What should be added to `-5/6` to get `-2/3` ?

Answer

To solve the problem of what should be added to \(-\frac{5}{6}\) to get \(-\frac{2}{3}\), we can follow these steps:

### Step 1: Set up the equation
Let \( x \) be the number that we need to find. The equation can be set up as:
\[ -\frac{5}{6} + x = -\frac{2}{3} \]

### Step 2: Isolate \( x \)
To find \( x \), we need to isolate it on one side of the equation. We can do this by adding \(\frac{5}{6}\) to both sides:
\[ x = -\frac{2}{3} + \frac{5}{6} \]

### Step 3: Find a common denominator
To add the fractions \(-\frac{2}{3}\) and \(\frac{5}{6}\), we need a common denominator. The least common multiple (LCM) of 3 and 6 is 6. We can convert \(-\frac{2}{3}\) to have a denominator of 6:
\[ -\frac{2}{3} = -\frac{2 \times 2}{3 \times 2} = -\frac{4}{6} \]

### Step 4: Add the fractions
Now we can add the two fractions:
\[ x = -\frac{4}{6} + \frac{5}{6} = \frac{-4 + 5}{6} = \frac{1}{6} \]

### Step 5: Conclusion
Thus, the number that should be added to \(-\frac{5}{6}\) to get \(-\frac{2}{3}\) is:
\[ \boxed{\frac{1}{6}} \]

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