Math Tricks

**caveman1917** · 01-09-2012, 09:04 AM

Originally Posted by grapes

I think Coelacanth was talking about the complex numbers as well.

Ah yes, i see, that makes sense

That's what you get for not reading the linked material...

**grapes** · 02-03-2012, 10:16 AM

Originally Posted by grapes

I got a better one. Start with

3 x 7 = 3 x 7

Using the commutative law

3 x 3 = 7 x 7

9 = 49

Subtracting 9s from both sides

0 = 4

OK, since you're all OK with that, here's one of the best ones:

To reduce the fraction

, just cancel the 6s.

**Mike_A** · 04-06-2012, 10:55 AM

I still remember when I was explaining a math problem to a classmate while the teacher was explaining something on the chalkboard. He apparently thought that I wasn't paying attention and asked me the answer. I immediately solved it in my head and that's when I realized my strong point.
I've always enjoyed doing math in the head. I think it helps keeping the mind sharp. There's so many ways that you can go in doing this.
This is how I look at it:
37 x 43 =(30 + 7)(40 + 3)
Using (A+B)(C+D)=AC+AD+BC+BD
30 x 40 = 1200
30 x 3 = 90
The sum of the two is 1290.
40 x 7 = 280
1290 + 280 = 1490 + 80 = 1570
7 x 3 = 21
1570 + 21 = 1591
Our teachers taught us to work from right to left. When it comes to doing it in the head, I think it's easier to work from left to right.
There are some cases where you can use algebra formulas to help do it in the head.
A(B+C) = AB + AC
(A + B) ^2 = A^2 + 2AB + B^2
And so on...

**grapes** · 04-20-2012, 05:43 AM

Originally Posted by Mike_A

I've always enjoyed doing math in the head. I think it helps keeping the mind sharp. There's so many ways that you can go in doing this.
This is how I look at it:
37 x 43 =(30 + 7)(40 + 3)
Using (A+B)(C+D)=AC+AD+BC+BD
30 x 40 = 1200

That's a good approach in general. Most people find it easier to keep track of things that way, by doing the larger values first when doing it in their head.

In that particular example, there is a short cut:
37 x 43 = (40-3)(40+3)
Which is the difference of two squares:
40^2 - 3^2 = 1600 - 9 = 1591
Same answer of course, and you have to subtract, but a lot less to keep track of.

**Mike_A** · 04-20-2012, 08:30 AM

Originally Posted by grapes

That's a good approach in general. Most people find it easier to keep track of things that way, by doing the larger values first when doing it in their head.

In that particular example, there is a short cut:
37 x 43 = (40-3)(40+3)
Which is the difference of two squares:
40^2 - 3^2 = 1600 - 9 = 1591
Same answer of course, and you have to subtract, but a lot less to keep track of.

Yes, I also do it that way (depending on which way feels like it will be easiest). It also helps to visualize the numbers as if they're floating in front of you.

**grapes** · 04-20-2012, 08:57 AM

The difference of two squares trick is one reason to memorize, or be familiar with, the squares.

If two integers are an even value apart, their product will always be the difference of two squares:
45 x 37 = (41+4)(41-4) = 41^2 - 4^2
Or you can do tricks like:
45 x 37 = 45 x 35 + 2(45) = (40+5)(40-5) + 2(45) = 40^2 - 5^2 + 90 = 1600 + 65