Question

Divide each of the below options:
(i) $18\div \dfrac{2}{3}$
(ii) $1\dfrac{2}{3}\div 5$
(iii) $20\div \dfrac{5}{6}$

Answer 1

Hint: We need to divide the numbers in form of $\dfrac{p}{q}$, or say fractions. To divide a fraction by another number, convert the number into a fraction, i.e. $\dfrac{p}{q}\div \dfrac{a}{b}$. Then, convert the division into multiplication. We can write the answer as: \[\dfrac{p}{q}\times \dfrac{b}{a}\]. The multiplication is the answer for the division.

Complete step-by-step solution:
(i) $18\div \dfrac{2}{3}$
We can write it as: $\dfrac{18}{1}\div \dfrac{2}{3}$
We know that multiplication and division are reciprocals of each other.
Now, converting the division into multiplication, we get:
$\begin{align}
  & =\dfrac{18}{1}\times \dfrac{3}{2} \\
 & =27 \\
\end{align}$
(ii) $1\dfrac{2}{3}\div 5$
We need to convert the mixed fraction into improper fraction.
So, we can write $1\dfrac{2}{3}$ as $\dfrac{5}{3}$
We can write $1\dfrac{2}{3}\div 5$ as: $\dfrac{5}{3}\div \dfrac{5}{1}$
Now, converting the division into multiplication, we get:
$\begin{align}
  & =\dfrac{5}{3}\times \dfrac{1}{5} \\
 & =\dfrac{1}{3} \\
\end{align}$
(iii) $20\div \dfrac{5}{6}$
We can write it as: $\dfrac{20}{1}\div \dfrac{5}{6}$
We know that multiplication and division are reciprocals of each other.
Now, converting the division into multiplication, we get:
$\begin{align}
  & =\dfrac{20}{1}\times \dfrac{6}{5} \\
 & =24 \\
\end{align}$

Note: Students might make mistakes while converting the mixed fractions into improper fractions. A mixed fraction is written in the form of $A\dfrac{p}{q}$, A is a whole number, and $\dfrac{p}{q}$ is a proper fraction. To convert a mixed fraction into an improper fraction, firstly multiply A with q and then add p and substitute in the place of p in $\dfrac{p}{q}$, i.e. $A\dfrac{p}{q}=\dfrac{Aq+p}{q}$.
Instead of doing this, students might write the mixed fraction as $A\dfrac{p}{q}=A\times \dfrac{p}{q}$, which is a wrong notation.