1. Problem: Calculate $\frac{21}{5} \times \frac{9}{23}$ and verify if it equals $\frac{84}{115}$. 2. Formula: Multiplying fractions is done by multiplying numerators and denominators: $$\frac{a}{b} \times \frac{c}{d} = \frac{a \times c}{b \times d}$$ 3. Calculation: $$\frac{21}{5} \times \frac{9}{23} = \frac{21 \times 9}{5 \times 23} = \frac{189}{115}$$ 4. Simplify: Check if $\frac{189}{115}$ can be simplified. The greatest common divisor (GCD) of 189 and 115 is 1, so it cannot be simplified further. 5. Compare: Given result is $\frac{84}{115}$. Since $\frac{189}{115} \neq \frac{84}{115}$, the given equality is false. 6. Final answer: $$\frac{21}{5} \times \frac{9}{23} = \frac{189}{115} \neq \frac{84}{115}$$