1. The problem is to evaluate the expression $3 \times \frac{2}{3} - 1 \times \frac{3}{4}$.\n\n2. We use the rule that multiplication of a whole number by a fraction is done by multiplying the whole number by the numerator and then dividing by the denominator: $a \times \frac{b}{c} = \frac{a \times b}{c}$.\n\n3. Calculate $3 \times \frac{2}{3}$:\n$$3 \times \frac{2}{3} = \frac{3 \times 2}{3} = \frac{6}{3} = 2.$$\n\n4. Calculate $1 \times \frac{3}{4}$:\n$$1 \times \frac{3}{4} = \frac{1 \times 3}{4} = \frac{3}{4}.$$\n\n5. Now subtract the two results:\n$$2 - \frac{3}{4} = \frac{8}{4} - \frac{3}{4} = \frac{8 - 3}{4} = \frac{5}{4}.$$\n\n6. The final answer is $\frac{5}{4}$ or $1 \frac{1}{4}$.