What is $\dfrac{-9}{10}$ divided by $\dfrac{-6}{15}?$

Hint: We know that the reciprocal of a fraction can be obtained by interchanging the numerator and denominator. We also know that when we divide two fractions, we need to take the reciprocal of the divisor and multiply it with the dividend.

Complete step-by-step solution:
Let us consider the given problem.
We are asked to find the value obtained when $\dfrac{-9}{10}$ is divided by $\dfrac{-6}{15}.$
We know that the given numbers are fractions. In this problem, the fraction $\dfrac{-9}{10}$ is the dividend and the fraction $\dfrac{-6}{15}$ is the divisor.
We know that when we divide a fraction with another, we take the reciprocal of the latter and instead of dividing, we multiply the former with the reciprocal we have obtained.
So, in this case $\dfrac{-6}{15}$ is the divisor and we need to take the reciprocal of this fraction.
We know that the reciprocal of a fraction can be obtained by interchanging the numerator and the denominator.
So, the reciprocal of $\dfrac{-6}{15}$ is equal to $\dfrac{-15}{6}$ and, as shown, there will not be any change in the sign of the original fraction.
Now, to find the required quotient, we need to multiply the given dividend with the obtained reciprocal.
So, we will get $\dfrac{-9}{10}\times \dfrac{-15}{6}=\dfrac{-9}{2}\times \dfrac{-1}{2}.$
Since the product of two negative numbers is a positive number, we will get $\dfrac{-9}{10}\times \dfrac{-15}{6}=\dfrac{9}{4}.$
We can also express this fraction as a decimal number. And we will get $\dfrac{9}{4}=2.25.$
Hence the required quotient is $\dfrac{9}{4}=2.25.$

Note: We know that the product of two negative numbers is always a positive number. We also know that the sign of the reciprocal of a number is the same as the number. The number that is divided is called the dividend, the number that divides is called the divisor, the number that is obtained is called quotient and the number that is remained is called the remainder.