CLASS-1
CONCEPT OF MULTIPLICATION

CONCEPT OF MULTIPLICATION -


MULTIPLICATION – 

Multiplication is a fundamental arithmetic operation that combines two or more numbers to find their total value when they are repeated a certain number of times. It is denoted by the "×" symbol or by placing numbers next to each other without any operation symbol.

For example:-

  1. In its basic form, multiplication of two numbers is represented as: a × b, where "a" and "b" are the numbers being multiplied.
  2. Multiplication of three numbers can be represented as: a × b × c, where "a," "b," and "c" are the numbers being multiplied.
  3. In general, multiplication of "n" numbers can be represented as: a₁ × a₂ × a₃ × ... × aₙ, where "a₁," "a₂," ..., "aₙ" are the numbers being multiplied.

The result of a multiplication operation is called the "product."

Some key properties and concepts related to multiplication include:

  1. Commutative Property: The order of the numbers being multiplied does not affect the result. a × b = b × a
  2. Associative Property: The grouping of the numbers being multiplied does not affect the result. (a × b) × c = a × (b × c)
  3. Multiplicative Identity: Multiplying any number by 1 gives the same number. a × 1 = a
  4. Multiplicative Zero Property: Any number multiplied by 0 equals 0. a × 0 = 0
  5. Distributive Property: Multiplication distributes over addition (and subtraction).  a × (b + c) = (a × b) + (a × c)
  6. Multiplication with Negative Numbers: The product of a positive number and a negative number is negative, while the product of two negative numbers is positive. -a × b = -(a × b) (-a) × (-b) = a × b

Multiplication has many practical applications, including calculating areas and volumes, scaling quantities, determining total costs, and solving various mathematical problems. It is also an essential operation in algebra and higher mathematics, forming the basis for advanced concepts like exponentiation and logarithms.


Some other way of understanding -

Multiplication is one of the fundamental arithmetic operations in mathematics. It is the process of repeatedly adding a number to itself a certain number of times. In other words, it is a shorthand method of addition.

In its simplest form, multiplication is represented using the "×" symbol or by placing numbers adjacent to each other. For example:

  1. Using the "×" symbol:    3 × 4 = 12
  2. Without the "×" symbol:   3 * 4 = 12

In this case, 3 is multiplied by 4, resulting in the product 12.

Key Concepts and Properties of Multiplication:-

  1. Multiplicand and Multiplier: In the expression 3 × 4 = 12, "3" is the multiplicand, "4" is the multiplier, and "12" is the product.
  2. Commutative Property: The commutative property of multiplication states that the order of the numbers being multiplied does not affect the result. In other words, a * b = b * a. For example: 3 * 4 = 4 * 3 = 12.
  3. Associative Property: The associative property of multiplication states that the grouping of numbers being multiplied does not affect the result. In other words, (a * b) * c = a * (b * c). For example: (2 * 3) * 4 = 2 * (3 * 4) = 24.
  4. Identity Element: The identity element for multiplication is "1." Any number multiplied by 1 remains unchanged. For example: 5 * 1 = 5.
  5. Zero Property: The zero property of multiplication states that any number multiplied by 0 equals 0. For example: 6 * 0 = 0.
  6. Distributive Property: The distributive property of multiplication over addition states that multiplying a number by the sum of two other numbers is the same as multiplying the number separately by each of the two numbers and then adding the products. In other words, a * (b + c) = (a * b) + (a * c). For example: 2 * (3 + 4) = (2 * 3) + (2 * 4) = 14.

Multiplication is used extensively in various areas of mathematics, science, engineering, and everyday life. It is essential for performing calculations, scaling quantities, calculating areas and volumes, solving equations, and much more. Additionally, it lays the foundation for more advanced mathematical concepts like exponents and logarithms.

Multiplication is the summation of repeated addition of the same number through a simple way with an investment of minimum time. The sign of multiplication is ‘X‘.

Suppose there is a number which has been kept in a group 5 times and the number is 2.

We could have done in addition = 2 + 2 + 2 + 2 + 2 = 10 ( Answer), but instead of repeated addition of 2 for 5 times we can use short method and that is = 5 X 2 = 10 (Answer).

Example – Suppose a person for a special ceremony he went to buy new clothes for his home member, and he had purchased 2 shirts each for his 3 boy child and set of 2 long skirts for his 4 girl child.

Now the question is how many shirts and long skirts did he purchase for his children?

In repeated addition we can say he has purchased shirts = 2 + 2 + 2 = 6 no.s and long skirts = 2 + 2 + 2 + 2 = 8 no.s

But we can give the answer in a simple way with an investment of less time, i.e the person has purchased 2x3 (instead of adding 2 by 3 times) = 6 shirts and  2 x 4 (instead of adding 2 by 4 times) = 8 long skirts.

Instead of adding 2 three times, we can write 2 x 3 = 6 , and

Instead of adding 2 four times, we can write 2 x 4 = 8.

Here 6 and 8 are called the PRODUCTS.