Can We Share? - Relationship between Multiplication and Division

Equal Sharing: Division is the process of sharing a total number of items equally among a specific number of groups. For example, if you have 12 chocolates and 3 boxes, you place one chocolate in each box repeatedly until all are gone. You will see 4 chocolates in each box, which means $12 \div 3 = 4$.

Equal Grouping: This involves finding how many groups can be formed from a total when we know how many items go into each group. Imagine 15 buttons. If you put 5 buttons on each shirt, you can visualize 3 shirts being covered. This is written as $15 \div 5 = 3$.

Division as Repeated Subtraction: Division can be understood as subtracting the same number over and over until you reach zero. To solve $20 \div 5$, you subtract 5 from 20 ($20 - 5 = 15$, $15 - 5 = 10$, $10 - 5 = 5$, $5 - 5 = 0$). Since you subtracted 5 four times, the answer is 4.

The Inverse Relationship: Multiplication and division are opposite operations. If you know that $4 \times 6 = 24$, you automatically know two division facts: $24 \div 4 = 6$ and $24 \div 6 = 4$. You can visualize this as a Fact Family Triangle with 24 at the top and 4 and 6 at the bottom corners.

Parts of a Division Sentence: In the equation $18 \div 2 = 9$, 18 is the 'Dividend' (the total amount), 2 is the 'Divisor' (the number of groups or items per group), and 9 is the 'Quotient' (the result).

Division by 1 and Itself: When any number is divided by 1, the quotient is the number itself ($8 \div 1 = 8$). When a number is divided by itself, the quotient is always 1 ($8 \div 8 = 1$). Imagine having 8 balls and 1 bag; the bag gets all 8. If you have 8 balls and 8 bags, each bag gets only 1.

The Role of Zero: Zero divided by any number is always zero ($0 \div 5 = 0$). However, we cannot divide any number by zero because we cannot share items among 'zero' groups.