Education-Did you learn casting out nines in arithmatic?

[Hank77]

I never learned this and neither did my kids, but my grandson is home schooled in an online Christian program and this is where we learned this really cool and easy way to check your answers to addition, multiplication, division. It can be used for subtraction as well but isn't as easy or shorter/quicker.
It's called casting out 9s.

If anyone is interested please post and I will show you how to do it.

 

[akmom]

Yep! I learned that back in my homeschool/private school days. Would that be the BEKA curriculum? Pretty cool trick.

 

[Hieronymus]

I never learned this and neither did my kids, but my grandson is home schooled in an online Christian program and this is where we learned this really cool and easy way to check your answers to addition, multiplication, division. It can be used for subtraction as well but isn't as easy or shorter/quicker.
It's called casting out 9s.

If anyone is interested please post and I will show you how to do it.

I don't think i know what you mean.
I'm curious what it is.

 

[akmom]

Add all the digits in a number together. Keep doing it until you get a single digit.

So if you had 5,280 then you would add it all up 5+2+8+0 = 15, so keep going 1+5 = 6.
You don't even have to cast out nines. But if you do, you get the same answer quicker. Try this:

1,392 is 1+3+9+2 = 15, so keep going:
15 is 1+5 = 6.
If you go through and cross out all the 9's, you'll get the same answer:
1,392 is 1+3+2 = 6.

So why would you do any of this? Well, it's kind of a nifty way to double-check your math if you are doing it by hand.

5,280
+1,760
7,040

Add up all the digits in the above problem until you get a single digit:

5+2+8+0 = 15 ... 6
1+7+6+0 = 14 ... 5
7+0+4+0 = 11 ... 2

Now 6+5 should equal 2:

6+5 = 11, then 1+1 = 2

Basically add up all the digits on one side of the equation and you should get the same answer on the other side. It works. Casting out the 9's makes it faster. It's just the way our Base 10 math system works. In any other number system, it would work with whatever the highest digit was in that system. (I'd give binary as an example, but that's kind of silly, because everything obviously equals 1 when you add a bunch of 0's and 1's together.)

 

[grasping the after wind]

I never learned this and neither did my kids, but my grandson is home schooled in an online Christian program and this is where we learned this really cool and easy way to check your answers to addition, multiplication, division. It can be used for subtraction as well but isn't as easy or shorter/quicker.
It's called casting out 9s.

If anyone is interested please post and I will show you how to do it.

I was taught that in grammar school back in the 1960s. Probably fourth grade but I' m not sure it has been a while. I thought it was standard practice like pointing out that when multiplying by nine up to 9X 10 the product's individual numbers will add up to 9 and from 2X9 to 9X9 the first digit will be one less than the number being multiplied by 9.

 

[Hank77]

Yep! I learned that back in my homeschool/private school days. Would that be the BEKA curriculum? Pretty cool trick.

Yep, it's A Beka.

I don't think i know what you mean.
I'm curious what it is.

akmom, explained how it works in addition. It is a method for checking to see if you have gotten the correct answer to a problem.
When it is really helpful is when checking an answer to a long multiplication or division problem.

72962
x 68453
4994467786

1) 72962 - cast out (ignore) the 7 and 2 because they add up to 9, cast out the digit 9, that leaves just the 6 and 2. Add 6+2=8
2) 68453 - cast out as above. 6 and 3, 4 and 5, the leaves 8+3=11, add 1+1=2
3) Add the final digit from each factor. 8+2=10 1+0= 1 This is the single digit number you arrive at.
4) 4994467786 - cast out as above. 9,9. Add 4+4+4+6+7+7+8+6=46, add 4+6=10, 1+0=1

The final single digit from the factors is the same as the final digit from the product, 1. You can be at least 99% sure that your answer is correct. This is much faster, easier, and probably more accurate, depending on how well you divide, than dividing 4994467786 by 72962 to see if the quotient is 68453.

 

[Hieronymus]

Completely new to me.
Thanks for showing me.