addition

[hanuman_2000]

Hello Teachers!

 

 

How to add number from 21+22+............+30?

 

IS there any simolest method?

 

 

Thanks.

[jordan]

I assume you mean simplest?

 

If so, probably just realize that they average to 25.5 and there are ten so it's 255.

[hanuman_2000]

Hello teachers!

 

I meany really what you assumes.Sorry for typing mistake.

 

This question is specially for a student in 4th standard and as you may know that at this stage .they really don noy know about average.

 

If there is any other simplest way?

 

Thanks.

[Deified]

You could use Gauss's method: 21+30=51

22+29=51

23+28=51 etc. And since there are five pairs, 51*5=255

Or, in formulaic terms: Let x represent the sum of the first and last values, let y represent the number of values

 

x*n/2

 

I believe this works, I just derived the formula now.

[Primarygun]

(First term + last term)x (last term-first term+1)/2

[Primarygun]

For interval is 1.

[Deified]

Yes that is a more elegant formula, primarygun.

[Mart]

How to add number from 21+22+............+30?

Get some paper and a pencil.

Kid first needs to be able to add 1 + 2 + 3 + 4 + . . . . + 10

Start with 1 + 2 = ?

Continue with 1 + 2 + 3 = ?

A triangle of dots can help to visualise the process.

*

* *

* * *

* * * *

When the kid feels comfortable with that they may spot the connection with the original problem 21 = 21 -20 = 1 , 22 = 22 - 20 = 3

If not spot it for them but beware of rushing them

[bloodhound]

the sum of 1 to n can be written explicitely as n(n+1)/2..... but ur looking for some from 21 + .... +30

 

now think about it...

 

and please stop with the teachers thing

[Panic]

bloodhound if some one is having a problem with general math what make you think they will understand algebra???? let's take it down a notch!

 

like mart said... here is a good visual of what he said 21+22+23+...+30 =

(20+1)+

(20+2)+

(20+3)+

(20+4)+

(20+5)+

(20+6)+

(20+7)+

(20+8)+

(20+9)+

(20+10)

20x10 + (1+2+3+4+5+6+7+8+9+10)

 

200 + (1+2+3+4+5+6+7+8+9+10)

on thing to remember is that

(1+2+3+4+5) = 15

6+7+8+9 = 30

so (1+2+3+...+10) = 55

 

200+(55)=255

[Dave]

The way I think about it is this (which is equivalent to what everyone else is saying, more or less):

 

20 + 21 + 22 + ... + 30 = (1 + 2 + 3 + ... + 30) - (1 + 2 + ... + 19)

 

So if you have a way for adding up the first however many numbers you choose, then simply using that a couple of times will give you the answer.

[fuhrerkeebs]

Why not use that famous (I think it's famous) formula Gauss came up with to sum all of the number from 1 to x, such that it equals (x)(x-1)/2, and if you want to sum on the interval a to b, use ((b)(b-1)-(a)(a-1))/2. There's a very nice, intuitive way to figure out the formula for the young kids which I'm sure is easy to find after a quick google.

 

[edit]Sorry, I just noticed that bloodhound pretty much posted the same thing.

[Mart]

Why not use that famous (I think it's famous) formula Gauss came up with to sum all of the number from 1 to x' date=' such that it equals (x)(x-1)/2, and if you want to sum on the interval a to b, use ((b)(b-1)-(a)(a-1))/2. There's a very nice, intuitive way to figure out the formula for the young kids which I'm sure is easy to find after a quick google.

 

[edit']Sorry, I just noticed that bloodhound pretty much posted the same thing.

We're all trying to find some way to explain this to hanuman_2000. he needs to feed back to us which explanations suit him.