To solve the expression [tex]\(\frac{5}{\frac{9}{4}}\)[/tex], we can go through the following detailed, step-by-step solution:
1. Understanding the expression: We need to divide the number 5 by the fraction [tex]\(\frac{9}{4}\)[/tex].
2. Reciprocal step: Dividing by a fraction is equivalent to multiplying by its reciprocal. Therefore, we can rewrite the expression:
[tex]\[
\frac{5}{\frac{9}{4}} = 5 \times \frac{4}{9}
\][/tex]
3. Multiplication step: Next, we multiply the numerator (5) by the reciprocal of the denominator ([tex]\(\frac{4}{9}\)[/tex]):
[tex]\[
5 \times \frac{4}{9}
\][/tex]
4. Calculation step: To proceed with the multiplication, we multiply the numerators and keep the denominator as is:
[tex]\[
5 \times \frac{4}{9} = \frac{5 \times 4}{9} = \frac{20}{9}
\][/tex]
5. Dividing step: Now, we need to perform the division:
[tex]\[
\frac{20}{9}
\][/tex]
6. Result interpretation: Converting [tex]\(\frac{20}{9}\)[/tex] to a decimal, we get approximately:
[tex]\[
\frac{20}{9} \approx 2.2222222222222223
\][/tex]
Therefore, the value of [tex]\(\frac{5}{\frac{9}{4}}\)[/tex] is approximately [tex]\(2.2222222222222223\)[/tex].
In summary, the detailed, step-by-step solution to [tex]\(\frac{5}{\frac{9}{4}}\)[/tex] involves rewriting the division as a multiplication by the reciprocal, performing the multiplication, and then converting the fraction to a decimal, resulting in an approximate value of [tex]\(2.2222222222222223\)[/tex].
