Although this blog is mostly for parenting tips, this article is somewhat out of place, not to mention scaring some parents with maths - but nevertheless it can be something taught to children for fun and for good use.
This post is about some simple ways to do multiplication using very large numbers. But please not that these are not general techniques and only work with certain groups of numbers.
1. Squaring of Forty Somethings : eg, 42 * 42
Represent this as 4x * 4x, where x represents a digit
let a = 15 + x
let b = (10-x)^2, also b must always be two digits, even if the answer is less than 10
Answer is "a b"
Example: for 42 * 42, x = 2
So a = 15 + 2 = 17
b = (10-2)^2 = 8^2 = 64
Answer: 42 * 42 = 1764
2. Squaring of Fifty Somethings : eg, 52 * 52
Represent this as 5x * 5x, where x represents a digit
let a = 25 + x
let b = x^2, also b must always be two digits, even if the answer is less than 10
Answer is "a b"
Example: for 52 * 52, x = 2
So a = 25 + 2 = 27
b = 2^2 = 4 = 04
Answer: 52 * 52 = 2704
3. Squaring of Two digits ending in Five : eg, 65 * 65
Represent this as x5 * x5, where x represents a digit
let a = x.(x+1)
Then the answer is "a 25"
Example: for 65 * 65 -> x=6
So a = 6 x 7 = 42
Answer is "4225"
4. Multiplying two Ninety Something together: eg: 97 * 94
- Represent this as 9x * 9y
- Let a = 100 -x and let b = 100-y
- Answer is "(9x-b) * a.b". Note that a.b result must occupy two digits, so if a.b=7, then write "07"
Example: 97 * 94
a = 100-97 = 3, b=100-94 = 6
Answer = "(97-6) * 3.6" = "91 * 18" = 9118
5. Multiplying two numbers ending in 1s, eg: 21 x 81
- Represent this as x1 * y1
- Let a = x.y, b = x+y
- Answer: "a b 1"
Example 21 x 81
a = 2*8 = 16, b = 2+8 = 10, Note b must occupy ONE digit only, any extra digits get added to the front number.
Answer: "16" "10" "1" Since b=10, the "1" digit gets added to the front number, 16 +1.
So answer is "17 0 1"
