Find there rational numbrs equivalent to `- 2/3.`

Answer

To find three rational numbers equivalent to \(-\frac{2}{3}\), we will follow these steps:

### Step 1: Understand the concept of equivalent rational numbers
Equivalent rational numbers are obtained by multiplying or dividing the numerator and denominator of a fraction by the same non-zero integer. This keeps the value of the fraction the same.

### Step 2: Start with the given rational number
The given rational number is \(-\frac{2}{3}\).

### Step 3: Find the first equivalent rational number
To find an equivalent rational number, we can multiply both the numerator and denominator by the same number. Let's choose \(2\):
\[ -\frac{2 \times 2}{3 \times 2} = -\frac{4}{6} \]
So, the first equivalent rational number is \(-\frac{4}{6}\).

### Step 4: Find the second equivalent rational number
Now, let's multiply both the numerator and denominator by \(3\):
\[ -\frac{2 \times 3}{3 \times 3} = -\frac{6}{9} \]
So, the second equivalent rational number is \(-\frac{6}{9}\).

### Step 5: Find the third equivalent rational number
Finally, let's multiply both the numerator and denominator by \(4\):
\[ -\frac{2 \times 4}{3 \times 4} = -\frac{8}{12} \]
So, the third equivalent rational number is \(-\frac{8}{12}\).

### Final Answer
The three rational numbers equivalent to \(-\frac{2}{3}\) are:
1. \(-\frac{4}{6}\)
2. \(-\frac{6}{9}\)
3. \(-\frac{8}{12}\)

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