What should be added to `(-3)/(5)` to get `(-1)/(3)` ?

Options

A. `(4)/(5)`
B. `(8)/(15)`
C. `(4)/(15)`
D. `(2)/(5)`

Answer

To solve the problem of what should be added to \(-\frac{3}{5}\) to get \(-\frac{1}{3}\), we can follow these steps:

### Step 1: Set up the equation
We need to find a number \(x\) such that:
\[ -\frac{3}{5} + x = -\frac{1}{3} \]

### Step 2: Isolate \(x\)
To find \(x\), we can rearrange the equation:
\[ x = -\frac{1}{3} + \frac{3}{5} \]

### Step 3: Find a common denominator
To add the fractions \(-\frac{1}{3}\) and \(\frac{3}{5}\), we need a common denominator. The least common multiple of 3 and 5 is 15.

### Step 4: Convert the fractions
Convert \(-\frac{1}{3}\) and \(\frac{3}{5}\) to have a denominator of 15:
\[ -\frac{1}{3} = -\frac{1 \times 5}{3 \times 5} = -\frac{5}{15} \]
\[ \frac{3}{5} = \frac{3 \times 3}{5 \times 3} = \frac{9}{15} \]

### Step 5: Add the fractions
Now we can add the two fractions:
\[ x = -\frac{5}{15} + \frac{9}{15} = \frac{9 - 5}{15} = \frac{4}{15} \]

### Step 6: Conclusion
Thus, the number that should be added to \(-\frac{3}{5}\) to get \(-\frac{1}{3}\) is:
\[ \frac{4}{15} \]

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