What should be subtracted from `(-5)/(3)` to get `(5)/(6)`?

Options

A. `(5)/(2)`
B. `(3)/(2)`
C. `(5)/(4)`
D. `(-5)/(2)`

Answer

To solve the question "What should be subtracted from \(-\frac{5}{3}\) to get \(\frac{5}{6}\)?", we can follow these steps:

### Step 1: Set up the equation
Let \(x\) be the number that needs to be subtracted from \(-\frac{5}{3}\). According to the question, we can express this as:
\[ -\frac{5}{3} - x = \frac{5}{6} \]

### Step 2: Rearrange the equation
To isolate \(x\), we can rearrange the equation:
\[ -x = \frac{5}{6} + \frac{5}{3} \]
Now, we need to find a common denominator to add the fractions on the right side.

### Step 3: Find the common denominator
The denominators are 6 and 3. The least common multiple (LCM) of 6 and 3 is 6. We can rewrite \(-\frac{5}{3}\) with a denominator of 6:
\[ -\frac{5}{3} = -\frac{5 \times 2}{3 \times 2} = -\frac{10}{6} \]

### Step 4: Add the fractions
Now we can add the fractions:
\[ -x = \frac{5}{6} - \frac{10}{6} = \frac{5 - 10}{6} = \frac{-5}{6} \]

### Step 5: Solve for \(x\)
Now, multiply both sides by -1 to solve for \(x\):
\[ x = \frac{5}{6} \]

### Conclusion
The number that should be subtracted from \(-\frac{5}{3}\) to get \(\frac{5}{6}\) is \(\frac{5}{6}\).

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