Question

Divide (1). \[\dfrac{2}{3}\div -\dfrac{4}{5}\] (2). \[-\dfrac{6}{7}\div -15\].

Answer 1

Hint: In this problem, we have to find the value of the given divisions. We can see that we will have a fraction divided by another fraction. In these types of problems, we can use the reciprocal method to divide it. We can take the denominator and reciprocal it and multiply it with the fraction in the numerator and simplify it to get the answer.

Complete step by step answer:
Here we have to divide the given expressions.
We should know that if we have a fraction divided by another fraction, then we can use the reciprocal method to divide it. We can take the denominator and reciprocal it and multiply it with the fraction in the numerator and simplify it
(1). \[\dfrac{2}{3}\div -\dfrac{4}{5}\]
 We can now write the given expression as,
\[\Rightarrow \dfrac{\dfrac{2}{3}}{-\dfrac{4}{3}}\]
We can now take reciprocal in the above step, we get
\[\Rightarrow \dfrac{2}{3}\times -\dfrac{3}{4}=-\dfrac{1}{2}=-0.5\]
Therefore, the simplified form of the given expression 1). \[\dfrac{2}{3}\div -\dfrac{4}{5}=-0.5\]
(2). \[-\dfrac{6}{7}\div -15\].
We can now write the given expression as,
\[\Rightarrow \dfrac{-\dfrac{6}{7}}{-\dfrac{15}{1}}\]
We can now take reciprocal in the above step, we get
\[\Rightarrow -\dfrac{6}{7}\times -\dfrac{1}{15}=+\dfrac{2}{35}=0.0571\]
Therefore, the simplified form of the given expression (2). \[-\dfrac{6}{7}\div -15=0.0571\].

Note: We should always remember that if we have a fraction divided by another fraction, then we can use the reciprocal method to divide it. We can take the denominator and reciprocal it and multiply it with the fraction in the numerator. We should also remember that if we multiply a negative and a negative, we get a positive.