A fraction when added to `(7)/(3)` gives 4. The said fraction is:

Options

A. `1(2)/(3)`
B. `-(1)/(2)`
C. `(2)/(3)`
D. `(11)/(2)`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Define the fraction
Let the unknown fraction be represented as \( x \).

### Step 2: Set up the equation
According to the problem, when this fraction \( x \) is added to \( \frac{7}{3} \), the result is 4. We can write this as:
\[ x + \frac{7}{3} = 4 \]

### Step 3: Isolate the fraction
To find \( x \), we need to isolate it on one side of the equation. We can do this by subtracting \( \frac{7}{3} \) from both sides:
\[ x = 4 - \frac{7}{3} \]

### Step 4: Convert 4 to a fraction
To perform the subtraction, we need to express 4 as a fraction with a denominator of 3. We can write:
\[ 4 = \frac{12}{3} \]
Now the equation looks like:
\[ x = \frac{12}{3} - \frac{7}{3} \]

### Step 5: Perform the subtraction
Now that both fractions have the same denominator, we can subtract the numerators:
\[ x = \frac{12 - 7}{3} = \frac{5}{3} \]

### Step 6: Convert to mixed fraction
The fraction \( \frac{5}{3} \) can be converted to a mixed fraction. Dividing 5 by 3 gives us 1 with a remainder of 2. Thus, we can write:
\[ \frac{5}{3} = 1 \frac{2}{3} \]

### Conclusion
The fraction that, when added to \( \frac{7}{3} \), gives 4 is:
\[ \frac{5}{3} \text{ or } 1 \frac{2}{3} \]