Evaluate: `((2)/(3)xx(9)/(8))-((5)/(44)xx(-11)/(15))-((35)/(28)div(21)/(-14))`

Answer

To evaluate the expression \(\frac{2}{3} \times \frac{9}{8} - \frac{5}{44} \times \left(-\frac{11}{15}\right) - \left(\frac{35}{28} \div \frac{21}{-14}\right)\), we will follow these steps:

### Step 1: Evaluate the first term
Calculate \(\frac{2}{3} \times \frac{9}{8}\).

\[ \frac{2 \times 9}{3 \times 8} = \frac{18}{24} \]

Now, simplify \(\frac{18}{24}\):

\[ \frac{18 \div 6}{24 \div 6} = \frac{3}{4} \]

### Step 2: Evaluate the second term
Calculate \(\frac{5}{44} \times \left(-\frac{11}{15}\right)\).

\[ \frac{5 \times (-11)}{44 \times 15} = \frac{-55}{660} \]

Now, simplify \(\frac{-55}{660}\):

\[ \frac{-55 \div 55}{660 \div 55} = \frac{-1}{12} \]

### Step 3: Evaluate the third term
Calculate \(\frac{35}{28} \div \frac{21}{-14}\). We change the division to multiplication:

\[ \frac{35}{28} \times \frac{-14}{21} \]

Now simplify \(\frac{35}{28}\):

\[ \frac{35 \div 7}{28 \div 7} = \frac{5}{4} \]

Now calculate:

\[ \frac{5}{4} \times \frac{-14}{21} = \frac{5 \times -14}{4 \times 21} = \frac{-70}{84} \]

Now simplify \(\frac{-70}{84}\):

\[ \frac{-70 \div 14}{84 \div 14} = \frac{-5}{6} \]

### Step 4: Combine all terms
Now substitute back into the expression:

\[ \frac{3}{4} - \left(-\frac{1}{12}\right) - \left(-\frac{5}{6}\right) \]

This becomes:

\[ \frac{3}{4} + \frac{1}{12} + \frac{5}{6} \]

### Step 5: Find a common denominator
The least common multiple (LCM) of 4, 12, and 6 is 12. Now convert each fraction:

\[ \frac{3}{4} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12} \]
\[ \frac{1}{12} = \frac{1}{12} \]
\[ \frac{5}{6} = \frac{5 \times 2}{6 \times 2} = \frac{10}{12} \]

### Step 6: Add the fractions
Now we can add them:

\[ \frac{9}{12} + \frac{1}{12} + \frac{10}{12} = \frac{9 + 1 + 10}{12} = \frac{20}{12} \]

Now simplify \(\frac{20}{12}\):

\[ \frac{20 \div 4}{12 \div 4} = \frac{5}{3} \]

### Final Answer
Thus, the final answer is:

\[ \frac{5}{3} \]