To determine if the proportion [tex]\(\frac{27}{8} = \frac{9}{4}\)[/tex] is true, we can use the method of cross-multiplication. This method involves multiplying the numerator of each fraction by the denominator of the other fraction.
Let's follow these steps:
1. Cross-multiply the numerator of the first fraction by the denominator of the second fraction:
[tex]\[
27 \times 4 = 108
\][/tex]
2. Cross-multiply the numerator of the second fraction by the denominator of the first fraction:
[tex]\[
9 \times 8 = 72
\][/tex]
3. Compare the two results from the cross-multiplications:
[tex]\[
108 \quad \text{and} \quad 72
\][/tex]
Since [tex]\(108 \neq 72\)[/tex], the two fractions are not equal.
Therefore, the proportion [tex]\(\frac{27}{8} = \frac{9}{4}\)[/tex] is \textbf{False}.
