To add numbers with different denominators, a student is consistently using the product of the denominators as a common denominator. Is this correct? Why or why not? Give an example to support your answer

To add numbers with different denominators, a student is consistently using the product of the denominators as a common denominator. Is this correct? Why or why not? Give an example to support your answer

Hi,

let the two fractions be:

The sum becomes then:

The numerator and denominator of this result might be large numbers but the result itself is always correct.