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We are tasked with subtracting the fractions \(-\frac{1}{35} - \frac{11}{20}\).

### Steps:
1. **Find the least common denominator (LCD):**
   - The denominators are 35 and 20.
   - The LCD of 35 and 20 is the least common multiple (LCM) of these numbers.
     \[
     \text{Prime factors of } 35 = 5 \times 7
     \]
     \[
     \text{Prime factors of } 20 = 2^2 \times 5
     \]
     The LCM is \(2^2 \times 5 \times 7 = 140\).

2. **Rewrite both fractions with the common denominator:**
   - For \(-\frac{1}{35}\), multiply both numerator and denominator by 4:
     \[
     -\frac{1}{35} = -\frac{1 \times 4}{35 \times 4} = -\frac{4}{140}
     \]
   - For \(-\frac{11}{20}\), multiply both numerator and denominator by 7:
     \[
     -\frac{11}{20} = -\frac{11 \times 7}{20 \times 7} = -\frac{77}{140}
     \]

3. **Subtract the numerators:**
   \[
   -\frac{4}{140} - \frac{77}{140} = \frac{-4 - 77}{140} = \frac{-81}{140}
   \]

Thus, the result of the subtraction is:
\[
-\frac{81}{140}
\]

Let me know if you would like further clarification on any step or a more detailed explanation!

### Related Questions:
1. How do you find the least common denominator for fractions?
2. Can you explain how to simplify a fraction after subtraction?
3. How can you convert improper fractions to mixed numbers?
4. What is the difference between subtracting positive and negative fractions?
5. How would the approach change if the fractions had different signs?

### Tip:
Always check whether the resulting fraction can be simplified by finding the greatest common divisor (GCD) of the numerator and denominator.

Learn how to subtract the fractions -1/35 and 11/20 by finding the least common denominator (LCD) and using the subtraction formula. The solution provides detailed steps to help students in Grades 6-8 understand how to subtract fractions with different denominators.

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