Question

A fraction bears the same ratio to \[\dfrac{1}{7}\] as \[\dfrac{3}{7}\] does to \[\dfrac{5}{9}\] . Find the fraction?

Answer 1

Hint: Here in the given question we need to find the required fraction, we know that if for a given pair of number which bears the same ratio then they are proportional to each other; hence we need to find the new fraction which will be proportional to the rest of the fraction.

Complete step by step answer:
Here in the given question we need to solve by assuming a new number which will be proportional to the rest of the fraction, on solving we get:
 Let “x” be the fraction that bears the same ration to the given fraction, now we have:
\[
   \Rightarrow x:\dfrac{1}{7}::\dfrac{3}{7}:\dfrac{5}{9} \\
   \Rightarrow x:\dfrac{1}{7} = \dfrac{3}{7} \times \dfrac{9}{5} \\
   \Rightarrow x:\dfrac{1}{7} = \dfrac{{27}}{{35}} \\
   \Rightarrow x = \dfrac{{27}}{{35}} \times \dfrac{1}{7} \\
   \Rightarrow x = \dfrac{{27}}{{245}} \\
 \]
Here we get the required fraction for the given data.

Note: Here we get a required ratio, for the fraction which are in the given proportion and then solved accordingly. To solve the ratio and proportion we need to equate the values accordingly and then solve for the desired values.