Division - Long Division Method

Division as Equal Distribution: Division is the process of splitting a larger group into smaller, equal groups. For example, if you have $15$ cookies and share them equally among $3$ friends, each friend gets $5$ cookies ($15 \div 3 = 5$).

The Four Parts of Division: Every long division problem has four components: the Dividend (the total being divided), the Divisor (the number we divide by), the Quotient (the answer), and the Remainder (what is left over).

Visualizing the Division Bracket: In the long division method, visualize the Dividend sitting inside a 'house' or a bracket. The Divisor stands outside to the left, and the Quotient is written on top of the 'roof'.

The DMSB Steps: To solve long division, remember the steps: Divide (check how many times the divisor fits), Multiply (divisor times the quotient digit), Subtract (find the difference), and Bring Down (carry the next digit from the dividend down).

Understanding the Remainder: The Remainder is the value left over at the end of the calculation. Visually, it is the number at the very bottom after all digits have been brought down. Importantly, the Remainder must always be smaller than the Divisor ($Remainder < Divisor$).

Zero and One Properties: Any number divided by $1$ is the number itself ($12 \div 1 = 12$). Zero divided by any number is zero ($0 \div 8 = 0$). You cannot divide a number by zero.

Relationship with Multiplication: Division is the inverse (opposite) of multiplication. If $4 \times 5 = 20$, then we know $20 \div 4 = 5$ and $20 \div 5 = 4$. This is helpful for checking your work.