Rewrite 19/30 and 13/20 so that they have a common denominator then then, use < , = , or >

Must determine the LCD.  Think:  what is the smallest (least) number divisible by both 30 and 20?  You could, of course, just multiply 30 and 20, obtaining 600, but that would not be the LCD.

Note that 30 and 20 share the common factor 10.  Multiplying 3 and 2 together produces 6.  The LCD is 10*6 = 60.  Note that both 30 and 20 divide into 60 with no remainder.

Then  19/30  = 2(19) / 2[30]  = 38/60, and 

13/20 = 3(13) / 3[20]  = 39/60.

Which is larger, 38/60 or 39/60?

Write the relationship between these 2 numbers using the appropriate inequality operator.

The decimal expansion would be .27 repeated