Question

Multiply $\dfrac{6}{{13}}$ by the reciprocal of $\dfrac{{ - 7}}{{16}}$.

Answer 1

Hint: This question is based on the Fractions. In this question two fractional numbers are given and we have to do the multiplication of these numbers also one more condition is given that we have to find the reciprocal of one number and then do the multiplication. The reciprocal of a number is obtained when the number is divided by 1.

Complete step-by-step answer:
Given:
Let us assume the two fractional numbers are $x$ and $y$ respectively. Then according to the question,
We have given,
$x = \dfrac{6}{{13}}$
And,
$\Rightarrow y = \dfrac{{ - 7}}{{16}}$
Now according to the definition of the reciprocal. The reciprocal of the number $y = \dfrac{{ - 7}}{{16}}$ can be calculated in the following way –
Reciprocal of
$\Rightarrow y = \dfrac{1}{y}$
So,
Reciprocal of
$
\Rightarrow y = \dfrac{1}{{\left( {\dfrac{{ - 7}}{{16}}} \right)}}\\
 = \dfrac{{ - 16}}{7}
$
So now multiplying the $x$ and the reciprocal of $y$ we get,
$\Rightarrow x \times \dfrac{1}{y} = \left( {\dfrac{6}{{13}}} \right) \times \left( {\dfrac{{ - 16}}{7}} \right)$
Solving this we get,
$
x \times \dfrac{1}{y} = \dfrac{{ - 6 \times 16}}{{13 \times 7}}\\
 = \dfrac{{ - 96}}{{91}}
$
Since the numerator is greater than the denominator, we can write this in the mixed fractional form.
So, the mixed fractional form of $\dfrac{{ - 96}}{{91}}$ is given by –
$\Rightarrow \dfrac{{ - 96}}{{91}} = - 1\dfrac{5}{{91}}$
Therefore, the correct answer in the lowest form is - 1\dfrac{5}{{91}}$

Note: It should be noted that if the value of the numerator is greater than the value of the denominator then we use the method of division to convert the simple fraction into the mixed fraction. In this method we divide the numerator value by the denominator value. The quotient obtained by the division will make the base number of the mixed fraction while the remainder will be the numerator of the fractional part of the mixed fraction and the denominator would be the divisor.
For example, in the given question we have to change $\dfrac{{ - 96}}{{91}}$ into mixed fractional form. So, we divide the numerator $ - 96$ by the denominator $91$. So, we have –
Divisor $ = 91$
Dividend $ = - 96$
Quotient $ = - 1$
And,
Reminder $
 = 96 - 91\\
 = 5
$
Therefore, the mixed fractional form of the number $\dfrac{{ - 96}}{{91}}$ is $ - 1\dfrac{5}{{91}}$