Whether the ratios \frac{9}{11} and \frac{81}{99} are equivalent ratios.

Concept used: 
Equivalent fractions are those fractions that represent the same value or number but have different numerators and denominators. In their simplified forms, equivalent fractions are reduced to the same fraction.
The smallest number that can be divided by the sum or difference of all the fractions is known as the least common denominator, or LCD.

If two fractions have the same denominator, then we can compare them by their numerators. The fraction with the greater numerator will be greater than the other fraction. 
Calculation: 
In order to check whether the fractions ${\displaystyle \frac{9}{11}}$ and ${\displaystyle \frac{81}{99}}$ are equivalent or no, first reduce both the fractions in the simplest form. And then check whether both fractions are equal or no. 
Here observe that in the first fraction, ${\displaystyle \frac{9}{11}}$ there is no other common factor than 1. Also observe that in the second fraction ${\displaystyle \frac{81}{99}}$ the HCF of numerator and denominator is 9. So the fraction can be simplified further dividing up and down by 9 and after 7 the fraction can be simplified further as shown below, 
${\displaystyle \frac{81}{99}=\frac{9}{11}}$ 
So, in reduced form the ratios are ${\displaystyle \frac{9}{11}\text{and}\frac{9}{11}}$. The numerator of the first ratio is equal to the numerator of the second, so they are equal. 
Thus, the given ratios are equivalent.

Answer is given below (on video)