Question
Which model verifies the quotient
3
2
÷
1
8
?
2 area models. 1 model has 8 shaded parts. The second has 4 shaded parts and 4 unshaded parts.
An area model with 16 shaded parts and 8 unshaded parts.
An area model with 2 shaded parts and 22 unshaded parts.
3
2
÷
1
8
?
2 area models. 1 model has 8 shaded parts. The second has 4 shaded parts and 4 unshaded parts.
An area model with 16 shaded parts and 8 unshaded parts.
An area model with 2 shaded parts and 22 unshaded parts.
Answers
GPT-4o mini
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:
1. **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.
2. **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.
3. **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.
4. **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.
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:
1. **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.
2. **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.
3. **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.
4. **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.