math help

[Zac'sbabygirl]

hey guys can someone help with my hw. I have to add the numbers 1 through 499 togather but he wants us to find a simple way to do it

[pocketsempty]

hey guys can someone help with my hw. I have to add the numbers 1 through 499 togather but he wants us to find a simple way to do it


Well, numbers 1-10 equals 55, 11-20 equals 155, 21-30 equals 255. Ok there is a pattern. Do you see it?
Split 100 into 11 parts. Part 1 is 1-10 equals 55, Part 2 is 11-20 equals 155, Part 3 is 21-30 equals 255 etc. So you automatically know Part 4 will equal 355, Part 5 will equal 455 etc.
You will not need to add up all the numbers up now b/c each part will have '55 at the end just place the numbers 1 thru 10 in front of the 11 parts respectively. Now add up those new numbers (55+155+255,etc.) should equal 6105. Ok now, let me think...
The pattern is 1,2,3,4,5,6,etc in front of 55. Ok so you are going up to 490 right? 49 is the last number to put in front of '55. Now to skip all that crazy addition, relax.
You know the total for Parts 1 thru 11 (Part 1 thru 11 is now considered Sub-Division 1) is 6105, but wait that has 11 parts b/c of the numbers 1-10. (There are 10 Parts for every sub-division.). This Part is really the "zero section" (055). Take the "zero section" and subtract it from the Sub-division 1 Total (6105-55=6050). But remember 6105 is your total for sub-division 1
Now use 6050 as your "new" ending. You may ask why...Each Sub-division has 10 parts b/b there is no "zero section" anymore. Wait forgot to tell you Sub-division 1(parts 1-11) represents the numbers 1-110. For numbers 111-210 it will be Sub-Division 2. Remember 6050 is your "ending" just 1 in front of 6050 so it becomes 16050. 16050 is the Total for Sub-Division 2. Sub-Division 3 just place 2 into for 6050.(26050) Continue by placing numbers 3 and 4 into of Sub-Division 4 and 5. (36050 and 46050) should be the totals for Sub-Division 4 and 5.
Add up Sub-Division 1 thru 5 together. (Total is )
Wait not done b/c Sub-Division 5 are numbers 411-510. We just want numbers 411-490. Numbers 491 thru 500 equals 4955 and numbers 501 thru 510 equals 5055. (4955+5055=10010) Take the total for the Sub-Division and subtract 10010 from it. (130305 - 10010= 120295)

Question: Add numbers 1 thru 490 together to get answer.
The Answer: is 120,295.

Sry it took so long to explain. I couldn't figure out a way to explain it in a simple way. It went alot faster in my head. lol. Hopefully its the right answer but I'm positive it is by "my math".
PM me if you have questions or need me to explain it better.

gl

[pocketsempty]

hey guys can someone help with my hw. I have to add the numbers 1 through 499 togather but he wants us to find a simple way to do it


A much easier way.
I think it was my boy Archimedes helped make this formula.
n(n+1)/2.
n represents all the numbers you are using.(490)
490(490+1)/2 = 120,295
Its that simple!!!!

Another easy way, 1+490=491, 2+489=491, 3+488=491, etc. How many pairs will there be?(490/2= 245 pairs). Take 245 and multiply it by 491. What do you get? 120,295.
Many ways to solve the problem.

[ElPiedra]

A much easier way.
I think it was my boy Archimedes helped make this formula.
n(n+1)/2.

Ah, that good old formula, saved me a lot of paper space...

[jayc]

asked for 499 so answer would be 124,750

[pocketsempty]

asked for 499 so answer would be 124,750

thx pal. Totally messed this one up. lol. nice catch.

[cupcake]

490(490+1)/2 = 120,295

My dad explained to me so many stuff, I only got that part xDxD

[KawaiiSky]

good luck! XD thats confusing!