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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

WARNING: THIS WAY TO DO IT IS ALL BACKWARDS BUT IT WORKS.

Wanna easy way to do 92 minus 46 in your head??

6 minus 2 is 4, and now make the 4 a 6 instead because 4 + 6 is 10.

So the answer is 46.

Here's another one:

Let's do 81 minus 27.

7 minus 1 is 6, so make the 6 a 4 instead because 6 + 4 is 10.

So the answer is 54.

**igloo** **myrtilles** **fourmis**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Here's another one:

Let's do 44 minus 22.

This one is easy, you don't have to turn it around.

4 minus 2 is 2, so answer is 22.

**igloo** **myrtilles** **fourmis**

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Okay, here's another one.

A hard kind.

What is 41 minus 29 ?

9 minus 1 is 8, so make the 8 a 2 because 8 + 2 is 10.

So the answer is either 2, 12, 22, or 32.

What do you think it is??

Well between 29 and 41 is the thirtys, and the thirtys is about ten numbers.

From 30 to 40, there are 11 numbers.

Anyway 29 is just smaller than 30 and 41 is just larger than 39 so the answer is the 12 answer.

**igloo** **myrtilles** **fourmis**

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

i always do my subtraction in a similar way to that

for example: 123-78

the first two digits (right to left) are 3-8, 8-3 is 5, so i have to take 5 away from 10, which is 5, so the last digit is 5

the next two digits are 2-7, but i had to go below 0 before, so its now 2-8, 8-2 = 6, 10-6 is 4, so the next digit is 4

then lastly we have 1-0, but i had to go below 0 before, so its now 1-1 = 0.

so the answer is 123-78 = 45

----

notice the way i use the carry digit underneath with the small ones like you would in addition by hand on paper.

the bits in red i would do in my head, only writing the black bits (apart from the 0, which i would normally not write)

*Last edited by luca-deltodesco (2006-12-12 09:50:33)*

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The End Of All Things To Come.

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**Ricky****Moderator**- Registered: 2005-12-04
- Posts: 3,791

Sorry to go a little off topic but I just remembered this trick when I read this post:

98 ÷ 49

Cancel out the 9's leaves:

8 ÷ 4 = 2

Thus, 98 ÷ 49 = 2

"In the real world, this would be a problem. But in mathematics, we can just define a place where this problem doesn't exist. So we'll go ahead and do that now..."

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Luca, I love it!! Very sweet that you already did it this way, so awesome!!

And Ricky, Hi Ricky!!

So Luca, how old were you when you figured that method out?? or was it taught to you??

**igloo** **myrtilles** **fourmis**

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**luca-deltodesco****Member**- Registered: 2006-05-05
- Posts: 1,470

John E. Franklin wrote:

Luca, I love it!! Very sweet that you already did it this way, so awesome!!

And Ricky, Hi Ricky!!

So Luca, how old were you when you figured that method out?? or was it taught to you??

i was always taught the carry the 10 sortof method, but i always found it confusing and harder, and i came up with this method myself while i was in early primary school, and since then i havnt found a better method

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

That's a very interesting way of subtracting. The traditional way is to carry a ten from the left if you need a bigger number, but your way moves a ten from right to left so that the number being subtracted gets smaller. Both work of course, but the top one if more well-known.

I think I like your way better though. When I had a problem such as 304-57, for example, then I'd get really confused because I'd want to carry a ten over from the next column, but the next column wouldn't have any. So then I'd need to carry over from the hundreds and then use one of the tens that I'd just carried and carry it over again and my work would have lots of scribbles all over it.

But your way would have made problems like that much easier to deal with. Well done. You've converted me into a bottom-adder. (Better name suggestions welcome )

To Ricky, I was reminded of something similar to your thing when I read John's post, but before I read yours.

19/95

Cancel the 9's: 1/5

Great minds and all that.

Why did the vector cross the road?

It wanted to be normal.

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

something usefull when handling money. When giving change you are usually required to subtract varying amounts from nice round numbers such as 2000, 1000, 500 or 100 when doing this, a trick that seems to work for me is to look at the end of the number you are subtracting, and add the first digit that produces 10, after that, its 9 all the way, untill you get to the last, where it becomes one less.

Take a look at this

500000000000000

249580309345985

250419690654015

On top is a nice round number. Below is a number subtracted from it and beneath that is the difference. Note the last digits of the bottom two rows add up to 10, but the rest all add up to 9 except for the first which add up to one less then the last digit at the top left.

However, when you subtract a number that ends in zero, you need to keep writing zero's until you get to a non zero number, then apply the same process for instance

7000000

2346600

first digit is 0, write 0, move to the next, next digit also zero, move to the next, next digit is 6 write a 4 to get 10, all the remaining digits add up to 9 except the last which adds to 1 less then the top number.

And you can see:

7000000

2346600

4653400

note this only works with numbers like 9000, 6000, 20000, 50 and so on. Basicly single digits followed by a bunch of zeros.

It makes sense if you think about how borrowing works when you subtract from a line of zero's.

*Last edited by mikau (2006-12-12 18:04:44)*

A logarithm is just a misspelled algorithm.

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

When subtracting with numbers, I mainly just find the difference between the two numbers I am using. I have different methods for 3 or more, however.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Um, that's just the definition of subtracting things. There's no reason why you'd do it any other way. If you mean you do it all in one go, then you still actually do the subtracting units with a ten carried if needed and then subtracting tens, it's just that it's in your head and quickly.

Why did the vector cross the road?

It wanted to be normal.

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,664

mikau wrote:

It makes sense if you think about how borrowing works when you subtract from a line of zero's.

Indeed!

Instead of:

7000000

2346600

Imagine:

6999999

2346600

4653399

Then add 1:

4653400

But I agree, the simple rule of "first non-zero is out of 10, rest out of 9" is very usable.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

Gracias!

A logarithm is just a misspelled algorithm.

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

I hate that borrowing rule. Takes a bit long in my opinion, I stick with my original statement.

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

Devanté - you still havn't explained your method however.

On-topic:

When I was in primary school, sometimes we were made to show the borrowing thing. I HATED when we had to do it. If I've understood this topic correctly, I think I'm doing it the same way you guys. It just seems much more obvious to me.

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**Toast****Real Member**- Registered: 2006-10-08
- Posts: 1,321

Ricky wrote:

Sorry to go a little off topic but I just remembered this trick when I read this post:

98 ÷ 49

Cancel out the 9's leaves:

8 ÷ 4 = 2

Thus, 98 ÷ 49 = 2

Can you please explain further how this works, because I've tested variations such as 29/92 and 95/39 and they don't work...

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**mikau****Member**- Registered: 2005-08-22
- Posts: 1,504

I think that trick Ricky used is meant to be a joke. If not then do explain!

A logarithm is just a misspelled algorithm.

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

mathsyperson wrote:

all in one go

If you mean that for instance I take 456-123 and just count on from 123 to get to 456, then yes, that is what I do.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Seriously? You'd start at 123 and count until you got to 456? That would take you ages and be fairly pointless, considering the triviality of the sum. I'm probably misunderstanding you. Any other way though, and you'd have to do it in more than one step.

Why did the vector cross the road?

It wanted to be normal.

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**Toast****Real Member**- Registered: 2006-10-08
- Posts: 1,321

For simple sums like 73-36, to find the difference I often get lazy with the standard methods and subtract in parts. I would find 70-40 then add 3 and 4.

I know I really should do it the proper way, it's becoming a bad habit now.

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

mathsyperson wrote:

Seriously? You'd start at 123 and count until you got to 456? That would take you ages and be fairly pointless, considering the triviality of the sum. I'm probably misunderstanding you. Any other way though, and you'd have to do it in more than one step.

A bit like number lines. For 456-123, I would do: 123 + 300 + 33.

Hard to explain.

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**Patrick****Real Member**- Registered: 2006-02-24
- Posts: 1,005

Devanté wrote:

mathsyperson wrote:A bit like number lines. For 456-123, I would do: 123 + 300 + 33.

Hard to explain.

Now I think I get it to give another example:

521-214

you'd do:

214+300+7= 521

so the difference is 307

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

Yep, that's what I'd do.

Another example;

12253-591

=591+10000+1500+162

Occasionally I might do it a different way. But I have been able to tackle every subtraction problem so far with this method.

For 12253-591, rather than using my method I would just do:

(12253-600)+9

= 11662.

*Last edited by Devanté (2006-12-17 19:11:57)*

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**John E. Franklin****Member**- Registered: 2005-08-29
- Posts: 3,588

Let me try an example that combines both luca and mikau knowledge.

12345

- 6789

______

5 from 9 is 4, swap for 6 due to 10 sum.

4 from 8 is 4, swap for 5 due to 9 sum.

3 from 7 is 4, swap for 5 due to 9 sum.

2 from 6 is 4, swap for 5 due to 9 sum.

1 minus 1 is 0, we are done, based on luca.

So answer is 05556.

**igloo** **myrtilles** **fourmis**

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**Devantè****Real Member**- Registered: 2006-07-14
- Posts: 6,400

12345-6789

= (+6000)-444

= 5556

Using my method this would only take a second or two...

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