1. The problem states that Keiko received $\frac{5}{8}$ of the 72 votes cast for class vice-president. We need to find how many votes she received. 2. The formula to find the part of a total is: $$\text{Part} = \text{Fraction} \times \text{Total}$$ 3. Substitute the given values: $$\text{Votes received} = \frac{5}{8} \times 72$$ 4. Multiply the fraction by the total votes: $$\frac{5}{8} \times 72 = \frac{5 \times 72}{8}$$ 5. Simplify the fraction by canceling common factors: $$\frac{5 \times \cancel{72}}{\cancel{8}} = 5 \times 9 = 45$$ 6. Therefore, Keiko received 45 votes. Final answer: **45 votes**