Respuesta :
Answer:
49/6
Explanation:
In order to add the mixed numbers given, we first convert the mixed numbers to improper fractions.
Now,
[tex]3\frac{7}{3}=3+\frac{7}{3}[/tex]The number 3 can be rewritten as
[tex]7=3\cdot\frac{3}{3}[/tex]which helps us rewrite our mixed fraction as
[tex]3+\frac{7}{3}=3\cdot\frac{3}{3}+\frac{7}{3}[/tex][tex]=\frac{9}{3}+\frac{7}{3}[/tex]adding the numerators gives
[tex]\frac{16}{3}[/tex]Hence,
[tex]3\frac{7}{3}=\frac{16}{3}[/tex]Similarly,
[tex]2\frac{5}{6}=2+\frac{5}{6}[/tex]the number 2 can be rewritten as
[tex]2=2\cdot\frac{6}{6}=\frac{12}{6}[/tex]therefore, the mixed number becomes
[tex]2+\frac{5}{6}=\frac{12}{6}+\frac{5}{6}[/tex][tex]=\frac{17}{6}[/tex]Hence,
[tex]2\frac{5}{6}=\frac{17}{6}[/tex]Now with mixed numbers rewritten as improper fractions, we are ready to add
[tex]3\frac{7}{3}+2\frac{5}{6}=\frac{16}{3}+\frac{17}{6}[/tex]rewriting 16/3 as 16/3 * 2/2 gives
[tex]\frac{16}{3}=\frac{32}{6}[/tex]therefore, we have
[tex]\frac{16}{3}+\frac{17}{6}=\frac{32}{6}+\frac{17}{6}[/tex]and now we just add the denominators to get
[tex]\frac{32}{6}+\frac{17}{6}=\frac{49}{6}[/tex]Hence,
[tex]3\frac{7}{3}+2\frac{5}{6}=\frac{49}{6}[/tex]which is our answer!
