{7/4} \times \frac{2}{1} = \frac{14}{4} = \frac{7}{2} = 3.5\quad \text{(exactly 3 and 1/2)} \] This expression results in exactly 3 and 1/2 units.
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StartFraction 7 Over 4 EndFraction divided by one-third = 3 and one-half:
- Dividing by 1/3 means you're determining how many third-units are in 7/4. We calculate: \[ \frac{7/4}{1/3} = \frac{7/4} \times 3 = \frac{21}{4} = 5.25\quad \text{(not 3 and 1/2)} \]
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StartFraction 7 Over 4 EndFraction divided by two-thirds = 3 and one-half:
- Dividing by 2/3 means you're determining how many two-thirds units are in 7/4. We calculate: \[ \frac{7/4}{2/3} = \frac{7/4} \times \frac{3}{2} = \frac{21}{8} = 2.625\quad \text{(not 3 and 1/2)} \]
Given this reasoning, the model best represents the first option:
StartFraction 7 Over 4 EndFraction divided by one-half = 3 and one-half.
1 answer