Answer:
[tex]\frac{3}{4}[/tex]
Step-by-step explanation:
The given question is: [tex]\frac{8}{9}+(-\frac{5}{6})*\frac{1}{6}[/tex]. We are asked to simplify the given expression.
Using order of operations (PEMDAS), we will remove parenthesis first as:
[tex]\frac{8}{9}-\frac{5}{6}*\frac{1}{6}[/tex]
Since multiplication comes before addition or subtraction, so we will multiply first as:
[tex]\frac{8}{9}-\frac{5*1}{6*6}[/tex]
[tex]\frac{8}{9}-\frac{5}{36}[/tex]
Make a common denominator:
[tex]\frac{8\times 4}{9\times 4}-\frac{5}{36}[/tex]
[tex]\frac{32}{36}-\frac{5}{36}[/tex]
Combine numerators:
[tex]\frac{32-5}{36}[/tex]
[tex]\frac{27}{36}[/tex]
[tex]\frac{9\times 3}{9\times 4}[/tex]
[tex]\frac{3}{4}[/tex]
Therefore, the simplified form of our given expression would be [tex]\frac{3}{4}[/tex].
