Question

How do you find the ratio of $x$ to $y$ given $5x=6y$?

Answer 1

Hint: We explain the process to get ratio of two numbers $x$ and $y$. From the equation $5x=6y$, we try to describe the relation between the denominator and the numerator. We use the G.C.D of the denominator and the numerator to divide both of them. We get the simplified form as the G.C.D is 1.

Complete step by step solution:
The ratio is used to find the unitary value of a particular number with respect to the other number.
Therefore, for the ratio of any two numbers $x$ and $y$, we can express it as $\dfrac{x}{y}$. Ratios work like fractions. The numbers become the numerator and denominator of the ratio.
Simplified form is achieved when the G.C.D of the denominator and the numerator is 1.
This means we can’t eliminate any more common root from them other than 1.
For the fraction $\dfrac{x}{y}$, we first find the G.C.D of the denominator and the numerator. If it’s 1 then it’s already in its simplified form and if the G.C.D of the denominator and the numerator is any other number d then we need to divide the denominator and the numerator with d and get the simplified fraction form as $\dfrac{{}^{x}/{}_{d}}{{}^{y}/{}_{d}}$.
For the equation $5x=6y$, we get $\dfrac{x}{y}=\dfrac{6}{5}$.

Note: The process is similar for both proper and improper fractions or ratios. In case of mixed fractions, we need to convert it into an improper fraction and then apply the case. Also, we can only apply the process on the proper fraction part of a mixed fraction.