# Multiply Like A Pro

I’m going to teach you how to multiply any two numbers between 1 and 100, in your head, as quickly as it takes to input them in a calculator. And it’s dead simple.

(It does require some memorization though)

So, I figured out this technique – probably somebody else figured it out before me, but I’ve never heard of it before – that reduces the task of multiplying any two numbers together into some addition, some subtraction, and one division by two. It’s pretty simple. In fact, it all just boils down to one equation: If your eyes glazed over at the above equation, be strong! Do the FOIL method and check it out for yourself. This is about as hard as the math gets.

Cool! What does that equation mean, though? Well, any two numbers (we’ll call them ‘a’ and ‘b’) can be rewritten in terms of ‘x’ and ‘n’ —  That is, we say that n is half of the difference between our numbers a and b, and that x is the number halfway between a and b. Now, b = x – n and a = x+n! Therefore, for any a and b, We’re going to run through these formulas using some example numbers, to keep you following along, before we talk about how to solve x2 – n2. Let’s take the following two sets of numbers:

23 x 41
49 x 74

These numbers are big enough that most people wouldn’t even bother try to multiply them in their heads. Is it easier with this new method? (Yes.)

First, find n, half of the difference between the two numbers…

23 x 41:
41 – 23 = 18
n = (18 / 2) = 9

74 x 49:
74 – 49 = 25
n = (25 / 2) = 12.5

So the halfway point between 23 and 41 is

23+9 = 32

And the halfway point between 49 and 74 is

49 + 12.5 = 61.5

This means that…

23 x 41 = 322 – 92
49 x 74 = 61.52 – 12.52

But what are 61.52 , 12.52 , 322 and 92?

This is the hard part of the method. I don’t expect you to be able to solve 61.52 in your head. Instead, you’re going to have to memorize 100 squares – the square of every integer from 0 to 100. Yeah.

It’s a lot of work, but it’s entirely doable. There’s only 100 numbers, and you probably already know the squares of, like, 30 of them. If you’re thinking of giving up now, just think of all the sexy mathematician ladies (or dudes) you’ll be picking up at parties once you’ve memorized these and can multiply in a second!

If sexy mathematician ladies (or dudes) aren’t enough to make you memorize all 100 squares, though, there are tricks you can use to calculate squares very quickly in your head. I’m not going to talk about them here. I’m not supporting your laziness. But if you’re interested, you should read up on Vedic Mathematics, it’s got some pretty cool stuff about mental algebra.

But seriously, go the hardcore route, memorize this table. If you do so, you’ll already know the squares of all those integers-plus-one-half like 61.52 (but more on that later):

x x2 x x2 x x2 x x2
0 0 25 625 50 2500 75 5625
1 1 26 676 51 2601 76 5776
2 4 27 729 52 2704 77 5929
3 9 28 784 53 2809 78 6084
4 16 29 841 54 2916 79 6241
5 25 30 900 55 3025 80 6400
6 36 31 961 56 3136 81 6561
7 49 32 1024 57 3249 82 6724
8 64 33 1089 58 3364 83 6889
9 81 34 1156 59 3481 84 7056
10 100 35 1225 60 3600 85 7225
11 121 36 1296 61 3721 86 7396
12 144 37 1369 62 3844 87 7569
13 169 38 1444 63 3969 88 7744
14 196 39 1521 64 4096 89 7921
15 225 40 1600 65 4225 90 8100
16 256 41 1681 66 4356 91 8281
17 289 42 1764 67 4489 92 8464
18 324 43 1849 68 4624 93 8649
19 361 44 1936 69 4761 94 8836
20 400 45 2025 70 4900 95 9025
21 441 46 2116 71 5041 96 9216
22 484 47 2209 72 5184 97 9409
23 529 48 2304 73 5329 98 9604
24 576 49 2401 74 5476 99 9801

Now, here’s a cool trick: even though we need to know integers-plus-one-half like 61.5 for this method, we already know them if we know the square of that number’s closest integer (rounded down). This is because:

(x+0.5)2
= (x+0.5)(x+0.5)
= x2 + x + 0.25

And for bonus points, we can ignore that “+ 0.25” completely! It’s just going to be subtracted out by the second half of our equation! Forget about it! Therefore…

61.52 = 612 + 61 = 3721 + 61 = 3782
12.52 = 122 + 12 = 144 + 12 = 156

Now, it should be easy for you solve those two problems.

23 x 41 = 322 – 92 = 1024 – 81 = 943
49 x 74 = 61.52 – 12.52 = (3721 + 61) – (144 + 12) = 3782 – 156 = 3626

And there you go! To recap this method:

• Find half of the difference between the two numbers you’re trying to multiply
• Add that to the smaller number to get the midpoint between your two numbers
• Midpoint squared minus half-of-difference squared equals your result!
• If the number is an integer-plus-one-half, remember that (x+0.5)2 = x2 + x (for our purposes)

There’s no reason you can’t use this method to multiply two numbers over 100, either! You just have to memorize your squares tables up to the highest number you’re willing to multiply.

I hope you get tons of use out of this and impress all the sexy mathematician ladies (or dudes)!

## 2 thoughts on “Multiply Like A Pro”

1. luis

And that’s why I always use my phone!

2. luis

This trick it’s hard for me, but is a very good exercise to my brain.