Certainly! To determine the means of the given proportion [tex]\(\frac{2}{3}=\frac{20}{30}\)[/tex], you need to find the products of the means. The means of a proportion are the numbers that are multiplied across the equal sign when simplifying the ratios.
The proportion given is:
[tex]\[ \frac{2}{3} = \frac{20}{30} \][/tex]
In a proportion of the form [tex]\(\frac{a}{b} = \frac{c}{d}\)[/tex], the means (which we refer to as the cross-products) are calculated by multiplying the denominator of one ratio by the numerator of the other ratio. We'll follow these steps:
1. Identify the Numbers in the Proportion:
- The numerator of the first fraction is [tex]\(2\)[/tex].
- The denominator of the first fraction is [tex]\(3\)[/tex].
- The numerator of the second fraction is [tex]\(20\)[/tex].
- The denominator of the second fraction is [tex]\(30\)[/tex].
2. Compute the Cross-Products:
- First, multiply the denominator of the first fraction ([tex]\(3\)[/tex]) by the numerator of the second fraction ([tex]\(20\)[/tex]).
[tex]\[
3 \times 20 = 60
\][/tex]
- Second, multiply the numerator of the first fraction ([tex]\(2\)[/tex]) by the denominator of the second fraction ([tex]\(30\)[/tex]).
[tex]\[
2 \times 30 = 60
\][/tex]
3. Identify the Means:
- Both cross-products are equal to [tex]\(60\)[/tex].
Therefore, the means of the proportion [tex]\(\frac{2}{3}=\frac{20}{30}\)[/tex] are [tex]\(60\)[/tex] and [tex]\(60\)[/tex].
