1. The problem is to verify and explain the division $14560 \div 416 = 35$. 2. Division means splitting $14560$ into $416$ equal parts and finding how many parts there are. 3. The formula for division is $\text{Dividend} \div \text{Divisor} = \text{Quotient}$. Here, $14560$ is the dividend, $416$ is the divisor, and $35$ is the quotient. 4. To check, multiply the quotient by the divisor: $$416 \times 35 = ?$$ 5. Calculate $416 \times 35$: $$416 \times 35 = 416 \times (30 + 5) = 416 \times 30 + 416 \times 5$$ $$= 12480 + 2080 = 14560$$ 6. Since $416 \times 35 = 14560$, the division is correct. 7. Step-by-step division: - Divide $1456$ (first four digits) by $416$, which goes $3$ times because $416 \times 3 = 1248$. - Subtract $1248$ from $1456$ to get $208$. - Bring down the last digit $0$ to make $2080$. - Divide $2080$ by $416$, which goes exactly $5$ times because $416 \times 5 = 2080$. - Subtract $2080$ from $2080$ to get $0$, so no remainder. 8. Therefore, $14560 \div 416 = 35$ is correct and verified by multiplication and long division steps.