Let's carefully solve the expression step-by-step. The given expression is:
[tex]\[
\frac{14}{\frac{14}{9}} + \left( \frac{11}{8} \right)
\][/tex]
### Step 1: Simplify the first term
First, we need to simplify [tex]\(\frac{14}{\frac{14}{9}}\)[/tex].
This can be re-written using the reciprocal property of fractions:
[tex]\[
\frac{14}{\frac{14}{9}} = 14 \times \frac{9}{14}
\][/tex]
### Step 2: Perform the multiplication
Now, multiply:
[tex]\[
14 \times \frac{9}{14} = 14 \times \frac{9}{14} = \frac{14 \times 9}{14} = \frac{126}{14} = 9
\][/tex]
So,
[tex]\[
\frac{14}{\frac{14}{9}} = 9
\][/tex]
### Step 3: Simplify the second term
Next, simplify [tex]\(\frac{11}{8}\)[/tex].
The fraction [tex]\(\frac{11}{8}\)[/tex] is already in its simplest form:
[tex]\[
\frac{11}{8} = 1.375
\][/tex]
So,
[tex]\[
\frac{11}{8} = 1.375
\][/tex]
### Step 4: Add the simplified terms
Add the two simplified terms together:
[tex]\[
9 + 1.375 = 10.375
\][/tex]
### Step 5: Conclusion
Therefore, we have:
[tex]\[
\frac{14}{\frac{14}{9}} + \left( \frac{11}{8} \right) = 9 + 1.375 = 10.375
\][/tex]
So, the final numerical result is:
[tex]\[
\boxed{10.375}
\][/tex]
