To solve the given expression [tex]\(\frac{2}{4 \times \frac{1}{2} - 1}\)[/tex], we will break it down into smaller steps and simplify each part:
1. Simplify the expression inside the parentheses:
[tex]\[
4 \times \frac{1}{2}
\][/tex]
2. Perform the multiplication:
[tex]\(4 \times \frac{1}{2}\)[/tex] simplifies to:
[tex]\[
4 \times 0.5 = 2
\][/tex]
3. Subtract 1 from the result of the multiplication:
[tex]\[
2 - 1
\][/tex]
4. Calculate the subtraction:
[tex]\(2 - 1\)[/tex] simplifies to:
[tex]\[
1
\][/tex]
5. Now, we can rewrite our original expression with the simplified denominator:
[tex]\[
\frac{2}{1}
\][/tex]
6. Perform the division:
[tex]\(\frac{2}{1}\)[/tex] simplifies to:
[tex]\[
2
\][/tex]
So, the value of the expression [tex]\(\frac{2}{4 \times \frac{1}{2} - 1}\)[/tex] is:
[tex]\[
2
\][/tex]
Therefore, the step-by-step solution to the expression is [tex]\(\boxed{2}\)[/tex].
