Long Multiplication
Long Multiplication is a special method for multiplying larger numbers.
It is a way to multiply numbers larger than 10 that only needs your knowledge of the ten times Multiplication Table.
Let us say we want to multiply
612 × 24
- First we multiply 612 × 4 (=2,448),
- then we multiply 612 × 20 (=12,240),
- and last we add them together (2,448 + 12,240 = 14,688).
But we can do better!
When we multiply 612 × 20 we only need to multiply 612 × 2 and place the result one column over (so it is the same as multiplying by 20).We just have to be careful about lining up the columns. n simple algebra, multiplication is the process of calculating the result when a number 
is taken b times. The result of a multiplication is called the product of a and b, and each of the numbers a and b is called a factor of the product ab. Multiplication is denoted axb, a.b, (a)(b), or simply ab. The symbol x is known as the multiplication sign. Normal multiplication is associative, commutative, and distributive.
is taken b times. The result of a multiplication is called the product of a and b, and each of the numbers a and b is called a factor of the product ab. Multiplication is denoted axb, a.b, (a)(b), or simply ab. The symbol x is known as the multiplication sign. Normal multiplication is associative, commutative, and distributive.
More generally, multiplication can also be defined for other mathematical objects such as groups, matrices, sets, and tensors.
Karatsuba and Ofman (1962) discovered that multiplication of two 
digit numbers can be done with a bit complexity of less than 
using an algorithm now known as Karatsuba multiplication.
digit numbers can be done with a bit complexity of less than using an algorithm now known as Karatsuba multiplication.
Eddy Grant's pop song "Electric Avenue" (Electric Avenue, 2001) includes the commentary: "Who is to blame in one country; Never can get to the one; Dealin' in multiplication; And they still can't feed everyone, oh no.
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