To find the ratio in simplest form between [tex]\(\frac{2}{3}\)[/tex] and [tex]\(\frac{3}{2}\)[/tex], follow these steps:
1. Write the problem as a division of two fractions:
[tex]\[
\frac{\frac{2}{3}}{\frac{3}{2}}
\][/tex]
2. Apply the rule for dividing fractions (you multiply by the reciprocal):
[tex]\[
\frac{2}{3} \div \frac{3}{2} = \frac{2}{3} \times \frac{2}{3}
\][/tex]
3. Multiply the numerators and the denominators:
[tex]\[
\left(\frac{2 \times 2}{3 \times 3}\right) = \frac{4}{9}
\][/tex]
4. So, the simplest form of the ratio of [tex]\(\frac{2}{3}\)[/tex] to [tex]\(\frac{3}{2}\)[/tex] is:
[tex]\[
\frac{4}{9}
\][/tex]
Thus, the ratio in simplest form is [tex]\(\frac{4}{9}\)[/tex].
