Sure! Let's solve the expression [tex]\(\frac{\frac{5}{3}}{\frac{9}{4}}\)[/tex] step by step.
1. Understand the problem: We have a complex fraction, which means we need to divide one fraction by another.
2. Rewrite the division as multiplication:
When you divide by a fraction, you multiply by its reciprocal. So, we rewrite the given expression [tex]\(\frac{\frac{5}{3}}{\frac{9}{4}}\)[/tex] using the reciprocal of [tex]\(\frac{9}{4}\)[/tex]. The reciprocal of [tex]\(\frac{9}{4}\)[/tex] is [tex]\(\frac{4}{9}\)[/tex].
Therefore:
[tex]\[
\frac{\frac{5}{3}}{\frac{9}{4}} = \frac{5}{3} \times \frac{4}{9}
\][/tex]
3. Multiply the fractions:
To multiply two fractions, multiply the numerators together and the denominators together.
So, we have:
[tex]\[
\frac{5}{3} \times \frac{4}{9} = \frac{5 \times 4}{3 \times 9} = \frac{20}{27}
\][/tex]
4. Simplify the fraction:
The fraction [tex]\(\frac{20}{27}\)[/tex] is already in its simplest form since 20 and 27 have no common factors other than 1.
So, the simplified value of the expression [tex]\(\frac{\frac{5}{3}}{\frac{9}{4}}\)[/tex] is:
[tex]\[
\frac{5}{3} \div \frac{9}{4} = \frac{20}{27}
\][/tex]
5. Decimal Representation:
If we convert the fraction [tex]\(\frac{20}{27}\)[/tex] to a decimal, we get approximately [tex]\(0.7407407407407408\)[/tex].
Thus, the answer is
[tex]\(\frac{\frac{5}{3}}{\frac{9}{4}} \approx 0.7407407407407408\)[/tex].
