Which of the fractions given below, when added to `(13)/(5)`, gives 1 ?

Options

A. `-(8)/(15)`
B. `-(7)/(5)`
C. `-(26)/(10)`
D. `-(48)/(30)`

Answer

To solve the question, we need to find which fraction, when added to \( \frac{13}{5} \), results in 1. Let's break it down step by step.

### Step 1: Set up the equation
Let the fraction we are looking for be \( x \). According to the problem, we have:
\[ \frac{13}{5} + x = 1 \]

### Step 2: Isolate \( x \)
To find \( x \), we need to isolate it on one side of the equation. We can do this by subtracting \( \frac{13}{5} \) from both sides:
\[ x = 1 - \frac{13}{5} \]

### Step 3: Convert 1 to a fraction
To perform the subtraction, we need to express 1 as a fraction with the same denominator as \( \frac{13}{5} \). The denominator is 5, so we can write:
\[ 1 = \frac{5}{5} \]

### Step 4: Perform the subtraction
Now we can substitute this back into our equation:
\[ x = \frac{5}{5} - \frac{13}{5} \]
Since both fractions have the same denominator, we can subtract the numerators:
\[ x = \frac{5 - 13}{5} = \frac{-8}{5} \]

### Step 5: Check the options
Now we need to check if \( \frac{-8}{5} \) is one of the options provided in the question. If it is not listed, we can also express it in a different form, but since the question states that we are looking for a fraction, we conclude that \( \frac{-8}{5} \) is the correct answer.

### Final Answer
The fraction that, when added to \( \frac{13}{5} \), gives 1 is:
\[ \frac{-8}{5} \]