To solve the equation \(-2 \frac{1}{4} = r - \frac{4}{5}\), follow these steps:

1. **Convert mixed number to improper fraction:**

   \(-2 \frac{1}{4}\) can be converted to an improper fraction. 

   \[
   -2 \frac{1}{4} = -\left(2 + \frac{1}{4}\right) = -\frac{9}{4}
   \]

2. **Write the equation with improper fractions:**

   \[
   -\frac{9}{4} = r - \frac{4}{5}
   \]

3. **Isolate \(r\):**

   To isolate \(r\), add \(\frac{4}{5}\) to both sides of the equation.

   \[
   -\frac{9}{4} + \frac{4}{5} = r
   \]

4. **Find a common denominator:**

   The common denominator of 4 and 5 is 20.

   \[
   -\frac{9}{4} = -\frac{9 \times 5}{4 \times 5} = -\frac{45}{20}
   \]
   \[
   \frac{4}{5} = \frac{4 \times 4}{5 \times 4} = \frac{16}{20}
   \]

5. **Add the fractions:**

   \[
   -\frac{45}{20} + \frac{16}{20} = \frac{-45 + 16}{20} = \frac{-29}{20}
   \]

6. **Simplify the fraction (if possible):**

   The fraction \(\frac{-29}{20}\) is already in simplest form.

So, the value of \(r\) is:

\[
r = \frac{-29}{20}
\]

Would you like details on any specific step or have any questions?

Here are some related questions:

1. How do you convert mixed numbers to improper fractions?
2. What is the process to find a common denominator?
3. How can you check your solution to an equation?
4. What is the difference between proper and improper fractions?
5. How do you simplify fractions?

**Tip:** When solving equations involving fractions, always look for a common denominator to make addition or subtraction straightforward.

Learn how to solve the equation -2 1/4 = r - 4/5 with step-by-step instructions. This solution covers converting mixed numbers to improper fractions, finding common denominators, and isolating variables. Suitable for students in Grades 6-8.

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