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The given expression to simplify is:

\[
\frac{4m^2n - 28mn}{-4m}
\]

### Step-by-step simplification:

1. **Factor the numerator**: 
   The terms in the numerator share a common factor of \( 4mn \). Factor this out:

   \[
   4mn(m - 7)
   \]

   So the expression becomes:

   \[
   \frac{4mn(m - 7)}{-4m}
   \]

2. **Simplify the fraction**: 
   Now, cancel the common factors in the numerator and denominator. Both the numerator and denominator have a common factor of \( 4m \):

   \[
   \frac{4mn(m - 7)}{-4m} = \frac{n(m - 7)}{-1}
   \]

3. **Final simplification**: 
   The negative sign can be applied to the entire expression:

   \[
   -n(m - 7)
   \]

   Distribute the negative sign:

   \[
   = -nm + 7n
   \]

### Final Answer:
The simplified expression is:

\[
7n - nm
\]

Would you like a more detailed explanation of any part? Here are a few related questions to consider:

1. How do you factor terms with common variables?
2. What are the rules for simplifying algebraic fractions?
3. How do you distribute negative signs over expressions?
4. What are some techniques for factoring polynomials?
5. How can you check if your simplified answer is correct?

**Tip**: When simplifying expressions, always look for the greatest common factor (GCF) before moving on to other operations.

Simplify the expression: \(\frac{4m^2n - 28mn}{-4m}\).

Learn how to simplify the rational expression \(\frac{4m^2n - 28mn}{-4m}\) with a step-by-step solution. This problem covers key algebraic concepts, including factoring, properties of fractions, and the distributive property. Suitable for students in Grades 8-10.

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