To determine an integer that could be used as the denominator of the fraction [tex]\(\frac{1}{d}\)[/tex] such that the value of the fraction is less than 23%, follow these steps:
1. Understand the problem: We need the fraction [tex]\(\frac{1}{d}\)[/tex] to be less than 23%.
2. Convert percentage to decimal: 23% can be written as 0.23.
3. Form the inequality: Set up the inequality
[tex]\[
\frac{1}{d} < 0.23.
\][/tex]
4. Isolate the variable [tex]\(d\)[/tex]:
[tex]\[
1 < 0.23d.
\][/tex]
5. Solve for [tex]\(d\)[/tex]:
[tex]\[
d > \frac{1}{0.23}.
\][/tex]
6. Calculate [tex]\(\frac{1}{0.23}\)[/tex]:
[tex]\[
\frac{1}{0.23} \approx 4.35.
\][/tex]
7. Determine the smallest integer greater than 4.35:
The smallest integer that is greater than 4.35 is 5.
Therefore, one integer that could be used as the denominator of the fraction [tex]\(\frac{1}{d}\)[/tex] to make its value less than 23% is [tex]\(d = 5\)[/tex].
