How do you personally multiply these two numbers together in your head? You know, the step by step process that you use to come to your conclusion.

365 + 365

Easy enough I suppose, but I’m no savant. I had to work it out in my head for about 8 seconds.

What intrigued me about it, was when I later reviewed how I came to the correct answer (yes, for no good reason at all).

I took 365, and brought it down as far as I could to a 100 base (if you can call it that). So… 300+300 = 600.

I then took 65 x 2 and thought to myself “what do I have left over after 100?” 15. Okay, so 15x2 is 30. Result 600+100+30 = 730

Does anybody else do this, and how can I improve on getting the answer in a simpler way?

Multiply?

for multiplying i’d use a calculator here. To add them, I calculate 2*(350 + 15) = 2350 + 215 = 700 + 30 = 730.

It’s easier for me to calculate 360 + 370, so that’s what I do.

I use the pretty much the same method as you do Parental Advisory. Smaller two digit numbers I can just multiply.

I guess I did it the long way.
5 + 5 = 10 carry the one.
_ _ 0

6 + 6 + 1 = 13 carry the one.

_ 3 0

3 + 3 + 1 = 7

7 3 0

Knead to Know is right, that’s ain’t multiplyin’ !

I say 65x2 = 130 and 300x2 = 600. Then 600+130 = 730.

When I see that, I know that 65 + 65 is going to be over 100, and I know that 300 + 300 is 600, so BOOM, I’m in the 700s.

Then, anything like 65+65 or 85+85 is just “in there”.

I still need to process it, though. Some people just fire it off.

I do it pretty much like this, although the method changes (I think) with different numbers.

Joe

I do ((2 * 36) * 10) + 10, but then, I’m odd

Lets multiply, just for kicks…
Multiplying a number by itself is pretty easy, even for large numbers. Just as you can factor 365+365 into 2300 + 260 + 25 (or any other method described here) You can factor the product as well
365
365
= (300+60+5)(300+60+5)
= 300
300 + 6060 + 55 + 2*(30060) + 2(3005) + 2(60*5)
= 90000+3600+25+36000+3000+600=133225

Missed the Edit Window…
Let me explain more if its not clear how to do this in your head…
You are multiplying each digit of the first number by each digit in the second number, adding the appropriate number of zeros, then adding up the results. The first three terms are easy, because you are just squaring 3, 6, and 5. Then you double each combination possible, 36, 35, and 6*5. Keeping track of the zeros is the hard part, then you have to add 6 numbers together, but they are all nice, neat numbers with lots of zeros.

I look at closest round number (350), and double the two parts I get: 350x2=700 and the remaining 15x2=30, hence 730.

If the problem were something like 392+392, I’d round up (400x2=800) and then subtract what’s left (8x2=16), coming up with 784.

I use radcon math - I will round the initial numbers to something I find convenient to manipulate: In this case 375. Which works out to 300 + 300 + 150 = 750. Then just subtract the amount I rounded by - 20, to get 730.

Of course, that’s only because I needed an exact answer. For most uses, I’d find 750 useful enough for rough calculations.

Twice 36 is 72, so twice 360 is 720

5+5 is 10

720+10 = 730

I did something very similar to InvisibleWombat’s first solution, although I rounded each instance of 365 up to 400, added them together (or multiplied 400x2, which gets the same result when using numbers of equal value) to get 800, then doubled 35 (400-365) to get 70, which I then subtracted from 800 to get 730.

I’ve said it before (although not in this arena): you want to learn how to do math quickly in your head, you work at a high school concessions counter. There’s no pressure like the kind experienced when a high school football fan orders three hot dogs, two Butterfingers and a large Coke, and he wants exact change back from his \$10 bill.

Doubling numbers is easy, so twice 36 is 72, which gives you 720, plus 10.

This is the way I did it in my head.

300 + 300 = 600
60 + 60 = 120
5 + 5 = 10

600+120+10=730

If we’re talking addition, put me down for

360+360 = 720
5+5=10
730