How to quickly multiply numbers between 1-100

First instructable, yay!

In this instructable, I will teach you an easy method I created for multiplying numbers between 1 and 100 with relative ease.

All I ask is that you have a decent understanding of math
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Step 1: Pick two numbers

Picture of Pick two numbers
The first part of this trick requires two numbers. So, pick any two. The trick works a bit better when at least one number is 10 or more. So, for this instructable, I will choose 15 x 19.

Step 2: Dissect the numbers

We can break the equation 19 x 15 down into

19 x (10 + ((1/2) 10))


15 x (20 - 1)

Now the first one might seem a little harder, but it's really not. If you have a five in the equation, you can simply multiply a number by 10 (which is simple, just add a 0 at the end), and then take half of it. So 19 x 5 = half of 19 x 10.

That means that 19 x 5 = (1/2) 190

But for now, let's just stick with the second equation because it is simpler.

Step 3: Multiply out

Picture of Multiply out
Okay, so we have 15 x (20 - 1)

The distributive property states that we can distribute the 15 to the other numbers, meaning we have (15 x 20) - (15 x 1)

I am sorry for these really short pages, btw.

Step 4: Do some more simple math

Picture of Do some more simple math
15 x 20 is the same as doubling 15 x 10.

Since multiplication has the commutative property, it doesn't matter what order we multiply the numbers in. 15 x 10 x 2 is exactly the same as 10 x 2 x 15, and 2 x 15 x 10, using that rule, we can find that:

2 x (15 x 10) = 2 x 150 = 300

and since we still have to subtract 15 x 1 (which equals 15), we just subtract 15 from 300, giving us 285
This is actually how I've always multiplied in my head.
Vedic math is simpler. Say you want to multiply 21 and 23.


There are the 3 steps:

a) Multiply vertically on the left: 2 x 2 = 4.
This gives the first figure of the answer.
b) Multiply diagonally and add: 2 x 3 + 1 x 2 = 8
This gives the middle figure.
c) Multiply vertically on the right: 1 x 3 = 3
This gives the last figure of the answer.

Final answer = 483

Works for any two 2 digit numbers. Sometime you have to carry numbers but its still easy. You know how you read about people who can multiply huge numbers? This is how they do it.
Gotta say I currently use rapid mental application of the distributive property, however I just started reading some concepts from vedic math, which is very fascinating.
Actually, people who learn to multiply huge numbers usually start by memorizing the multiplication tables up to 100x100.
The other way is easier for me. It's basically just two steps. 23*20=460, 460+23=483
Wow that's cool too. Sometimes the distributive property, used in this instructable, still amazes me.