To solve the given mathematical expression:
[tex]\[ -\frac{1}{35} \div \frac{-11}{12} \times 7 \div \frac{-9}{22} \][/tex]
we need to follow these steps:
### Step 1: Simplify the division of fractions
Recall that dividing by a fraction is the same as multiplying by its reciprocal. Therefore, we can rewrite the division operations as multiplication operations.
#### Simplifying [tex]\(-\frac{1}{35} \div \frac{-11}{12}\)[/tex]:
[tex]\[ -\frac{1}{35} \div \frac{-11}{12} = -\frac{1}{35} \times \frac{12}{-11} \][/tex]
Simplify the multiplication of fractions:
[tex]\[ -\frac{1}{35} \times \frac{12}{-11} = \frac{1}{35} \times \frac{12}{11} \][/tex]
Multiply the fractions:
[tex]\[ \frac{1 \times 12}{35 \times 11} = \frac{12}{385} \][/tex]
#### Simplifying [tex]\( 7 \div \frac{-9}{22} \)[/tex]:
[tex]\[ 7 \div \frac{-9}{22} = 7 \times \frac{22}{-9} \][/tex]
Simplify the multiplication of fractions:
[tex]\[ 7 \times \frac{22}{-9} = \frac{7 \times 22}{-9} = \frac{154}{-9} = -\frac{154}{9} \][/tex]
### Step 2: Multiply the intermediate results
Now we multiply the two intermediate results:
[tex]\[ \frac{12}{385} \times -\frac{154}{9} \][/tex]
Multiply the numerators and the denominators:
[tex]\[ \frac{12 \times -154}{385 \times 9} = \frac{-1848}{3465} \][/tex]
Simplify the fraction:
[tex]\[ \frac{-1848}{3465} = -\frac{8}{15} \][/tex]
### Final Result
Thus, the value of the given expression is:
[tex]\[
-\frac{8}{15}
\][/tex]
So, the correct answer from the given choices is:
[tex]\[
-\frac{8}{15}
\][/tex]
