To determine the extremes of the given proportion [tex]\(\frac{3}{4} = \frac{6}{8}\)[/tex], let's go through the following steps:
1. Understanding Proportions: A proportion is an equation stating that two ratios are equivalent. In the proportion [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex], the first and last terms [tex]\(a\)[/tex] and [tex]\(d\)[/tex] are called the extremes, while the second and third terms [tex]\(b\)[/tex] and [tex]\(c\)[/tex] are called the means.
2. Identifying Terms in the Proportion: The given proportion is [tex]\(\frac{3}{4} = \frac{6}{8}\)[/tex]. Breaking this down:
- The numerator of the first ratio is 3.
- The denominator of the first ratio is 4.
- The numerator of the second ratio is 6.
- The denominator of the second ratio is 8.
3. Determining the Extremes: According to the definition of extremes in a proportion, the extremes are the first term of the first ratio and the last term of the second ratio.
- The first term of the first ratio ([tex]\(\frac{3}{4}\)[/tex]) is 3.
- The last term of the second ratio ([tex]\(\frac{6}{8}\)[/tex]) is 8.
Hence, the extremes of the given proportion [tex]\(\frac{3}{4} = \frac{6}{8}\)[/tex] are:
[tex]\[
\boxed{3 \text{ and } 8}
\][/tex]
So the correct answer is:
A. 3 and 8
