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.
Answer: one dollar and 56 cents
Step-by-step explanation:
11 cents= one peny is one cent
6 dimes= 60 cents, one dime is 10 cents
3 qurters= 75 cents, one quaters is 25 cents
2 nicales= 10 cents, one nicale is 5 cents
one dollar is 100 cents
The answer is 15/8 hope it helps
Answer:
$9
Step-by-step explanation:
These are given:
Total = 22
Cost for shoes = 4
Total games played = 2
Cost per game (g)= ?
So,
22 = 4 + 2(g)
-4 -4
18 = 2g
divide by 2
9 = g
$9 per game
