Let's evaluate each expression step by step to determine which one equals [tex]\(\frac{2}{3}\)[/tex].
1. Expression 1: [tex]\( 8 + \left( \frac{24}{12} \right) \times 4 \)[/tex]
- First, calculate [tex]\(\frac{24}{12} = 2\)[/tex].
- Then, evaluate [tex]\(2 \times 4 = 8\)[/tex].
- Finally, add [tex]\(8 + 8 = 16\)[/tex].
2. Expression 2: [tex]\(\frac{8 + 24}{12 \times 4}\)[/tex]
- First, calculate [tex]\(8 + 24 = 32\)[/tex].
- Then, evaluate [tex]\(12 \times 4 = 48\)[/tex].
- Finally, perform the division [tex]\(\frac{32}{48} = \frac{2}{3}\)[/tex].
3. Expression 3: [tex]\( 8 + \frac{24}{12 \times 4} \)[/tex]
- First, calculate [tex]\(12 \times 4 = 48\)[/tex].
- Then, evaluate [tex]\(\frac{24}{48} = \frac{1}{2}\)[/tex].
- Finally, add [tex]\(8 + \frac{1}{2} = 8.5\)[/tex].
4. Expression 4: [tex]\( 8 + \frac{24}{12} \times 4 \)[/tex]
- First, calculate [tex]\(\frac{24}{12} = 2\)[/tex].
- Then, evaluate [tex]\(2 \times 4 = 8\)[/tex].
- Finally, add [tex]\(8 + 8 = 16\)[/tex].
From the evaluations, we observe that:
- Expression 1 results in 16.
- Expression 2 results in [tex]\(\frac{2}{3}\)[/tex].
- Expression 3 results in 8.5.
- Expression 4 results in 16.
Therefore, the expression that has a value of [tex]\(\frac{2}{3}\)[/tex] is [tex]\(\frac{8 + 24}{12 \times 4}\)[/tex].
