What number should be added to -1 so as to get `(5)/(7)`?

Options

A. `(-11)/(7)`
B. `(-12)/(7)`
C. `(12)/(7)`
D. `(11)/(7)`

Answer

To solve the problem, we need to find the number \( x \) that should be added to \(-1\) to get \(\frac{5}{7}\).

### Step-by-Step Solution:

1. **Set up the equation**: We can express the problem mathematically as:
\[ -1 + x = \frac{5}{7} \]

2. **Isolate \( x \)**: To find \( x \), we need to isolate it on one side of the equation. We can do this by adding \( 1 \) to both sides:
\[ x = \frac{5}{7} + 1 \]

3. **Convert \( 1 \) to a fraction**: Since we are adding a fraction to a whole number, we need to express \( 1 \) as a fraction. We can write \( 1 \) as \(\frac{7}{7}\):
\[ x = \frac{5}{7} + \frac{7}{7} \]

4. **Add the fractions**: Now that both numbers are in fraction form, we can add them:
\[ x = \frac{5 + 7}{7} = \frac{12}{7} \]

5. **Conclusion**: Therefore, the number that should be added to \(-1\) to get \(\frac{5}{7}\) is:
\[ x = \frac{12}{7} \]

### Final Answer:
The number that should be added to \(-1\) to get \(\frac{5}{7}\) is \(\frac{12}{7}\).

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