Question

How do you divide \[\dfrac{4}{245}\div \dfrac{8}{343}\]?

Answer 1

Hint: In this problem, we have to divide the given fraction. We can first find the multiples of 245 and 343. We can write the multiplies. We know that, to divide by a fraction, we have to reciprocal a fraction in the denominator by inverting and multiply it to the first fraction. We can then cancel the similar terms to get the final answer.

Complete step-by-step solution:
We know that the given fraction is,
 \[\Rightarrow \dfrac{4}{245}\div \dfrac{8}{343}\] ……… (1)
We know that the multiples of 245 and 343 are,
\[\begin{align}
  & \Rightarrow 245=7\times 7\times 5 \\
 & \Rightarrow 343=7\times 7\times 7 \\
\end{align}\]
We can now apply the above values in (1), we get
\[\Rightarrow \dfrac{4}{7\times 7\times 5}\div \dfrac{8}{7\times 7\times 7}\]
We know that, to divide by a fraction, we have to reciprocal a fraction in the denominator by inverting and multiply it to the first fraction.
We get,
\[\Rightarrow \dfrac{4}{7\times 7\times 5}\times \dfrac{7\times 7\times 7}{8}\]
We can now cancel the similar terms in both the numerator and the denominator, we get
\[\Rightarrow \dfrac{4}{5}\times \dfrac{7}{8}\]
we can now simplify the above step by cancelling terms, we get
\[\Rightarrow \dfrac{1}{5}\times \dfrac{7}{2}=\dfrac{7}{10}\]
Therefore, the answer is \[\dfrac{7}{10}\].

Note: Students make mistakes while finding the multiples of the given number to be cancelled to get a simplified form, we should always remember that to divide by a fraction, we have to reciprocal a fraction in the denominator by inverting and multiply it to the first fraction. We can also directly cancel the similar terms without replacing the number with its multiples when we know to cancel with multiplication tables.