A fraction when added to `17/3` gives 4. What is the said fraction?

Options

A. `-1/1`
B. `-1(2)/3`
C. `9/2`
D. `2/3`

Answer

To solve the problem step by step, we need to find the fraction \( X \) that, when added to \( \frac{17}{3} \), equals \( 4 \).

### Step-by-Step Solution:

1. **Set Up the Equation**:
We know from the problem statement that:
\[ X + \frac{17}{3} = 4 \]

2. **Isolate the Fraction**:
To find \( X \), we need to isolate it on one side of the equation. We can do this by subtracting \( \frac{17}{3} \) from both sides:
\[ X = 4 - \frac{17}{3} \]

3. **Convert 4 to a Fraction**:
To perform the subtraction, we need to express \( 4 \) as a fraction with a common denominator. The denominator of \( \frac{17}{3} \) is \( 3 \). We can write \( 4 \) as:
\[ 4 = \frac{12}{3} \]
Now, we can rewrite the equation:
\[ X = \frac{12}{3} - \frac{17}{3} \]

4. **Perform the Subtraction**:
Since the fractions have the same denominator, we can subtract the numerators:
\[ X = \frac{12 - 17}{3} = \frac{-5}{3} \]

5. **Convert to Mixed Fraction (if needed)**:
The fraction \( \frac{-5}{3} \) can also be expressed as a mixed number. To convert it:
- Divide \( 5 \) by \( 3 \):
- \( 5 \div 3 = 1 \) (whole number)
- Remainder is \( 2 \)
Thus, \( \frac{-5}{3} \) can be written as:
\[ -1 \frac{2}{3} \]

### Final Answer:
The fraction is \( \frac{-5}{3} \) or as a mixed number, it is \( -1 \frac{2}{3} \).