What should be added to `-6/8` to get `5/6` ?

Answer

To find out what should be added to \(-\frac{6}{8}\) to get \(\frac{5}{6}\), we can follow these steps:

### Step 1: Set up the equation
Let \(x\) be the number that we need to add to \(-\frac{6}{8}\). The equation can be set up as:
\[ -\frac{6}{8} + x = \frac{5}{6} \]

### Step 2: Isolate \(x\)
To find \(x\), we can rearrange the equation:
\[ x = \frac{5}{6} + \frac{6}{8} \]

### Step 3: Find a common denominator
The denominators of the fractions are 6 and 8. The least common multiple (LCM) of 6 and 8 is 24. We will convert both fractions to have this common denominator.

### Step 4: Convert \(\frac{5}{6}\) to have a denominator of 24
To convert \(\frac{5}{6}\):
\[ \frac{5}{6} = \frac{5 \times 4}{6 \times 4} = \frac{20}{24} \]

### Step 5: Convert \(\frac{6}{8}\) to have a denominator of 24
To convert \(\frac{6}{8}\):
\[ \frac{6}{8} = \frac{6 \times 3}{8 \times 3} = \frac{18}{24} \]

### Step 6: Add the two fractions
Now we can add the two fractions:
\[ x = \frac{20}{24} + \frac{18}{24} = \frac{20 + 18}{24} = \frac{38}{24} \]

### Step 7: Simplify the fraction
Now we simplify \(\frac{38}{24}\):
\[ \frac{38}{24} = \frac{19}{12} \]

### Final Answer
Thus, the number that should be added to \(-\frac{6}{8}\) to get \(\frac{5}{6}\) is:
\[ \frac{19}{12} \]

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