Find: `2(1)/(3)div(-3(1)/(2))`

Answer

To solve the problem \( 2 \frac{1}{3} \div (-3 \frac{1}{2}) \), we will follow these steps:

### Step 1: Convert Mixed Numbers to Improper Fractions
First, we need to convert the mixed numbers into improper fractions.

For \( 2 \frac{1}{3} \):
- Multiply the whole number (2) by the denominator (3): \( 2 \times 3 = 6 \)
- Add the numerator (1): \( 6 + 1 = 7 \)
- So, \( 2 \frac{1}{3} = \frac{7}{3} \)

For \( -3 \frac{1}{2} \):
- Multiply the whole number (3) by the denominator (2): \( 3 \times 2 = 6 \)
- Add the numerator (1): \( 6 + 1 = 7 \)
- Since it's negative, we have \( -3 \frac{1}{2} = -\frac{7}{2} \)

### Step 2: Rewrite the Division as Multiplication
Now we rewrite the division of fractions as multiplication by the reciprocal.

\[ \frac{7}{3} \div -\frac{7}{2} = \frac{7}{3} \times -\frac{2}{7} \]

### Step 3: Multiply the Fractions
Now we multiply the fractions:

\[ \frac{7 \times -2}{3 \times 7} = \frac{-14}{21} \]

### Step 4: Simplify the Fraction
Next, we simplify the fraction \( \frac{-14}{21} \).

- Both the numerator and the denominator can be divided by their greatest common divisor (GCD), which is 7:
\[ \frac{-14 \div 7}{21 \div 7} = \frac{-2}{3} \]

### Final Answer
Thus, the final answer is:
\[ 2 \frac{1}{3} \div (-3 \frac{1}{2}) = -\frac{2}{3} \]

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