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:
x+y=100
3x+8y=25
Step-by-step explanation:
So there are around 3 essay questions
Answer:
2. 92 ounces of Sprite
3. 1/6 do not want mustard on their ham sandwiches
4. 6 hours playing volleyball
5. 32 portions
Step-by-step explanation:
2. Sam has 8 cans of Sprite. Each can is 11 2/4 ounces
We can simplify 2/4 to 1/2
Multiply the number of cans by the ounces per can
8 * 11 1/2
8 * 11.5
92 ounces
3. 1/2 of the students want ham. 1/3 of those do not want mustard
We multiply 1/2*1/3 = 1/6
1/6 of the students do not want mustard on their ham sandwiches
4. 8 hours at the beach. 3/4 of the time was spent playing volleyball
Multiply this together
8*3/4 = 8/4*3 = 2*3 = 6 hours
5. We have 4 lbs of wings. We divide it into 1/8 lbs parts
4 ÷ 1/8
Copy dot flip
4 * 8/1
32 portions
Answer:
Step-by-step explanation:
The traditional home mortgage is usually borrowed for 30 years.
