Question

What is the quotient in $2\dfrac{4}{7}\div 1\dfrac{3}{6}$ ?

Answer 1

Hint: To solve this question first we need to convert the mixed fractions into improper fractions. Then we will divide the obtained fractions. To divide the fractions we will convert the division sign by multiplication sign and reciprocate the second fraction.

Complete step by step solution:
We have been given an expression $2\dfrac{4}{7}\div 1\dfrac{3}{6}$.
We have to find the quotient for the given expression.
Now, we know that quotients are obtained by dividing two numbers.
To divide the given fractions first we need to convert the given mixed fractions into improper fractions. Then we will get
\[\Rightarrow 2\dfrac{4}{7}=\dfrac{18}{7}\] and \[ 1\dfrac{3}{6}=\dfrac{9}{6}\]
Now, we have to find the quotient of $\dfrac{18}{7}\div \dfrac{9}{6}$
Now, we know that to divide the fractions we need to convert the division sign into multiplication and reciprocate the second fraction. Then we will get
\[\Rightarrow \dfrac{18}{7}\times \dfrac{6}{9}\]
Now, simplifying the above obtained equation by cancelling out the common factors we will get
\[\begin{align}
  & \Rightarrow \dfrac{18}{7}\times \dfrac{2}{3} \\
 & \Rightarrow \dfrac{6}{7}\times \dfrac{2}{1} \\
 & \Rightarrow \dfrac{12}{7} \\
\end{align}\]
Hence we get the quotient as \[\dfrac{12}{7}\].

Note: The point to be remembered is that to solve the division of fractions students must need to convert the sign. Also reciprocate the divisor as there is no need to reciprocate the dividend. We can also check the obtained answer by using the quotient rule which is given as $\text{Dividend=quotient}\times divisor+remainder$. Substituting the value and simplifying the obtained equation we can verify the answer.