Evaluate: `2 div (2)/(3)`

Options

A. `3`
B. `5`
C. `7`
D. `6`

Answer

To evaluate the expression \( 2 \div \left( \frac{2}{3} \right) \), we can follow these steps:

### Step 1: Rewrite the Division as Multiplication
We can rewrite the division of a number by a fraction as multiplication by the reciprocal of that fraction. Thus, we have:
\[ 2 \div \left( \frac{2}{3} \right) = 2 \times \left( \frac{3}{2} \right) \]

### Step 2: Convert Whole Number to Fraction
Next, we can express the whole number \( 2 \) as a fraction:
\[ 2 = \frac{2}{1} \]
So now we can rewrite the expression:
\[ \frac{2}{1} \times \frac{3}{2} \]

### Step 3: Multiply the Fractions
Now we can multiply the two fractions:
\[ \frac{2 \times 3}{1 \times 2} = \frac{6}{2} \]

### Step 4: Simplify the Fraction
Finally, we simplify the fraction \( \frac{6}{2} \):
\[ \frac{6}{2} = 3 \]

### Final Answer
Thus, the evaluated result of \( 2 \div \left( \frac{2}{3} \right) \) is:
\[ \boxed{3} \]

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