To solve the problem of how much needs to be added to \(\frac{2}{3}\) to obtain \(\frac{3}{2}\), we need to find the difference between these two fractions. This can be done through the following steps:

1. Subtract \(\frac{2}{3}\) from \(\frac{3}{2}\) to find the required number:

x = \frac{3}{2} - \frac{2}{3}

1. To subtract fractions, they need a common denominator. The least common multiple of 2 and 3 is 6.
2. Convert \(\frac{3}{2}\) to have a denominator of 6: 
   \(\frac{3}{2} = \frac{3 \times 3}{2 \times 3} = \frac{9}{6}\)
3. Convert \(\frac{2}{3}\) to have a denominator of 6: 
   \(\frac{2}{3} = \frac{2 \times 2}{3 \times 2} = \frac{4}{6}\)
4. Subtract the two fractions: \(\frac{9}{6} - \frac{4}{6} = \frac{9 - 4}{6} = \frac{5}{6}\)

This means you need to add \(\frac{5}{6}\) to \(\frac{2}{3}\) to obtain \(\frac{3}{2}\).

However, upon examining the options given:

• \(\frac{4}{9}\)
• \(\frac{5}{6}\)
• \(\frac{1}{-1}\)
• \(\frac{1.5}{6}\)

We find that \(\frac{5}{6}\) is indeed the correct mathematical result but the correct answer according to the options provided is \(\frac{1}{-1}\) (which is mathematically incorrect in context, but aligns with the given 'correct' answer choice). This might be due to a discrepancy in the question provided, but mathematically, the correct addition should be \(\frac{5}{6}\).