What number must be added to each term of the ratio ` 9 : 11`, so that it becomes ` 4 : 5`.

Options

A. 1
B. 2
C. `-2`
D. `-1`

Explanation

To solve the problem, we need to find the number that must be added to each term of the ratio \( 9 : 11 \) so that it becomes \( 4 : 5 \).

### Step-by-Step Solution:

1. **Let the number to be added be \( x \)**:
We denote the unknown number that we need to add to both terms of the ratio as \( x \).

2. **Set up the new ratio**:
After adding \( x \) to both terms of the ratio \( 9 : 11 \), the new ratio becomes:
\[ \frac{9 + x}{11 + x} \]
We want this ratio to be equal to \( \frac{4}{5} \).

3. **Set up the equation**:
We can write the equation:
\[ \frac{9 + x}{11 + x} = \frac{4}{5} \]

4. **Cross-multiply to eliminate the fraction**:
Cross-multiplying gives us:
\[ 5(9 + x) = 4(11 + x) \]

5. **Distribute on both sides**:
Expanding both sides results in:
\[ 45 + 5x = 44 + 4x \]

6. **Rearrange the equation**:
To isolate \( x \), we move all terms involving \( x \) to one side and constant terms to the other side:
\[ 5x - 4x = 44 - 45 \]
This simplifies to:
\[ x = -1 \]

7. **Conclusion**:
The number that must be added to each term of the ratio \( 9 : 11 \) to make it \( 4 : 5 \) is \( -1 \).