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]
