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
Step 1: 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
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
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
Step 5: Let's Try Another Problem
Say we have 51 x 42.
The larger the number, the more complex the math gets, but it's still well within the abilities of a human mind.
Your best bet for this problem is to go with 51 x (40 + 2)
51 x 40 is the same as 51 x 10 x 4
51 x 10 = 510, then multiply that by 4, which gives you 2040
we have one final step, which is to add 51 x 2, which equals 102.
This means, 2040 + 102 = 2142
Step 6: Numbers Close to 100
What if we have 99 x 99. It would be rather inefficient to try to multiply a number all the way up to 99.
So instead of doing the normal method of multiplying by 10, and then multiplying up to higher numbers, we can just multiply by 100.
99 x 99 = 99 x (100 - 1)
99 x 100 = 9900, and 99 x 1 = 99, so subtract the two, giving you
9900 - 99 = 9801
Step 7: Practice Practice Practice
Don't expect to be doing ridiculously fast mental math on day 1, just practice when you get a chance. If your at the grocery and want to find out how much 5 of the same item would cost, give it a try. Or if you see the score of a sports game, you can also give it a try.
Hope this helps you all!