2 4/7
1) Let's turn those mixed numbers into improper fractions, to make our calculations easier:
[tex]\begin{gathered} 4\frac{1}{2}=\frac{2\times4+1}{2}=\frac{9}{2} \\ 1\frac{3}{4}=\frac{4\times1+3}{4}=\frac{7}{4} \\ \end{gathered}[/tex]2) Now let's divide those improper fractions, reciprocating the second one and multiplying it by the first one:
[tex]\frac{9}{2}\colon\frac{7}{4}=\frac{9}{2}\times\frac{4}{7}=\frac{36}{14}=\frac{18}{7}[/tex]3) Hence, we can write that the quotient of that division 4 1/2 by 1 3/4 is equal to 18/7. To turn it into a Mixed Number let's divide 18/7 and write our Mixed Number equivalent to 18/7:
