(6/5-3/4)*2/3

To solve the expression \((\frac{6}{5} - \frac{3}{4}) \times \frac{2}{3}\), we first need to calculate \(\frac{6}{5} - \frac{3}{4}\).

1. Find a common denominator for the fractions \(\frac{6}{5}\) and \(\frac{3}{4}\). The least common denominator (LCD) of 5 and 4 is 20.

2. Convert each fraction:

   • \(\frac{6}{5} = \frac{6 \times 4}{5 \times 4} = \frac{24}{20}\)
   • \(\frac{3}{4} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}\)

3. Subtract the fractions: \[ \frac{24}{20} - \frac{15}{20} = \frac{24 - 15}{20} = \frac{9}{20} \]

4. Now, multiply the result by \(\frac{2}{3}\): \[ \frac{9}{20} \times \frac{2}{3} = \frac{9 \times 2}{20 \times 3} = \frac{18}{60} \]

5. Simplify \(\frac{18}{60}\):

   • The greatest common divisor (GCD) of 18 and 60 is 6.
   • Divide both the numerator and denominator by 6: \[ \frac{18 \div 6}{60 \div 6} = \frac{3}{10} \]

Thus, the final result of the expression \((\frac{6}{5} - \frac{3}{4}) \times \frac{2}{3}\) is \(\frac{3}{10}\).