1. **Stating the problem:** We need to multiply the fraction $\frac{3}{4}$ by several fractions: $\frac{2}{2}$, $\frac{6}{6}$, $\frac{3}{3}$, $\frac{4}{4}$, and $\frac{5}{5}$. We will find the product for each case. 2. **Formula used:** When multiplying fractions, multiply the numerators together and the denominators together: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. **Important rule:** Multiplying a fraction by $\frac{n}{n}$ (where $n$ is any nonzero number) is equivalent to multiplying by 1, so the value of the fraction does not change. 4. **Calculations:** - $\frac{3}{4} \times \frac{2}{2} = \frac{3 \times 2}{4 \times 2} = \frac{6}{8}$ - $\frac{3}{4} \times \frac{6}{6} = \frac{3 \times 6}{4 \times 6} = \frac{18}{24}$ - $\frac{3}{4} \times \frac{3}{3} = \frac{3 \times 3}{4 \times 3} = \frac{9}{12}$ - $\frac{3}{4} \times \frac{4}{4} = \frac{3 \times 4}{4 \times 4} = \frac{12}{16}$ - $\frac{3}{4} \times \frac{5}{5} = \frac{3 \times 5}{4 \times 5} = \frac{15}{20}$ 5. **Simplify each product if possible:** - $\frac{6}{8} = \frac{3}{4}$ (dividing numerator and denominator by 2) - $\frac{18}{24} = \frac{3}{4}$ (dividing numerator and denominator by 6) - $\frac{9}{12} = \frac{3}{4}$ (dividing numerator and denominator by 3) - $\frac{12}{16} = \frac{3}{4}$ (dividing numerator and denominator by 4) - $\frac{15}{20} = \frac{3}{4}$ (dividing numerator and denominator by 5) 6. **Conclusion:** Multiplying $\frac{3}{4}$ by any fraction of the form $\frac{n}{n}$ does not change its value. All products simplify back to $\frac{3}{4}$. **Final answer:** $$\frac{3}{4} \times \frac{2}{2} = \frac{3}{4}, \quad \frac{3}{4} \times \frac{6}{6} = \frac{3}{4}, \quad \frac{3}{4} \times \frac{3}{3} = \frac{3}{4}, \quad \frac{3}{4} \times \frac{4}{4} = \frac{3}{4}, \quad \frac{3}{4} \times \frac{5}{5} = \frac{3}{4}$$