How Many Times? - Word Problems on Multiplication

Multiplication as Repeated Addition: Multiplication is a quick way of adding the same number many times. For example, if you have $4$ groups of $3$ stars, instead of calculating $3 + 3 + 3 + 3 = 12$, you can simply say $4 \times 3 = 12$. Visually, imagine $4$ separate circles, each containing $3$ small stars; the total count of stars is the product.

The Multiplication Symbol: The symbol $\times$ is used to denote multiplication and is read as 'times'. In the expression $5 \times 2$, we say '5 times 2', which means the number $2$ is added $5$ times.

Multiplication Arrays: You can visualize multiplication using rows and columns. Imagine a grid of buttons with $3$ horizontal rows and $5$ vertical columns. The total number of buttons is $3 \times 5 = 15$. This helps in understanding that area or total count can be found by multiplying length by width.

Properties of Zero and One: Any number multiplied by $0$ always results in $0$ (e.g., $15 \times 0 = 0$). Any number multiplied by $1$ stays the same (e.g., $8 \times 1 = 8$). Imagine $5$ empty baskets; you have $5 \times 0 = 0$ fruits.

Commutative Property (Order of Numbers): The order in which you multiply two numbers does not change the result. For example, $4 \times 6 = 24$ and $6 \times 4 = 24$. Visually, if you rotate a chocolate bar that is $2$ squares wide and $5$ squares long, it becomes $5$ squares wide and $2$ squares long, but the total number of squares remains $10$.

Multiplying by $10$ and $100$: When you multiply a number by $10$, you simply write the number and put one $0$ at the end (e.g., $7 \times 10 = 70$). When multiplying by $100$, you add two zeros (e.g., $4 \times 100 = 400$).

Identifying Keywords in Word Problems: To solve word problems, look for keywords like 'each', 'every', 'per', 'in all', and 'total'. If the problem gives you the value of one item and asks for the value of many identical items, you must use multiplication.

Doubling and Tripling: 'Double' means to multiply a number by $2$, and 'triple' means to multiply a number by $3$. For example, if Rahul has $5$ marbles and Sonu has double that amount, Sonu has $5 \times 2 = 10$ marbles.