To solve the problem of finding the quotient [tex]\(\frac{\frac{7}{8}}{\frac{1}{4}}\)[/tex] and simplifying it completely, let's go step-by-step through the solution.
First, we need to understand how to handle the division of fractions. The division of fractions can be transformed into multiplication by the reciprocal of the divisor.
Given the problem:
[tex]\[
\frac{\frac{7}{8}}{\frac{1}{4}}
\][/tex]
We can rewrite this as:
[tex]\[
\frac{7}{8} \div \frac{1}{4}
\][/tex]
To perform the division, we multiply by the reciprocal of [tex]\(\frac{1}{4}\)[/tex]. The reciprocal of [tex]\(\frac{1}{4}\)[/tex] is [tex]\(\frac{4}{1}\)[/tex]. Thus, the problem becomes:
[tex]\[
\frac{7}{8} \times \frac{4}{1}
\][/tex]
Next, we multiply the numerators and the denominators:
[tex]\[
\frac{7 \times 4}{8 \times 1} = \frac{28}{8}
\][/tex]
Now, we simplify the fraction [tex]\(\frac{28}{8}\)[/tex]. To do this, we find the greatest common divisor (GCD) of the numerator and the denominator. The GCD of 28 and 8 is 4.
We then divide both the numerator and the denominator by their GCD:
[tex]\[
\frac{28 \div 4}{8 \div 4} = \frac{7}{2}
\][/tex]
The simplified fraction [tex]\(\frac{7}{2}\)[/tex] can also be expressed as a mixed number or a decimal. In this case, as a decimal:
[tex]\[
\frac{7}{2} = 3.5
\][/tex]
Therefore, the quotient is:
[tex]\[
3.5
\][/tex]
So, the number that belongs in the green box is:
[tex]\[
\boxed{3.5}
\][/tex]
