Evaluate the expression 3/10 x 5/2 - 2/3 and provide the answer in lowest terms.

To evaluate the expression ( \frac{3}{10} \times \frac{5}{2} - \frac{2}{3} ), we start by calculating the multiplication of the fractions.

First, multiply ( \frac{3}{10} ) and ( \frac{5}{2} ):

[

\frac{3 \times 5}{10 \times 2} = \frac{15}{20}

]

Now, simplify ( \frac{15}{20} ) by dividing both the numerator and the denominator by their greatest common divisor, which is 5:

[

\frac{15 \div 5}{20 \div 5} = \frac{3}{4}

]

Next, we need to subtract ( \frac{2}{3} ) from ( \frac{3}{4} ). To do this, we find a common denominator, which is 12 for the fractions ( \frac{3}{4} ) and ( \frac{2}{3} ):

Convert ( \frac{3}{4} ) to have a denominator of 12:

[

\frac{3}{4} = \frac{3 \