Multiplication Tips: Adding X by Z + Tricks for 10

[barthayn]

Are there any tricks other then adding X by Z in the multiplication chart? Like the one for ten. When multiplying a number by ten all you do is add a zero.

 

[rock.freak667]

You want something like http://en.wikipedia.org/wiki/Swami_Bharati_Krishna_Tirtha%27s_Vedic_mathematics"

 

[symbolipoint]

Are there any tricks other then adding X by Z in the multiplication chart? Like the one for ten. When multiplying a number by ten all you do is add a zero.

What?

Multiplication is not adding X by Y. Multiplication is repeated addition of a specific number. What is best is to know what multiplication means, and next, to determine the common multiplication basic facts for whole numbers zero through twelve, and then MEMORIZE them. This takes practice as also should rely on constructing a multiplication chart, and become familiar with this chart. As you examine this chart, you should look for patterns.

You noticed a pattern for multiplication by 10. You should also find a feature of multiples of 5. Any whole number which has a final digit of 0 or 5 is a multiple of 5. Keep checking your facts and look for other patterns.

 

[Mentallic]

Such patterns as:
multiplication by 2, the last digit is always even
multiplication by 3, the sum of all the digits is also a multiple of 3
multiplication by 5, last digit ends in 0 or 5
multiplication by 6, the last digit is always even and sum of digits is multiple of 3
multiplication by 9, sum of digits is multiple of 9

etc.

See if you can find others

 

[barthayn]

All I am asking for is ways to make mental multiplication easier. For example: 11 x 13 = ? You move 1 and 3 a part to make this : 1_3. Then you add 1+3 to get 4. Then put the sum, 4, in between to get 143. Therefore your answer is 143. Or the fives. All you do is divide by 2 then multiply by 10. For example 5 / 2 = 2.5. 2.5 x 10 = 25. Therefore 5 x 5, or 5^2, is 25.

 

[Count Iblis]

https://www.physicsforums.com/showthread.php?t=114789

 

[Pengwuino]

A common trick for multiplying two numbers together is multiplying sums of numbers and taking advantage of what we have memorized off say, the multiplication table we were all taught back in the day. For example: 11 x 13 = (10 + 1)*13 = 130 + 13 = 149. How about 18 x 15 = 18 * (10 + 5) = 180 + 90

 

[berkeman]

Cool thread, Count. Thanks.

barthayn -- check out this book. I found it a fun read, and very helpful for mental math:

"Rapid Math Tricks and Tips" by Julius

https://www.amazon.com/dp/0471575631/?tag=pfamazon01-20

 

[Mentallic]

What I've noticed for myself is that such math "tricks" that help speed up mental arithmetic usually have some odd unconventional reason for why they work. Because of this, I never managed to remember the techniques for long and would only be able to use them once or twice for fun.

Unless you need this for competitions or you multiply larger numbers mentally very often (multiple times a day), then like myself, you would probably find it more advantageous to use common understandable procedural methods such as pengwuino has used.

 

[Count Iblis]

It could be that our brians actually perform fast integer arithmetic all the time, but that we don't have access to these facilities, see here:

http://www.centreforthemind.com/publications/IntegerArithmetic.cfm

So, it is like using a very fast pc on which some software is installed but no software to do simple arithmetic. You can then still do artihmetic in a very clumsy way, e.g. by hijacking your word processor and using word count facilities to add up numbers.