1. The problem asks which partial quotients could be added to find the quotient of $465 \div 15$. 2. Partial quotients are parts of the division process where you break down the dividend into easier chunks to divide by the divisor. 3. We want to find two numbers that add up to the quotient $\frac{465}{15}$. 4. Calculate the exact quotient: $$\frac{465}{15} = 31$$ 5. Now check each option by adding the two partial quotients: - (a) $20 + 1 = 21$ (not 31) - (b) $30 + 1 = 31$ (correct) - (c) $30 + 9 = 39$ (not 31) - (d) $30 + 10 = 40$ (not 31) 6. Therefore, the correct partial quotients that add to the quotient are $30$ and $1$. Final answer: Option (b) 30 and 1.