To find the quotient of [tex]\(\frac{-\frac{5}{12}}{-\frac{15}{4}}\)[/tex] and simplify the answer completely, follow these steps:
1. Division of Fractions:
The division of two fractions is equivalent to multiplying the first fraction by the reciprocal of the second fraction. In other words:
[tex]\[
\frac{-\frac{5}{12}}{-\frac{15}{4}} = -\frac{5}{12} \times -\frac{4}{15}
\][/tex]
2. Multiplying the Fractions:
Multiply the numerators together and the denominators together:
[tex]\[
-\frac{5}{12} \times -\frac{4}{15} = \frac{-5 \times -4}{12 \times 15}
\][/tex]
Simplify the multiplication in the numerator and the denominator:
[tex]\[
\frac{20}{180}
\][/tex]
3. Simplifying the Fraction:
To simplify the fraction, divide the numerator and the denominator by their greatest common divisor (GCD). The GCD of 20 and 180 is 20.
Divide both the numerator and the denominator by 20:
[tex]\[
\frac{20 \div 20}{180 \div 20} = \frac{1}{9}
\][/tex]
The simplified form of the quotient is:
[tex]\[
\frac{1}{9}
\][/tex]
Thus, the number that belongs in the green box is:
[tex]\[
1
\][/tex]
