Question

How does one solve $9 \times \dfrac{6}{5}$ ?

Answer 1

Hint: For solving this particular question , we have two methods one is multiplication by repeated addition and another way to consider the whole number as a fraction by making its denominator unity that is one.

Complete step-by-step solution:
It is given that $9 \times \dfrac{6}{5}$ .
Method I :
We can calculate multiplication by repeated addition also. So, when we are multiplying a fraction by a whole number it is the same as adding the fraction for the whole number of times.
Therefore, we can evaluate $9 \times \dfrac{6}{5}$ as adding the fraction that is $\dfrac{6}{5}$ for the whole number that is nine times.
Therefore, we can write as follow ,
$ \Rightarrow 9 \times \dfrac{6}{5} = \dfrac{6}{5} + \dfrac{6}{5} + \dfrac{6}{5} + \dfrac{6}{5} + \dfrac{6}{5} + \dfrac{6}{5} + \dfrac{6}{5} + \dfrac{6}{5} + \dfrac{6}{5}$
Since the denominator are same , we just have to add all the numerators keeping the denominator same , therefore we get ,
$
   \Rightarrow 9 \times \dfrac{6}{5} = \dfrac{{(6 + 6 + 6 + 6 + 6 + 6 + 6 + 6 + 6)}}{5} \\
    \\
 $
$ = \dfrac{{54}}{5}$
Another way to consider this can be to rewrite the whole number as a fraction by making its denominator unity that is one.

Method II :
Consider the whole number $9$ as $\dfrac{9}{1}$ .
Therefore, we can write ,
$ \Rightarrow 9 \times \dfrac{6}{5} = \dfrac{9}{1} \times \dfrac{6}{5}$
Now , multiply the numerator by numerator and denominator by denominator as per the rules.
$ \Rightarrow 9 \times \dfrac{6}{5} = \dfrac{{54}}{5}$

Notes: In method second , when we rewrite the whole number as a fraction by making its denominator unity that is one , this will not affect our expression at all. Rule of multiplying two fractions stated as multiplying the numerator of the first number by the numerator of the second number and denominator of the first number by denominator of the second number.