Multiplication and its process to do it in few seconds

Multiplication and its process to do it in few seconds

Multiplication is a short process of finding the sum of a given number. The number to be repeated is called multiplicand and the number which indicates how many times the multiplicand is to be repeated is called multiplier. The sum of the repetitions obtained is called the product.
For example:
12 × 3 = (12 + 12 + 12) = 36.
Here 12 is the multiplicand, 3 is the multiplier and 36 is the product.

Facts on Multiplication:
The position of multiplicand and multiplier are interchangeable, i.e. 3 × 12 = 36.
→ The product of any number multiplied by zero is zero. e.g. 46 × 0 = 0.
→ Any number multiplied by 1 gives the same number. e.g. 456 × 1 = 456.
→ When multiplicand or multiplier or both have zeros at right end, we can neglect such zeros during multiplication and place as all the zeros at the end of the product so obtained.
For example:
120 × 30 = (12 × 300) → (12 × 3) and then suffix two zeros = 3600.

→ Rule of Products:
Odd × odd = odd; [7 × 7 = 49]
Odd × even = even; [9 × 8 = 72]
Even × even = even; [6 × 6 = 36]
→ The product of any r consecutive integers (numbers) is divisible by r!
→ The difference between 2 numbers-
xy - yx = divisible by 9.
87 - 78 = 9 → divisible by 9.
→ The square of an odd number when divided by 8 will always remainder 1. E.g. 72 = 49, on dividing by 8 it gives remainder 1.
→ 3n will always have an even number of tens. (e.g. 2 in 27, 8 in 81, 24 in 243 and so on.)

Different Short-cut on Multiplication:
Simply put as many zeros as there are in multiplier on the right side of the number which is multiplied and this gives the required product. For example,
12 × 10 = 120: (one zeros on 12). 234 × 100 = 23400: (two zeros on 234) and so on.

Short-Cut to find Multiplication By 11:
Here we write down the first number from right and then we proceed writing down the sum of two number from right.

Example:-
123 × 11 = 1353;( Here we have written first number 3 from right then 2nd digit will come by adding (2 + 5), 3^rd digit come from (2 + 1) and 4^th digit come from 1.) 5628 × 11 = 61908;( Here, we have written first digit 8 then 2nd digit has come from by adding (8 + 2 = 10) which gives zero with a carry 1, 3^rd digit (6 + 2 = 8 + carry 1 = 9), 4^th digit (6 + 5 = 11), here we also get a carry 1, 5^th digit come from (5+ carry 1 = 6)
562 × 11 = 6182.

→ Multiplications of two numbers where tens place digits are same and sum of the unit digits is 10.

Example:-
i) 62 × 68(Here tens digit in each number is 6 and sum of unit digits is 8 + 2 = 10)

Step by step explanation:
6 × (6 + 1) = 42
2 × 8 = 16.
Hence, 62 × 68 = 4216.

ii) 36 × 34 = ?
3 × (3 + 1) = 12
6 × 4 = 24
36 × 34 = 1224
→ Multiplication of a number which is made of only digit 9 by some other number.

Example:
i) 68732 × 9999 = 68732 × (10000 - 1)
= 687320000 - 68732
= 687251268
Hence on putting as many zeros as the number of 9 after the given number and from the resulting number given number is subtracted. Thus result so obtained is the required product.

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