What should be added to twice the rational number `(-7)/3 ` to get `3/7`

Options

A. `5`
B. `107/21`
C. `3/7`
D. `101/21`

Explanation

To solve the problem, we need to find out what should be added to twice the rational number \(-\frac{7}{3}\) to get \(\frac{3}{7}\). Let's break this down step by step.

### Step 1: Define the variable
Let \(x\) be the number that we need to add.

### Step 2: Write the equation
According to the problem, we need to add \(x\) to twice the rational number \(-\frac{7}{3}\) to get \(\frac{3}{7}\). This can be expressed as:
\[ 2 \times \left(-\frac{7}{3}\right) + x = \frac{3}{7} \]

### Step 3: Calculate twice the rational number
Now, let's calculate \(2 \times \left(-\frac{7}{3}\right)\):
\[ 2 \times \left(-\frac{7}{3}\right) = -\frac{14}{3} \]
So, we can rewrite our equation:
\[ -\frac{14}{3} + x = \frac{3}{7} \]

### Step 4: Isolate \(x\)
To isolate \(x\), we add \(\frac{14}{3}\) to both sides of the equation:
\[ x = \frac{3}{7} + \frac{14}{3} \]

### Step 5: Find a common denominator
To add the fractions \(\frac{3}{7}\) and \(\frac{14}{3}\), we need a common denominator. The least common multiple (LCM) of 7 and 3 is 21.

### Step 6: Convert fractions to have the same denominator
Convert \(\frac{3}{7}\) and \(\frac{14}{3}\) to have a denominator of 21:
\[ \frac{3}{7} = \frac{3 \times 3}{7 \times 3} = \frac{9}{21} \]
\[ \frac{14}{3} = \frac{14 \times 7}{3 \times 7} = \frac{98}{21} \]

### Step 7: Add the fractions
Now we can add the two fractions:
\[ x = \frac{9}{21} + \frac{98}{21} = \frac{9 + 98}{21} = \frac{107}{21} \]

### Conclusion
Thus, the value of \(x\) that should be added is:
\[ \frac{107}{21} \]