1. Provide a counterexample that shows the statement is false. Explain why the counterexample makes the statement false.

If two fractions have unlike denominators, then the LCD is the product of their denominators.

Answer:

Counterexample: 2/10 and 3/8

The product of the two denominators is 10*8 = 80

The LCD is found by mulitplying the non common prime factors and the common prime factors raised to the higher power:

10 = 2*5

8 = 2^3

LCD = (2^3) * 5 = 8 * 40.

This counterexample shows the statement is false.