Question

How do you multiply $\dfrac{1}{8}\times \dfrac{1}{9}$?

Answer 1

Hint: Multiply the numerator of ${{1}^{st}}$ with the numerator of ${{2}^{nd}}$ and the denominator of ${{1}^{st}}$ with the denominator of ${{2}^{nd}}$ to obtain the required solution. Do the necessary calculation and simplification as required.

Complete step-by-step solution:
Fraction multiplication: For the multiplication of two fractions, the numerators and denominators are multiplied separately with each other.
For the given question $\dfrac{1}{8}\times \dfrac{1}{9}$
Multiplying the numerator of ${{1}^{st}}$ with the numerator of ${{2}^{nd}}$ and the denominator of ${{1}^{st}}$ with the denominator of ${{2}^{nd}}$, we get
$\begin{align}
  & \dfrac{1}{8}\times \dfrac{1}{9} \\
 & \Rightarrow \dfrac{1\times 1}{8\times 9} \\
 & \Rightarrow \dfrac{1}{72} \\
\end{align}$
This is the required solution of the given question.

Note: Any fraction multiplication can be done in the above mentioned method. After the multiplication the fraction should be reduced if necessary. For example after the multiplication if we would get the result as $\dfrac{2}{72}$, then it should be further simplified. For further simplification we need to reduce the fraction. First we have to get the common factors of the numerator and the denominator, from which the greatest common factor can be obtained. Dividing both numerator and denominator by the greatest common factor we can get the simplified form of the fraction.
For $\dfrac{2}{72}$
As we know the common factor of ‘2’ and ‘72’ is ‘2’
So we can conclude that the greatest common factor of ‘2’ and ‘72’ is ‘2’.
Now dividing both numerator and denominator by the greatest common factor ‘2’ we get
$\begin{align}
  & \dfrac{2}{72} \\
 & \Rightarrow \dfrac{2\div 2}{72\div 2} \\
 & \Rightarrow \dfrac{1}{36} \\
\end{align}$
This is the simplified form of $\dfrac{2}{72}$.
The above simplification should be done if required.