8 7/8+1/2
1) We need to turn that Mixed number into an improper fraction, by keeping the denominator and multiplying it by the whole number, and then adding to the numerator of that Mixed Number:
[tex]8\frac{7}{8}=\frac{8\cdot8+7}{8}=\frac{71}{8}[/tex]2) Adding then:
[tex]\frac{71}{8}+\frac{1}{2}=\frac{8\colon8\times71+8\colon2\times1}{8}=\frac{71+4}{8}=\frac{75}{8}[/tex]Turning back to Mixed Number:
Dividing 75 by 8 and placing the quotient as the whole number, the divisor as the denominator, and the remainder as the numerator we have the mixed number back.
2)45.35 + 40 7/10
Rewriting 45.35 as a fraction:
[tex]\begin{gathered} 45.35\text{ =}\frac{4535}{100} \\ 40\frac{7}{10}+\frac{4535}{100} \\ \frac{407}{10}+\frac{4535}{100} \\ \frac{4070+4535}{100} \\ \frac{8605}{100} \\ \frac{1721}{20} \end{gathered}[/tex]Note that we've rewritten as fractions, and then turned them into improper ones, added them, and then simplified.
3) Hence, the answer is
[tex]\begin{gathered} a)9\frac{3}{8}\text{ or }\frac{75}{8} \\ b)\text{ }\frac{1721}{20} \end{gathered}[/tex]
