[tex]4\frac{2}{3}\ converted\ to\ improper\ fraction\\\\4\frac{2}{3}=4+\frac{2}{4}=\frac{4\cdot3}{3}+\frac{2}{3}=\frac{12}{3}+\frac{2}{3}=\frac{12+2}{3}=\frac{14}{3}\\\\11\frac{1}{4}\ converted\ to\ improper\ fraction\\\\11\frac{1}{4}=11+\frac{1}{4}=\frac{11\cdot4}{4}+\frac{1}{4}=\frac{44}{4}+\frac{1}{4}=\frac{44+1}{4}=\frac{45}{4}\\\\the\ product:\\\\4\frac{2}{3}\cdot11\frac{1}{4}=\frac{\not14^7}{3}\cdot\frac{45}{\not4_2}=\frac{7}{\not3_1}\cdot\frac{\not45^{15}}{2}=\frac{7}{1}\cdot\frac{15}{2}[/tex]
[tex]=\frac{7\cdot15}{1\cdot2}=\frac{105}{2}=\frac{104+1}{2}=\frac{104}{2}+\frac{1}{2}=52+\frac{1}{2}\\\\\huge\boxed{=52\frac{1}{2}\to\boxed{d.}}[/tex]
