Respuesta :
We want to calculate the following division
[tex]5\text{ }\frac{2}{3}\text{ / 4}[/tex]First, to do so, we will transform the mixed number to its equivalent fraction, so the division is easier. Given a mixed number of the form a b/c, its equivalent fraction is of the form
[tex]a\text{ }\frac{b}{c}\text{ = }\frac{a\cdot c+b}{c}[/tex]In our case, a = 5, b = 2 and c =3, so the equivalent fraction is
[tex]5\text{ }\frac{2}{3}\text{ = }\frac{5\cdot3+2}{3}\text{ = }\frac{17}{3}[/tex]Now, we will use the fact that the number 4 could be written as the fraction 4/1 and we will divide both fractions.
If we have one fraction a/b and we want to divide it by c/d we can do as follows
[tex]\frac{a}{b}/(\frac{c}{d})\text{ = }\frac{a}{b}\cdot\frac{d}{c}\text{ = }\frac{a\cdot d}{b\cdot c}[/tex]which is equivalent to"flip" the fraction that we are using to divide and then multiply. So we have the fraction 17/3 and we want to divide it by 4/1. So, we proceed as follows:
[tex]\frac{17}{3}/(\frac{4}{1})\text{ = }\frac{17}{3}\cdot\frac{1}{4}\text{ = }\frac{17}{12}[/tex]Since this fraction can not be simplified further, the final answer is 17/12
