Sunday, June 14, 2009

15 x 15

I'm not very good at multiplying in my head. I only gave up yesterday because it was taking far too long.

First I imagined the number 15, like this, a 1 and a 5. Then I imagined another number 15 directly below it, that is, the 1 under the 1, and the 5 under the 5.

Then I imagined a multiplication sign to the left of the bottom 1. No, I'm only joking. I didn't need to imagine that.

Then I proceeded with my calculation. 5 times 5 is 25. Put down the 5 and carry 2. That's 2 things to remember. The 2 is placed above an imaginary line which I also thought I didn't need to imagine. It would, however, have helped. Don't forget, I was listening to the largo movement of the Shostakovich Sonata for Cello and Piano in D minor at the same time.

Next, I calculated 1 times 5. An easy one, the answer is 5. Then I had to remember to add on the 2. That makes 7. This is where it gets kind of tricky. Where do you put the 7? And can you now forget about the 2? First things first. The 7 goes next to the 5. Which was where? Somewhere in the middle of my head. And the 7 goes next to that on the left. So I have 75. This represents 75 cents. So far so good. And yes, you can now forget about the 2.

Now it gets a little bit more musical. Rachel is playing beautifully, and every now and then her bow squeaks and there is a little glint of light playing over the front of her cello. I know too that her plait, which none of us can yet see, will be dyed red. 1 times 5 is 5. Put the 5 under the ......waaah! This is where I said to myself, You fool etc.

4 comments:

Andy Craig Photography said...

I am fascinated by the way different people visualise numbers and use these visuals to meorise temporarily the necessary parts.

You visualised the sum as you would have written it on a piece of paper. I see the problem as a set of logical steps with no visual equivalent; which is odd as I think I am quite a visual thinker normally (and I am rubbish at mental arithmetic).

To me, 15x15 is the sum of (10x15) + (5x15)

10x15 is easy and 5x15 is simply half that. Then add the two together.

Then check on a calculator!

A

Lynn Webber said...

Oh wow that's so clever! I knew 10x15 was easy but I thought 5x15 was hard. It never occurred to me that it was half that. Logic rules !

I have a rather childish way of adding up as well. I used to have to add up long columns of figures when doing our business accounts. I found the fastest way for me was to think of each digit as a set of dots,( eg 7 was a row of 4 dots plus a row of 3 dots ) and count them up very rapidly. For me it was quicker and more accurate ( usually) than using a calculator. I used to assure myself that it was kind of like the way Chinese people use an abacus.

Allan Webber said...

What heartache there is in numbers and their ways. I use 10x20 +5x5 to get the answer.

When young ( some time ago) I invented a means for all numbers multiplied by themeselves.

Bring one of them to the nearest value of 10 (15+5=20) and remember the number change(5).
alter your number by the same amount in the opposite direction(15-5=10)
Multiply the increased and the decreased number (10 x20=200).
Add the square of the number change (5x5=25) getting 225.

Lynn Webber said...

This maths is all very well if you want accuracy. My estimation of 15x15 to be about $2.80 resulted in mum giving me $3.00 and not asking for any change. And then she paid for my coffee because she hadn't repaid me for some milk I bought her last weekend. The milk only cost me $2.45, and the coffee was$3.00. So I did OK there as well. Mind you, she hasn't paid me for that postage.....