Question

To help you find the price of 12 apples, find
1
2
​
·
8
12
​
. Select all the equivalent values for
1
2
​
·
8
12
​
.
×
8
12
​

×
8
12
​

Number of Apples Price
8 $2
12 ?


2 ·
8
12
​


=
2 · 12
1 · 8

8
24
​


3

8
12
​


24

Answer 1

To find the price of 12 apples, we can start with the information given and simplify the expression \( \frac{1}{2} \cdot \frac{8}{12} \).

1. **Calculating the expression**:

We can multiply:

\[
\frac{1}{2} \cdot \frac{8}{12} = \frac{1 \cdot 8}{2 \cdot 12} = \frac{8}{24}
\]

2. **Simplifying**:

Now, we can simplify \( \frac{8}{24} \):

\[
\frac{8}{24} = \frac{1}{3}
\]

3. **Finding Equivalent Expressions**:

Now we must gather the equivalent values for \( \frac{1}{2} \cdot \frac{8}{12} \):

- \( \frac{8}{24} \) is equivalent because we derived it from the calculation.
- \( \frac{1}{3} \) is equivalent due to simplification.

**Choices you mentioned**:
- The expression \( \frac{8}{12} \) simplifies to \( \frac{2}{3} \), which is **not equivalent**.
- The expressions \( 2 \cdot \frac{8}{12} = \frac{16}{12} = \frac{4}{3} \) and \( 2 \cdot 12 \) also yield different values.
- The values 3, 24, and any other mentioned values do not seem to relate to the expressions found.

Thus, the equivalent values derived for \( \frac{1}{2} \cdot \frac{8}{12} \) are:

1. \( \frac{8}{24} \)
2. \( \frac{1}{3} \)

Let me know if you need further calculations or clarifications!