Question

How do you simplify $\dfrac{6}{7}\div \dfrac{4}{5}$?

Answer 1

Hint: In this problem we need to divide the two fractions and then we need to simplify the equation. We know that $\dfrac{a}{b}\div \dfrac{c}{d}=\dfrac{ad}{cb}$. So, we will first compare the given value with the value $\dfrac{a}{b}\div \dfrac{c}{d}$ and write the values of $a$, $b$, $c$, $d$. After that we will calculate the values of $ad$ and $cb$. Now we will use the formula $\dfrac{a}{b}\div \dfrac{c}{d}=\dfrac{ad}{cb}$ and substitute the values we have and simplify the equation to get the required result.

Complete step by step solution:
Given that, $\dfrac{6}{7}\div \dfrac{4}{5}$.
Comparing the above given value with $\dfrac{a}{b}\div \dfrac{c}{d}$, then we will get values of $a$, $b$, $c$, $d$as
$a=6$, $b=7$, $c=4$, $d=5$.
Now the value of $ad$ will be
$\Rightarrow ad=6\times 5=30$
And the value of $cb$ will be
$\Rightarrow cb=4\times 7=28$
Applying the known formula $\dfrac{a}{b}\div \dfrac{c}{d}=\dfrac{ad}{cb}$, then we will get
$\Rightarrow \dfrac{6}{7}\div \dfrac{4}{5}=\dfrac{30}{28}$
From the above equation we have the result of $\dfrac{6}{7}\div \dfrac{4}{5}$ as $\dfrac{30}{28}$. To simplify the obtained result which is a fraction we are going to consider the numerator and denominator individually and cancel the common factors.
Considering the denominator which is $28$. We have $1$, $2$, $4$, $7$, $14$, $28$ as factors for the denominator.
Considering the numerator which is $30$. We have $1$, $2$, $3$, $5$, $6$, $10$, $15$, $30$ as factors of the numerator.
From the factors of the numerator and denominator we are going to write the given value as
$\Rightarrow \dfrac{6}{7}\div \dfrac{4}{5}=\dfrac{2\times 15}{2\times 14}$
Canceling the common factor which is $2$ in both numerator and denominator, then we will get
$\Rightarrow \dfrac{6}{7}\div \dfrac{4}{5}=\dfrac{15}{14}$

Hence the simplified form of the given value $\dfrac{6}{7}\div \dfrac{4}{5}$ is $\dfrac{15}{14}$.

Note: We can also follow another method to solve the given value. When we need to divide the two fractions then we will multiply the inverse the dividend fraction. From this we can write the given value as
$\begin{align}
  & \Rightarrow \dfrac{6}{7}\div \dfrac{4}{5}=\dfrac{6}{7}\times \dfrac{5}{4} \\
 & \Rightarrow \dfrac{6}{7}\div \dfrac{4}{5}=\dfrac{30}{28} \\
\end{align}$
From this method also we have the same result.