im not sure iff this will make sense but theres a patern for every 5 numbers. 1,3,5,7,9 are the first five odd numbers and when u add them up it equals 25. and with 2,4,6,8,10 wen u add them up you get 30. if you keep doing that you get 50 more for each each time. so for odds 11,13,15,17,19 is 75 witch is 50 more than 25. evens is 12,14,16,18,20 witch is 80 also 50 more. but as i kept doing this i found an quicker and easier way. all 5 numbers in the even or odd set have the average of the middle number. 1,3,5,7,9. the average is 5 so all u really have to do instead of add u can multiply the midle number by 5. for odds, 5x5=25 thn 15x5=75 and so on. the middle number is the average so just multipy instead of add. same with evens isnt 6x5=30,thn 2nd set of evens 16x5=80 its the exact same as adding just quicker.for odds you always multiply the digit in the set that has a ones place of 5 like 25 would be for the set 21,23,25,27,29 and multiply by 5. evens is multiply the number in the set that the ones place is a 6 like 26. and multiply it by 5. like in the set 22,24,26,28,30 u multiply 26 by 5 because thats the averaged number. its confusing but it gets u the answer.
i noticed that every set of five even numbers is five more than the odd. Like on the first five odd 1+3+5+7+9=25 and the first five even 2+4+6+8+10=30 which is five more. Which mean that the next five and the next five and so on of each even and odd would have five more for the ven over the odd. So that means that the first five the even are 5 up then the next five the even are up 5 more so they are 10 up then 15,20,25,etc... So to find the answer you find how many groups off five there are and multiply them by five and you will know the difference of the even and the odd.
A couple people have probably already said this, but for every odd number there is an even higher even number. "1 and 2", 2 is even and bigger. "51 and 52", 52 is bigger!
Well I think that we have to listen to mrs. cooper. i don't think we need to add up all of the even and odd counting numbers. for example: 1+3=4 & 2+4=6 1+3+5+7=16 2+4+6+8=20 First the differnce in the summs is- +2 for the even #'s Then, the differnce in the sums is- +4 for the even #'s Somehow we can take this information and find an answer without adding up all of the even or all of the odd numbers. can't we?
If you look at the sum of the even numbers (2+4+...96+98+100) and the sum of the odds (1+3+5+...97+99) and subtract you will have: 2+4+6+...96+98+100 -1+3+5+...95+97+99 And if you subtract the first odd number from the first even you'll get one. The second odd from the second even you'll get one again, so there are fifty subtractions each with a difference of 1. So, one way to get the answer is to multiply 50 times 1. The answer is 50!
16 comments:
is the question asking to subtract the odd count numbers and the even count numbers?
im not sure iff this will make sense but theres a patern for every 5 numbers. 1,3,5,7,9 are the first five odd numbers and when u add them up it equals 25. and with 2,4,6,8,10 wen u add them up you get 30. if you keep doing that you get 50 more for each each time. so for odds 11,13,15,17,19 is 75 witch is 50 more than 25. evens is 12,14,16,18,20 witch is 80 also 50 more. but as i kept doing this i found an quicker and easier way. all 5 numbers in the even or odd set have the average of the middle number. 1,3,5,7,9. the average is 5 so all u really have to do instead of add u can multiply the midle number by 5. for odds, 5x5=25 thn 15x5=75 and so on. the middle number is the average so just multipy instead of add. same with evens isnt 6x5=30,thn 2nd set of evens 16x5=80 its the exact same as adding just quicker.for odds you always multiply the digit in the set that has a ones place of 5 like 25 would be for the set 21,23,25,27,29 and multiply by 5. evens is multiply the number in the set that the ones place is a 6 like 26. and multiply it by 5. like in the set 22,24,26,28,30 u multiply 26 by 5 because thats the averaged number. its confusing but it gets u the answer.
the answer is going to end with an odd number
sum of evens 2 + 4 + 6 + ...98+ 100
sum of odds 1 + 3 + 5 + 97 + 99
Remember...it is asking for the difference of the sums which makes you believe you have to find the sum first. But do you????????????
i noticed that every set of five even numbers is five more than the odd. Like on the first five odd 1+3+5+7+9=25 and the first five even 2+4+6+8+10=30 which is five more. Which mean that the next five and the next five and so on of each even and odd would have five more for the ven over the odd. So that means that the first five the even are 5 up then the next five the even are up 5 more so they are 10 up then 15,20,25,etc... So to find the answer you find how many groups off five there are and multiply them by five and you will know the difference of the even and the odd.
I think that Ben B. said, in extended form, that:
(6+16+26+36+46+...+96)times 5 is equal to the sum of even counting numbers in 101.
I think that both the Bens are right and we just need to do the same pattern to the evens.
what are counting numbers?
A couple people have probably already said this, but for every odd number there is an even higher even number. "1 and 2", 2 is even and bigger. "51 and 52", 52 is bigger!
Counting numbers are the same as Natural Numbers. (Numbers that you count with) Look in your notes or Google it if you are still unsure.
between every pair of numbers (1-2, 3-4) the difference goes up by one. so in the end, you will get the answer.
i think the answer is an even number
Well I think that we have to listen to mrs. cooper. i don't think we need to add up all of the even and odd counting numbers. for example: 1+3=4 & 2+4=6
1+3+5+7=16 2+4+6+8=20
First the differnce in the summs is- +2 for the even #'s
Then, the differnce in the sums is- +4 for the even #'s
Somehow we can take this information and find an answer without adding up all of the even or all of the odd numbers. can't we?
I don't understand the pattern. I understand what Ben is saying but I can't get any further than that...
Oh wait!
I understand what you do and I got pretty far, but it's taking me so long. There must be an easier way to solve it.
If you look at the sum of the even numbers (2+4+...96+98+100)
and the sum of the odds (1+3+5+...97+99) and subtract you will have:
2+4+6+...96+98+100
-1+3+5+...95+97+99
And if you subtract the first odd number from the first even you'll get one. The second odd from the second even you'll get one again, so there are fifty subtractions each with a difference of 1.
So, one way to get the answer is to multiply 50 times 1.
The answer is 50!
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