Let's break down the expression step by step:

Given expression: 

\[
0.6 \times 20\% - \frac{3}{7}
\]

1. **Convert the percentage to a decimal**:
   \[
   20\% = 0.2
   \]

2. **Multiply** \(0.6\) by \(0.2\):
   \[
   0.6 \times 0.2 = 0.12
   \]

3. **Subtract** \(\frac{3}{7}\) from \(0.12\):
   \[
   0.12 - \frac{3}{7}
   \]

4. **Convert** \(\frac{3}{7}\) to a decimal:
   \[
   \frac{3}{7} \approx 0.4286
   \]

5. **Subtract**:
   \[
   0.12 - 0.4286 \approx -0.3086
   \]

So, the result is approximately:

\[
\boxed{-0.3086}
\]

Would you like more details or have any questions? 

Here are some related questions:

1. How do you convert percentages to decimals?
2. What is the decimal equivalent of \(\frac{3}{7}\)?
3. How do you handle operations involving percentages in expressions?
4. What is the importance of order of operations in math?
5. How do you subtract a fraction from a decimal?

**Tip:** When subtracting fractions from decimals, it's often easier to convert the fraction to a decimal first!

Learn how to solve the expression 0.6 times 20% minus 3/7 step-by-step. This problem involves converting percentages to decimals, performing multiplication, subtraction of fractions from decimals, and following order of operations. Suitable for students in Grades 6-8.

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