Question

Write the product when \[\dfrac{6}{{13}}\] is multiplied by the reciprocal of \[\dfrac{{ - 7}}{{16}}\] ?

Answer 1

Hint: Here in the given question, we need to solve two fractions, here we know that while dividing two fractions we, multiply the numerator of the second fraction to the denominator of first fraction and denominator of the second fraction will be multiplied by the numerator of the first fraction.

Complete step by step answer:
Here in the given question we need to divide the two given fraction, here we need to solve by putting these terms in fraction form and thus solved accordingly, on solving we get:
We have:
\[ \Rightarrow \dfrac{6}{{13}} \div \dfrac{{ - 7}}{{16}}\]
Putting into fraction form we have:
\[ \Rightarrow \dfrac{{\dfrac{6}{{13}}}}{{\dfrac{{ - 7}}{{16}}}}\]
On solving we get:
\[ \Rightarrow \dfrac{6}{{13}} \times \dfrac{{16}}{{ - 7}} = \dfrac{{96}}{{ - 91}} = \dfrac{{ - 96}}{{91}}\]
Here we get the simplified fraction, here no common factors are present in the fraction except one, hence we have the simplified fraction and the answer for the given question.

Note: Here in the given question, we have to solve two fractions together, which need to be divided, hence solved accordingly. On solving fractions we need to consider the property related with the fractions operation, to get the right suitable and simplified answer. After obtaining a fraction we need to check the common factors in numerator and denominator to get the simplified and smallest fraction.