To determine the value of [tex]\( x \)[/tex] when [tex]\( 40\% \)[/tex] is expressed as the fraction [tex]\( \frac{x}{30} \)[/tex], follow these steps:
1. Understand the problem: We are given that [tex]\( 40\% \)[/tex] (which can be written as [tex]\( 0.40 \)[/tex]) is equivalent to the fraction [tex]\( \frac{x}{30} \)[/tex]. This can be turned into an equation for us to solve for [tex]\( x \)[/tex].
2. Set up the equation: Start by writing the relationship given in the problem mathematically.
[tex]\[
0.40 = \frac{x}{30}
\][/tex]
3. Solve for [tex]\( x \)[/tex]: To isolate [tex]\( x \)[/tex], multiply both sides of the equation by the denominator, which is 30, to get rid of the fraction.
[tex]\[
0.40 \times 30 = x
\][/tex]
4. Calculate the result: Perform the multiplication on the left-hand side.
[tex]\[
0.40 \times 30 = 12
\][/tex]
5. Conclusion: The value of [tex]\( x \)[/tex] is [tex]\( 12 \)[/tex].
Hence, when [tex]\( 40\% \)[/tex] is equal to the fraction [tex]\( \frac{x}{30} \)[/tex], the value of [tex]\( x \)[/tex] is [tex]\(\boxed{12}\)[/tex].
