In Examples 1 to 4, there are four options, out of which one is correct.
Choose the correct one.
Which of the following rational numbers is equivalent to `2/3`?

Options

A. `3/2`
B. `4/9`
C. `4/6`
D. `9/4`

Answer

To determine which of the given options is equivalent to \( \frac{2}{3} \), we will analyze each option step by step.

### Step 1: Understand the concept of equivalent fractions
Two fractions are equivalent if they represent the same value when simplified. To check if a fraction is equivalent to \( \frac{2}{3} \), we can simplify the fraction and see if it reduces to \( \frac{2}{3} \).

### Step 2: Check each option

#### Option 1: \( \frac{3}{2} \)
- This fraction is already in its simplest form.
- Since \( \frac{3}{2} \) does not equal \( \frac{2}{3} \), this option is incorrect.

#### Option 2: \( \frac{4}{9} \)
- This fraction is also in its simplest form.
- Since \( \frac{4}{9} \) does not equal \( \frac{2}{3} \), this option is incorrect.

#### Option 3: \( \frac{4}{6} \)
- We can simplify \( \frac{4}{6} \) by finding the greatest common divisor (GCD) of the numerator and denominator.
- The GCD of 4 and 6 is 2.
- Dividing both the numerator and denominator by 2:
\[ \frac{4 \div 2}{6 \div 2} = \frac{2}{3} \]
- Since \( \frac{4}{6} \) simplifies to \( \frac{2}{3} \), this option is correct.

#### Option 4: \( \frac{9}{4} \)
- This fraction is already in its simplest form.
- Since \( \frac{9}{4} \) does not equal \( \frac{2}{3} \), this option is incorrect.

### Conclusion
The only option that is equivalent to \( \frac{2}{3} \) is **Option 3: \( \frac{4}{6} \)**.

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