If `(m-n)/(n)=(4)/(9)`, what is the value of `(n)/(m)`?

Options

A. `(9)/(13)`
B. `(7)/(4)`
C. `(9)/(5)`
D. `(13)/(7)`

Answer

To solve the equation \(\frac{m-n}{n} = \frac{4}{9}\) and find the value of \(\frac{n}{m}\), we can follow these steps:

### Step 1: Cross-Multiply
We start with the equation:
\[ \frac{m-n}{n} = \frac{4}{9} \]
Cross-multiplying gives us:
\[ 9(m - n) = 4n \]

### Step 2: Distribute the 9
Next, we distribute the 9 on the left side:
\[ 9m - 9n = 4n \]

### Step 3: Combine Like Terms
Now, we want to isolate \(m\). We can add \(9n\) to both sides:
\[ 9m = 4n + 9n \]
This simplifies to:
\[ 9m = 13n \]

### Step 4: Solve for \(\frac{n}{m}\)
To find \(\frac{n}{m}\), we can rearrange the equation:
\[ \frac{n}{m} = \frac{9}{13} \]

### Final Answer
Thus, the value of \(\frac{n}{m}\) is:
\[ \frac{n}{m} = \frac{9}{13} \]