For Pat's rug, we have the following improper fraction:
[tex]11\frac{3}{12}=\frac{12(11)+3}{12}=\frac{132+3}{12}=\frac{135}{12}[/tex]For Lamar's rug we have:
[tex]4\frac{6}{11}=\frac{4(11)+6}{11}=\frac{44+6}{11}=\frac{50}{11}[/tex]Finally, for Alfred' rug we have:
[tex]8\frac{9}{12}=\frac{8(12)+9}{12}=\frac{96+9}{12}=\frac{105}{12}[/tex]