What rational number should be added to `(( - 3)/(7))` to get the greatest negative integer ?

Options

A. `4/7`
B. `3/7`
C. `(-4)/(7)`
D. `7/3`

Answer

To find the rational number that should be added to \(-\frac{3}{7}\) to get the greatest negative integer, we can follow these steps:

### Step 1: Identify the greatest negative integer
The greatest negative integer is \(-1\).

### Step 2: Set up the equation
We need to find a rational number \(x\) such that:
\[ -\frac{3}{7} + x = -1 \]

### Step 3: Rearrange the equation to solve for \(x\)
To isolate \(x\), we can rearrange the equation:
\[ x = -1 + \frac{3}{7} \]

### Step 4: Convert \(-1\) to a fraction with the same denominator
To add these two fractions, we need to express \(-1\) as a fraction with a denominator of 7:
\[ -1 = -\frac{7}{7} \]

### Step 5: Add the fractions
Now we can add the two fractions:
\[ x = -\frac{7}{7} + \frac{3}{7} = \frac{-7 + 3}{7} = \frac{-4}{7} \]

### Step 6: Conclusion
Thus, the rational number that should be added to \(-\frac{3}{7}\) to get the greatest negative integer is:
\[ \boxed{-\frac{4}{7}} \]

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