Question

How do you write the answer $\dfrac{6}{7} \times \dfrac{{14}}{{15}}$ in simplest form?

Answer 1

Hint: We have to solve the given fraction in the question. Do the multiplication of the fraction in the question. Multiply the numerator of the first fraction with the second fraction and denominator of the first fraction with denominator of the second fraction. Then, find the common factor of both the numerator and denominator of the multiplication of the fraction and then, convert it into its simplest form.

Complete Step by Step Solution:
In the question, we have to find the simplest form of the result of the fraction $\dfrac{6}{7} \times \dfrac{{14}}{{15}}$.
Therefore, first of all, we have to multiply both the fraction given in the question. To do this, we have to multiply the numerator of the first fraction with the second fraction and denominator of the first fraction with denominator of the second fraction. Therefore, multiplying the fraction in the question, we get –
$ \Rightarrow \dfrac{6}{7} \times \dfrac{{14}}{{15}}$
Now, multiplying numerator 6 with 14 and denominator 7 with 15, we get –
$ \Rightarrow \dfrac{{84}}{{105}}$
Now, finding the factor for 84 and 105. Hence, the common factor for 84 and 105 is 21. Therefore, now dividing the 21 with the numerator and denominator with the fraction, $\dfrac{{84}}{{105}}$ -
$
   \Rightarrow \dfrac{{84 \div 21}}{{105 \div 21}} \\
   \Rightarrow \dfrac{4}{5} \\
 $

Hence, the simplest form of the multiplication of fraction $\dfrac{6}{7} \times \dfrac{{14}}{{15}}$ is $\dfrac{4}{5}$.

Note:
We can also convert the multiplication of the fraction $\dfrac{6}{7} \times \dfrac{{14}}{{15}}$ without finding the common factors. As we know that, 6 and 15 are the multiples of 3 so, 6 and 15 can be divided by 3 as 2 and 5. So, the fraction becomes –
$ \Rightarrow \dfrac{2}{7} \times \dfrac{{14}}{5}$
Now, 14 can be divided by 7 and gives the result as 2. Hence, the fraction becomes –
$ \Rightarrow 2 \times \dfrac{2}{5}$
Now, the above fraction can be multiplied as –
$ \Rightarrow \dfrac{4}{5}$
Hence, this is the required fraction.