`(3+(5)/(-7))=?`

Options

A. `(-16)/(7)`
B. `(16)/(7)`
C. `(-26)/(7)`
D. `(-8)/(7)`

Answer

To solve the expression \(3 + \frac{5}{-7}\), we can follow these steps:

### Step 1: Understand the expression
The expression can be rewritten as:
\[ 3 + \left(-\frac{5}{7}\right) \]
This means we are adding 3 and the negative fraction \(-\frac{5}{7}\).

### Step 2: Convert 3 into a fraction
To add these two numbers, we can convert 3 into a fraction with a denominator of 1:
\[ 3 = \frac{3}{1} \]

### Step 3: Find a common denominator
The denominators we have are 1 and 7. The least common multiple (LCM) of 1 and 7 is 7.

### Step 4: Convert both fractions to have the same denominator
Now, we will convert \(\frac{3}{1}\) into a fraction with a denominator of 7:
\[ \frac{3}{1} = \frac{3 \times 7}{1 \times 7} = \frac{21}{7} \]

### Step 5: Rewrite the expression with the common denominator
Now we can rewrite the expression:
\[ \frac{21}{7} + \left(-\frac{5}{7}\right) = \frac{21 - 5}{7} \]

### Step 6: Perform the subtraction in the numerator
Now, we will subtract the numerators:
\[ 21 - 5 = 16 \]

### Step 7: Write the final answer
Thus, we have:
\[ \frac{21 - 5}{7} = \frac{16}{7} \]

So, the final answer is:
\[ 3 + \frac{5}{-7} = \frac{16}{7} \]

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