Tables and Shares - Word Problems on Multiplication and Division

Multiplication as Repeated Addition: Multiplication is a shortcut for adding the same number many times. For example, if you have 4 plates with 3 cookies each, it is $3 + 3 + 3 + 3$, which is $3 \times 4 = 12$. Visually, imagine 4 separate circles, each containing 3 small dots.

Arrays and Grids: An array is an arrangement of objects in rows and columns. A $5 \times 4$ array has 5 rows and 4 columns, forming a rectangular shape. The total number of items is found by multiplying the number of rows by the number of columns: $5 \times 4 = 20$.

Division as Equal Sharing: Division is used to split a large group into smaller, equal parts. If you have 20 marbles to share among 5 friends, you give each friend the same amount until the marbles are gone. Visually, this is like drawing 5 large boxes and placing one marble in each box repeatedly until all 20 are distributed.

Division as Repeated Subtraction: Division can be seen as subtracting the same number over and over again until you reach zero. For $12 \div 3$, you subtract 3 from 12 four times ($12 - 3 = 9, 9 - 3 = 6, 6 - 3 = 3, 3 - 3 = 0$), so the answer is 4.

The Division House and Parts: In a division problem like $15 \div 3 = 5$, the number being divided (15) is the Dividend, the number you divide by (3) is the Divisor, and the answer (5) is the Quotient. Visually, the Dividend sits inside the 'division house' bracket, the Divisor sits outside to the left, and the Quotient is written on the roof.

Fact Families: Multiplication and division are inverse (opposite) operations. If you know $6 \times 3 = 18$, you automatically know $18 \div 3 = 6$ and $18 \div 6 = 3$. This is often represented as a 'fact triangle' with the largest number at the top and the two factors at the bottom corners.

Remainders: Sometimes, a number cannot be shared perfectly into equal groups. The amount left over is called the Remainder ($R$). For example, if you share 10 candies between 3 children, each gets 3 candies and 1 candy is left over. This is written as $10 \div 3 = 3 \text{ Remainder } 1$.

Multiplying by 10 and 100: When multiplying a number by 10, shift the digits one place to the left and add a zero at the end ($25 \times 10 = 250$). When multiplying by 100, add two zeros ($25 \times 100 = 2500$). This looks like moving the number across a place-value chart.