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The image contains a mathematical expression asking to "Simplify the ratio" and the problem provided is:

\[
\frac{25 - 48w}{16w^2 - 40w}
\]

Let's simplify this expression step by step.

### Step 1: Factor the numerator and denominator
1. **Numerator**: \( 25 - 48w \)  
   This cannot be factored further as there is no common factor.

2. **Denominator**: \( 16w^2 - 40w \)  
   We can factor out the greatest common factor (GCF), which is \( 8w \).  
   So, \( 16w^2 - 40w = 8w(2w - 5) \).

Thus, the expression becomes:

\[
\frac{25 - 48w}{8w(2w - 5)}
\]

### Step 2: Check for further simplification
We cannot factor \( 25 - 48w \) any further, and it does not match with \( 2w - 5 \), so the expression is already in its simplest form.

### Final Simplified Form:
\[
\frac{25 - 48w}{8w(2w - 5)}
\]

This is the simplified version of the ratio.

Would you like further details or have any other questions? 

Here are 5 related questions:
1. How do you identify the greatest common factor (GCF) in expressions?
2. What methods can be used to factor quadratic expressions?
3. How can you check if a fraction can be simplified further?
4. What are the steps for simplifying a ratio involving variables?
5. Can factoring be used to simplify all algebraic fractions?

**Tip:** Always factor both the numerator and denominator first when simplifying ratios to identify possible cancellations.

Simplify the ratio 25 - 48w / 16w^2 - 40w.

Simplify the rational expression 25 - 48w / 16w^2 - 40w by factoring the numerator and denominator. Learn how to simplify complex algebraic fractions using common factors. Suitable for students in Grades 8-10.

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