Gauss' method for addition relies on the fact that you can 'pair' certain numbers together. Look at the example:
1+2+3+4+5+6+7+8+9+10
We could manually add all these together from left to right but a clever way to think about this is if we add together the ends of the sum (10+1) we get 11. If we then move one in from the ends and add these (2+9) we also get 11. This means that 1+2+...+9+10 is the same as 11+11+...+11+11.
Because each 2 numbers adds to 11 we know the total number of 11's we have to add together is the length of the sum divided by 2. In our case 5 (10 ÷ 2). We need to add 5 lots of 11 to get our answer. This is the same as 11 × 5 which is easily seen to be 55.
(If you add the 10 numbers together on a calculator you'll see 1+2+3+4+5+6+7+8+9+10 = 55) so this method really makes it a lot quicker.
Looking at your sequence, if we pair the ends together we get 401 (400+1) and we multiply this by the length of the sequence divided by 2. In your case, 200 (400 ÷ 2).
So the sum of all the numbers from 1 to 400 must be 401 × 200 = 80,200.
Remember the steps:
1. Pair the ends together and add them
2. Times this number by the length of the sequence halved
Hope this helps.
Hey there. So basically, find out how much the pencils and notebooks cost first.
The notebooks cost = $3.25
The pencils cost = $0.50
Then, think about what you need to figure out in this problem.
Jake has $20. You need to find how many notebooks Jake can buy in maximum after buying 8 pencils.
If Jake buys 8 pencils that costs $0.50 each, he spends $4 on the pencils.
So now, to find out how many notebooks he can buy, do 20 minus 4.
Jake's got $16 left.
If the notebooks cost $3.25 each, we need to find out how many notebooks he can buy by dividing them. So, 16 divided by 3.25 equals 4.923... and so on.
That means, Jake can buy 4 notebooks with his remaining money.
Answer:
54 units squared
Step-by-step explanation:
hope this helped!
Mr.willer needs 216 cans because 27 vans times 8 banks equals 216 and 23 times 9 equals 207 so he would need 9 more cans
