Find the quotient. Simplify your answer completely.

[tex]\[
\frac{\frac{5}{8}}{\frac{3}{2}} = \underline{[?]}
\][/tex]

Enter the number that belongs in the box.
[tex]\[
\square \quad \text{Enter}
\][/tex]



Answer :

To solve the expression [tex]\(\frac{\frac{5}{8}}{\frac{3}{2}}\)[/tex], we need to follow these steps:

1. Rewrite the division of fractions as multiplication:
When dividing by a fraction, you multiply by its reciprocal. So, we rewrite [tex]\(\frac{\frac{5}{8}}{\frac{3}{2}}\)[/tex] as [tex]\(\frac{5}{8} \times \frac{2}{3}\)[/tex].

2. Multiply the numerators together and the denominators together:
- Numerator: [tex]\(5 \times 2 = 10\)[/tex]
- Denominator: [tex]\(8 \times 3 = 24\)[/tex]

3. Form the resulting fraction:
So, we get [tex]\(\frac{10}{24}\)[/tex].

4. Simplify the resulting fraction:
To simplify [tex]\(\frac{10}{24}\)[/tex], we find the greatest common divisor (GCD) of 10 and 24. The GCD of 10 and 24 is 2. We then divide both the numerator and the denominator by their GCD:
[tex]\[ \frac{10 \div 2}{24 \div 2} = \frac{5}{12} \][/tex]

Thus, the quotient simplifies to [tex]\(\frac{5}{12}\)[/tex].

However, in numerical form, the result of [tex]\(\frac{5}{12}\)[/tex] is approximately [tex]\(0.4166666666666667\)[/tex].

Therefore, the number that belongs in the green box is:
[tex]\[ \boxed{0.4166666666666667} \][/tex]