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The problem involves subtracting two fractions: \(\frac{3}{35}\) and \(\frac{3}{20}\).

To subtract these fractions, we need a common denominator.

### Step 1: Find the Least Common Denominator (LCD)
The denominators are 35 and 20. The LCD of 35 and 20 can be found by determining the least common multiple (LCM) of these two numbers.

- The prime factorization of 35 is \(5 \times 7\).
- The prime factorization of 20 is \(2^2 \times 5\).

The LCM is \(2^2 \times 5 \times 7 = 140\).

So, the common denominator is 140.

### Step 2: Convert the Fractions
Now, convert each fraction to an equivalent fraction with a denominator of 140.

- For \(\frac{3}{35}\), multiply the numerator and denominator by \(\frac{4}{4}\):
  \[
  \frac{3}{35} = \frac{3 \times 4}{35 \times 4} = \frac{12}{140}
  \]

- For \(\frac{3}{20}\), multiply the numerator and denominator by \(\frac{7}{7}\):
  \[
  \frac{3}{20} = \frac{3 \times 7}{20 \times 7} = \frac{21}{140}
  \]

### Step 3: Subtract the Fractions
Now, subtract the two fractions:
\[
\frac{12}{140} - \frac{21}{140} = \frac{12 - 21}{140} = \frac{-9}{140}
\]

So, the result of the subtraction is \(\frac{-9}{140}\).

Would you like further details or have any questions?

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Here are 5 questions to consider:
1. How do you find the least common denominator for two fractions?
2. Why is it necessary to have a common denominator when subtracting fractions?
3. How would the result differ if the subtraction involved positive fractions?
4. What are the steps to simplify a fraction after performing operations on it?
5. How can you check if your subtraction result is correct?

**Tip:** When working with fractions, always simplify the final answer if possible by finding the greatest common divisor (GCD) of the numerator and denominator.

Subtract \(\frac{3}{35}\) and \(\frac{3}{20}\).

This page explains how to subtract the fractions \(\frac{3}{35}\) and \(\frac{3}{20}\) by finding a common denominator, converting the fractions, and performing the subtraction. It is suitable for students in Grades 6-8.

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