Respuesta :
We will investigate the basic mathematical operations involving mixed fractions.
We have the following indicated operation to be performed:
[tex]5\text{ }\frac{1}{6}\text{ - 2}\frac{2}{3}[/tex]Whenever we are dealing with basic mathematical oepraitons of either case:
[tex]\text{Multiplicaiton, Division, Subtraction, Addition}[/tex]We should always convert the mixed fractions into improper fractions. The following step outlines the conversion process:
[tex]\begin{gathered} \frac{5\cdot6\text{ + 1}}{6}\text{ - }\frac{2\cdot3+2}{3} \\ \\ \frac{31}{6}\text{ - }\frac{8}{3} \end{gathered}[/tex]Once we have expressed the mixed fraction into improper fractions. We then seek to determine the least common multiple of the denominators of the improper fractions.
The LCM of the two denominators 6 and 3 ) is:
[tex]\text{LCM ( 6 , 3 ) = 6}[/tex]The next step involves the conversion of each improper fraction's denominator to the result of the LCM expressed above i.e ( 6 ).
We see that the first improper fraction already has the number ( 6 ) in its denominator ; therefore, we will move to the second improper fraction and multiply and divide with ( 2 ) as follows:
[tex]\begin{gathered} \frac{31}{6}\text{ - }\frac{2}{2}\cdot\frac{8}{3} \\ \\ \frac{31}{6}\text{ - }\frac{16}{6} \end{gathered}[/tex]Once we have the common bases. We can apply the indicated operatior ( - ) and go ahead with the processof subtraction applicable to the numerator only!
[tex]\begin{gathered} \frac{31-16}{6} \\ \\ \frac{15}{6} \end{gathered}[/tex]Then we will go ahead and simplify the fraction by finding the common multiple of both the numerator and denominator as follows:
[tex]\frac{15}{6}\text{ = }\frac{5}{2}\ldots\text{ ( divisibility by 3 )}[/tex]Then we will express the improper fraction into a whole number as our answer:
[tex]2\frac{1}{2}\ldots\text{ Answer}[/tex]
