Tables and Shares - Division as Grouping

Division as Equal Grouping: Division is the process of splitting a large group into smaller, equal groups. For example, if you have $12$ buttons and you want to put them into groups of $3$, you will draw circles around sets of $3$ buttons until none are left. You will find that you have $4$ circles, which means $12 \div 3 = 4$.

Division as Equal Sharing: This involves distributing a total number of items equally among a specific number of groups. Imagine sharing $15$ chocolates among $5$ friends; you give one to each until they are finished. Each friend ends up with $3$ chocolates, showing $15 \div 5 = 3$.

The Terms of Division: In every division problem, there are four main parts. The 'Dividend' is the total number being divided. The 'Divisor' is the number you are dividing by. The 'Quotient' is the answer. If anything is left over, it is called the 'Remainder'. In $17 \div 5 = 3$ with $2$ left over, $17$ is the Dividend, $5$ is the Divisor, $3$ is the Quotient, and $2$ is the Remainder.

Repeated Subtraction: Division can be understood as subtracting the same number repeatedly until you reach zero. For $20 \div 5$, you subtract $5$ from $20$ multiple times: $20 - 5 = 15$, $15 - 5 = 10$, $10 - 5 = 5$, and $5 - 5 = 0$. Since you subtracted $5$ exactly $4$ times, $20 \div 5 = 4$.

Relationship with Multiplication: Multiplication and division are inverse (opposite) operations. They form 'Fact Families'. If you know that $8 \times 4 = 32$, then you automatically know that $32 \div 8 = 4$ and $32 \div 4 = 8$. This is why learning multiplication tables is essential for solving division quickly.

Division by 1 and Self: When any number is divided by $1$, the quotient is the number itself ($9 \div 1 = 9$). When a non-zero number is divided by itself, the quotient is always $1$ ($6 \div 6 = 1$). Visually, if you have $6$ sweets and give them all to $6$ people, everyone gets exactly $1$ sweet.

Division by 10 and 100: When dividing a number ending in zeros by $10$ or $100$, we can simply remove the corresponding number of zeros. For example, $500 \div 10 = 50$ (remove one zero) and $500 \div 100 = 5$ (remove two zeros).