How do you multiply 96 x 104 mentally?

Question

are there any math tricks or any way of multiplying 96 x 104 in your head??

Answer 1

Anytime you have a situation with

(a+x)*(a-x)

it results is

a^2 - x^2.

(100-4)*(100+4) = 100^2 - 4^2 = 10000 - 16 = 9984.

Answer 2

There is a short way to do this, and a longer way.

SHORT WAY:

104 x 96 = 100 x 100 - 4 x 4 = 10000 - 16 = 9984

LONG WAY:

1) 96 x 100 = 9600

2) We still have 4 leftover from the 104, so we need to add 4 x 96 to that result. But here instead I'd multiply 4 x 100 to get 400 and add it, so now we have 10000

3) The last leftover bit is now the excess 4 x 4 = 16, so now subtract that in to get 9984.

Answer 3

Obviously, others have given essentially the same answer, but the trick is to recognize that 96 x 104 can be expressed as (100 - 4) x (100 + 4) which when multiplied is the "difference of two perfect squares" 100^2 - 4^2. =10000 - 16 = 9984.

There is also application in terms of computing "tough" perfect squares that are near "easy" perfect squares, but the math is a little tougher. For example, if someone asks you to compute 97^2 in your head, this is tough at first glance. however if you recognize that 97^2 = (100-3)^2 it becomes easier. You simply figure that 100^2 = 10000 (easy to do in your head) and then do 3x(197) = 591 (easier in your head than 97^2) and subtract the 2 to get 9409 as the answer.

In general, the solution is found as Hard Square - Easy square = (difference between east and hard)*(sum of easy and hard) so Hard Square = Easy Square +/- (difference of easy and hard)*(sum of easy and hard)

It is pretty easy to execute if you try it a few times (as long as the square you are seeking is pretty sloce to an easy square).

It works especailly well for squares that exactly 1 away from an easy square (say 99). Since the math then becomes 100^2 - (difference)*(sum) = 10000 - 1*199 = 9801 (being a difference of only one, that one relatively tough multiplication gets very easy since 1*anything is easy)

Answer 4

Start with (96)(104) = (96)(100) + (96)(4) = 9600 + (96)(4)

You can then think of (96)(4) as (100)(4) - (4)(4)

So (96)(104) =(96)(100) + 4(100) - (4)(4)

= (100)(100) - (4)(4) = 10000 - 16

= 9984

Hope that helps!

Answer 5

Hmmm!!! fixing 104 x 106 devoid of multiplying immediately is very technical and difficult yet attempting slightly on the thank you to remedy that's going to contain using indices and operational symbols. 104 = one hundred+4 = 10²+4 106 = one hundred+6 = 10²+6 So, 104 x 106 is the comparable as (10²+4) x (10²+6) = 10²(10²+4)+6(10²+4) = 10²*10² + 10²*4 + 10²*6 + 6*4 = 10^(2+2) + 4 hundred + six hundred + 24 = 10^4 + a million,000 + 24 = 10,000 + a million,024 = eleven,024...Ans

Answer 6

104*96=100*96+4*96...
100*96 obviously equals 9600, and 96*4=100*4-4*4 equals 400-16 equals 384.
9600+384 equals 9984.

Answer 7

Pretend 96 is 100 and add two zeros to 104.
Subtract four 104s or 416

10400 - 416 = 9984

Answer 8

(96 x 100) +(100 x 4) - (4 x 4)
9600 + 400 - 16 =10,000 - 16 = 9984

Answer 9

I'd go for 100 times 96
9600
plus
4 times 90 (360)
makes 9960
plus 6 times 4 (24)
makes 9984

Answer 10

96x104=
(100-4) x (100+4)=
100^2 - 4^2=
10000 - 16 =
9984