Sure, let's go through the solution step-by-step:
1. Simplify [tex]\(\frac{4}{16}\)[/tex] to its lowest terms:
- The fraction is [tex]\(\frac{4}{16}\)[/tex].
- To simplify this, we need to find the greatest common divisor (GCD) of the numerator (4) and the denominator (16).
- The GCD of 4 and 16 is 4.
- We divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{4 \div 4}{16 \div 4} = \frac{1}{4}
\][/tex]
- So, [tex]\(\frac{4}{16}\)[/tex] simplifies to [tex]\(\frac{1}{4}\)[/tex].
2. Find an equivalent fraction that has a denominator of 32:
- We need an equivalent fraction to [tex]\(\frac{1}{4}\)[/tex] with a denominator of 32.
- To do this, we examine the relationship between the old denominator (4) and the new denominator (32).
- We note that [tex]\(32 \div 4 = 8\)[/tex].
- Hence, we multiply both the numerator and the denominator of the simplified fraction [tex]\(\frac{1}{4}\)[/tex] by 8:
[tex]\[
\frac{1 \times 8}{4 \times 8} = \frac{8}{32}
\][/tex]
- So, the equivalent fraction with a denominator of 32 is [tex]\(\frac{8}{32}\)[/tex].
After following these steps, we can see that [tex]\(\frac{4}{16}\)[/tex] simplifies to [tex]\(\frac{1}{4}\)[/tex], and its equivalent fraction with a denominator of 32 is [tex]\(\frac{8}{32}\)[/tex].
Thus, the correct answer from the given choices is:
[tex]\[
\boxed{\frac{1}{4}, \frac{8}{32}}
\][/tex]
