Divide and simplify, if possible

Explanation

Write \(1\frac{11}{16}\) as an improper fraction

$1\frac{11}{16} ÷ \frac34 = \frac{27}{16} ÷ \frac34$

Write \(\frac{27}{16}\) by the reciprocal of  \(\frac34\), which is \(frac43\)

$= \frac{27}{16} \cdot \frac43$

To simplify, factor 27 as a 3 • 9 and 16 as 4 • 4.  Then remove the common factors of 3 and 4 from the numerator and denominator.

$ \require{cancel} =\frac{\cancel{3}^1 \cdot 9 \cdot \cancel{4}^1}{\cancel{4}_1 \cdot 4 \cdot \cancel{3}_1}$

Multiply the remaining factors in the numerator and in the denominator.  The result is an improper fraction

$= \frac94$

Write the improper fraction \(\frac94\) as a mixed number by dividing 9 by 4

$= 2\frac14$