Let's solve the problem step by step. We need to create two expressions using the digits 3, 3, 8, and 8 each once and only once and make an expression equal to 24.
### Expression 1:
First, let's consider the expression:
[tex]\[ \frac{8}{3 - \left(\frac{8}{3}\right)} \][/tex]
To simplify this expression:
1. Compute the inner division [tex]\(\frac{8}{3}\)[/tex], which is approximately 2.666.
2. Next, subtract this result from 3:
[tex]\[ 3 - 2.666 = 0.334 \][/tex]
3. Finally, divide 8 by the result of the subtraction:
[tex]\[ \frac{8}{0.334} \approx 24 \][/tex]
So, the value of this expression is very close to 24.
### Expression 2:
Next, consider the expression:
[tex]\[ (8 + 8) - (3 - 3) \][/tex]
To simplify this expression:
1. Compute the addition [tex]\( 8 + 8 = 16 \)[/tex].
2. Compute the subtraction [tex]\( 3 - 3 = 0 \)[/tex].
3. Finally, subtract the result of the second operation from the first:
[tex]\[ 16 - 0 = 16 \][/tex]
So, the value of this second expression is 16.
### Combined Expression:
By putting both parts together:
[tex]\[ \frac{8}{3 - \left(\frac{8}{3}\right)} = 24 \][/tex]
[tex]\[ (8 + 8) - (3 - 3) = 16 \][/tex]
There you have the two separate expressions that use the digits 3, 3, 8, and 8 each once.
