If the product of two numbers is 5 and one of the number is $\frac{3}{2}$, then the sum of two numbers is

### Concept & Formula This is a basic algebraic operations problem. Use the given product to find the unknown number via division, and then compute the required sum using fractional arithmetic. $$ \text{Number 2} = \frac{\text{Product}}{\text{Number 1}} $$ ### Step-by-Step Solution * **Given:** The product is $5$. The first number is $\frac{3}{2}$. Let the second number be $x$. * **Calculation:** Set up the product equation. $x \times \frac{3}{2} = 5$ * Isolate $x$ by multiplying both sides by the reciprocal ($\frac{2}{3}$). $x = 5 \times \frac{2}{3} = \frac{10}{3}$ * **Deduction:** Now find the sum of the two numbers. $\text{Sum} = \frac{3}{2} + \frac{10}{3}$ * Find the Least Common Multiple (LCM) of the denominators ($2$ and $3$), which is $6$. $\text{Sum} = \frac{3 \times 3}{6} + \frac{10 \times 2}{6} = \frac{9}{6} + \frac{20}{6} = \frac{29}{6}$ * Convert the improper fraction to a mixed number. $\frac{29}{6} = 4 \text{ with a remainder of } 5 = 4 \frac{5}{6}$ ### Exam Strategy & Shortcut Notice that the sum is $\frac{3}{2} + \frac{10}{3} = 1.5 + 3.33 = 4.833$. Looking at the options, $4 \frac{5}{6}$ is the only option extremely close to $4.8$ (since $\frac{5}{6} \approx 0.833$). You can use quick decimal approximation to skip finding common denominators. ### Common Pitfall Students often incorrectly add fractions by adding the numerators and denominators straight across (e.g., getting $\frac{13}{5}$), skipping the critical step of finding a common denominator. ### Final Answer **Therefore, the correct answer is $4 \frac{5}{6}$.**