Multiplication can be introduced as the method of calculating the product of two or more numbers in mathematics. It is the simple mathematical operation that we use in our daily practices. Multiplication tables are the most common application.

Multiplication

Multiplication in a simpler term is defined as the process of repeatedly adding a number to another number in mathematics. 

Multiplication of two numbers, such as ‘a’ and ‘b,’ is expressed as ‘a’ multiplied by ‘b.’

When we multiply 2 by 3, for example, we are adding 3 to itself twice, resulting in 3 + 3 = 6. This is a straightforward method for children to multiply numbers.

Multiplication is represented with a cross sign() and, on occasion, a dot(.).

Multiplier x Multiplicand = Product is the multiplication formula.

Example: Product = 6 x 8 = 48

Product = 6 x 8 = 48  

Multiplication Properties

Multiplication has the following properties:

• Closure Property
• Commutative property
• Associative property
• Distributive property 
• Identity property
• zero property

Now let us understand each properties of multiplication in details,

Closure property of Multiplication 

An integer (-4 x 3 = -12) is the product of two numbers.

A fraction or a whole number can be produced by multiplying two fractions (1/2 x 2 = 1).

Commutative Property of Multiplication

If A and B are any two integers, then the commutative property of multiplication implies that A × B = B × A.

2 × 3 = 3 × 2 = 6 is one of the examples of commutative properties of multiplication.

Associative Property of Multiplication

If A, B, and C are any three integers, then A× (B × C) = (A × B) × C is the associative property of multiplication.

For example,2 × (5 × 4) = (2 × 5) × 4 = 40

Distributive property of Multiplication

If A, B, and C are any three numbers, then according to the distributive property of multiplication:

a × ( b +  c) = (a × b) + (a × c)

For example,

4 × (2 + 3) = 4 × 2 + 4 × 3 → 20

Identity Property of Multiplication

According to the identity characteristic of multiplication, if we multiply any value by 1, it retains its value, hence A 1 = A.

Consider the following scenario:

12 × 1 = 12

-3 × 1 = -3

Zero Property of Multiplication

Any number multiplied by 0 is equivalent to zero only, according to the zero property of multiplication.

Where A is any number, A 0 = 0.

For example,

9 × 0 = 0

Rules of multiplication

 When it comes to multiplying numbers, there are a few different principles to follow. They are as follows:

• When two real numbers are multiplied, the result is a real number.
• Any number multiplied by zero will give zero as a result.
• When an integer is multiplied by multiples of ten, the original number is padded with the same number of 0s. 4 1000 Equals 4000, for example.
• When the numbers are multiplied together, the sequence of the numbers doesn’t matter. Example: 2 × 3 × 4 × 5 = 5 × 4 × 3 × 2 = 3 × 2 × 4 × 5 = 120

Multiplication sign

The output result differs when two or more numbers are multiplied with different signs (+ and -), as shown in the sign rules below:

• When you multiply two positive numbers, you get a positive result.
• When one positive integer is multiplied by one negative integer, or vice versa, the result is negative.
• When any two negative integers are multiplied, a positive integer is obtained.

Multiplication of fraction

When two or more fractions are multiplied, the numerators and denominators are combined, resulting in:

(a/b) + (c/d) = (ac)/(bd) 

Eg 1. Multiply 3/4 and 5/2 .

= (3×5/4×2)

=15/8 

Multiplication of decimal

Calculating the product of decimals is the same as finding the product of integers. After multiplication, we must pay attention to the location of the decimal (.).Let’s have a look at an illustration.

Eg. 1. What will be the product of 1.2 and 3. 

Solution: 1.2* 3 = 3.6

Eg. 1. Multiply 4.2 and 1.5 

Solve this by deleting the decimals from 4.2 and 1.5 and treating them as whole numbers. Hence,

15 x 42 = 630

If we return the decimal, the product of the two decimal values will have the decimal up to two positions from right to left, as follows:

6.30 = 4.2 + 1.5

Conclusion

Multiplication is a method of evaluating the product of two or more than two numbers. It is the simple operation that we always use in our daily life. One of the most common applications we use in our daily life is Multiplication tables.