Math Question

[luckey-lasvegas]

How would you find the sum of the first 50 even numbers?

Ok I can't seem to wrap my head around this 6th grade math question. Could someone please help !

 

[hopefor4]

Even numbers are numbers that can be divided into equal groups. They always end in 0,2,4,6,8. SO you would add all of the numbers between 2 and 50 that are even. 2+4+6+8+10+12+14+16+18+20+22+24+26+28+30+32+34+36+38+40+42+44+46+48+50

I am in Canada, and in grade 6 here we are working on divinding decimals! My son in grade 8 is doing Math that I did in Grade 10 allgebra! It is crazy!

Michelle

 

[katied]

Assuming I understand the question, I would set up a spreadsheet in excel, have a column counting 1 - 50, and have a row counting even numbers. I'd then total the even number column. My total was 2550. I can email to you if you pm me with your personal email, if that helps.

 

[summermac]

That's the long way. But I googled and came up with this:
http://mathforum.org/k12/mathtips/sum.alleven.html

25x26
So the answer should be 650.

But the teacher likely wants it done the long way and then will show the formula trick later on. That always seemed to happen in my math classes growing up.

 

[katied]

Does that add the first 50 (cause I thought to get to 50 even numbers, you had to actually go up to 100?), or only the even numbers in 1 - 50? I guess 6th grade math is too hard for me to understand. Good luck!

 

[summermac]

Oh right, good point. If it's the FIRST 50 even number then it's actually 1-100.

So it'd be 50x51 using that formula I posted above
2550

 

[luckey-lasvegas]

I got 650 too using a calculater but I thought there would be a formula that they were looking for like x+2=50 so you would multiply each side by 1/2 to isolate the x but then the answer would be 25.

 

[jenlynn0808]

There is probably an easier way to do this, but this is how I figures it out. I wrote it out long so you could see how the pairs matched up.

If it is the first 50 even numbers the highest number you would use is 100 (going by even # 100 would be the fiftith # written). So I grouped the rest of the numbers so they would = 100. Then 50 is by itself also.

100 by itself
98 2
96 4
94 6
92 8
90 10
88 12
86 14
84 16
82 18
80 20
78 22
76 24
74 26
72 28
70 30
68 32
66 34
64 36
62 38
60 40
58 42
56 44
54 46
52 48
50 by itself (there isn't a number to match it with)

All the even numbers are written, there are 24 sets of 100, and the 100 and the 50 by themselves. 24x100=2400+150=2550

HTH

ETA-I teach elem., so this is how I would explain it to my fourth graders.

 

[jenlynn0808]

Even numbers are numbers that can be divided into equal groups. They always end in 0,2,4,6,8. SO you would add all of the numbers between 2 and 50 that are even. 2+4+6+8+10+12+14+16+18+20+22+24+26+28+30+32+34+36+38+40+42+44+46+48+50

I am in Canada, and in grade 6 here we are working on divinding decimals! My son in grade 8 is doing Math that I did in Grade 10 allgebra! It is crazy!

Michelle

I totally understand what you are saying, it seems like we are teaching them more complex ideas every year. In the Everyday Math Series we teach, I teach dividing with decimals in 4th grade.

 

[Faldred]

There's also:

let x[0] = 2 + 4 + 6 + 8 + 10 = 30

Then, the next 5 are:

x[1] = (10+2) + (10+4) + (10+6) + (10+8) + (10+10) = x[0] + (5*10) = 80

The next 5 are then:

x[2] = (20+2) + (20+4) + (20+6) + (20+8) + (20+10) = x[0] + (5*20) = 130

and so on.

This leads to a summation of:

Sum( x[0]..x[n] ) = ( 30 * n ) + ( Sum( 1..n ) * 50 ); where n > 0

Since n = 9 in this case (50 - first 5 all divided by 5), I come up with 2550.

 

[DRS_Are_Best]

There's also:

let x[0] = 2 + 4 + 6 + 8 + 10 = 30

Then, the next 5 are:

x[1] = (10+2) + (10+4) + (10+6) + (10+8) + (10+10) = x[0] + (5*10) = 80

The next 5 are then:

x[2] = (20+2) + (20+4) + (20+6) + (20+8) + (20+10) = x[0] + (5*20) = 130

and so on.

This leads to a summation of:

Sum( x[0]..x[n] ) = ( 30 * n ) + ( Sum( 1..n ) * 50 ); where n > 0

Since n = 9 in this case (50 - first 5 all divided by 5), I come up with 2550.

GEEK!!!!!!! (I can say this because I'm DW)