To solve the expression:

\[
\frac{1}{4} \cdot \frac{1}{5} - \frac{2}{3}
\]

### Step 1: Multiply the fractions
\[
\frac{1}{4} \cdot \frac{1}{5} = \frac{1 \cdot 1}{4 \cdot 5} = \frac{1}{20}
\]

### Step 2: Subtract \(\frac{2}{3}\) from \(\frac{1}{20}\)
To subtract these fractions, we need a common denominator. The least common multiple (LCM) of 20 and 3 is 60.

#### Convert \(\frac{1}{20}\) and \(\frac{2}{3}\) to have a denominator of 60:
\[
\frac{1}{20} = \frac{3}{60} \quad \text{(since \(1 \times 3 = 3\) and \(20 \times 3 = 60\))}
\]
\[
\frac{2}{3} = \frac{40}{60} \quad \text{(since \(2 \times 20 = 40\) and \(3 \times 20 = 60\))}
\]

#### Perform the subtraction:
\[
\frac{3}{60} - \frac{40}{60} = \frac{3 - 40}{60} = \frac{-37}{60}
\]

### Final Answer:
\[
\boxed{\frac{-37}{60}}
\]

Would you like more details or have any questions about this solution?

Here are 5 related questions to expand your understanding:
1. How do you find the least common multiple (LCM) of two numbers?
2. What is the process of converting fractions to have a common denominator?
3. How do you multiply two fractions together?
4. Why do we need to find a common denominator when subtracting fractions?
5. How can you simplify fractions, and why is it important?

**Tip:** When dealing with fractions, always simplify at each step to make calculations easier.

Learn how to multiply and subtract fractions with the problem 1/4 * 1/5 - 2/3. This solution includes finding a common denominator and performing operations on fractions. Suitable for students in Grades 5-7.

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