Additive inverse of `- (18)/(5) xx (16)/(7)` is

Options

A. `5 (33)/(35)`
B. `-5 (31)/(35)`
C. `5 (31)/(35)`
D. `1 (11)/(35)`

Answer

To find the additive inverse of the expression \(-\frac{18}{5} \times \frac{16}{7}\), we will follow these steps:

### Step 1: Calculate the product of the two fractions
We start by multiplying the two fractions:
\[ -\frac{18}{5} \times \frac{16}{7} = -\frac{18 \times 16}{5 \times 7} \]

### Step 2: Perform the multiplication in the numerator and denominator
Now, we calculate the products in the numerator and denominator:
\[ 18 \times 16 = 288 \]
\[ 5 \times 7 = 35 \]
So, we have:
\[ -\frac{288}{35} \]

### Step 3: Determine the additive inverse
The additive inverse of a number \(x\) is the number \(y\) such that \(x + y = 0\). Therefore, the additive inverse of \(-\frac{288}{35}\) is:
\[ \frac{288}{35} \]

### Final Answer
Thus, the additive inverse of \(-\frac{18}{5} \times \frac{16}{7}\) is:
\[ \frac{288}{35} \]

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