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Question
primary 5 | Maths
| Whole Numbers
One Answer Below
Anyone can contribute an answer, even non-tutors.
Can anyone tell me why is the last step 201x100?
Example...
1 + 200 = 201
2 + 199 = 201
3 + 198 = 201
4 + 197 = 201
5 + 196 = 201
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100 + 101 = 201 (last pair of number)
Total have 100 pair.
So, working = 100×201 = 20100.
Last number × (last number +1) ÷ 2
The last number is even number
Example 1+2+3+4+5+6
The last number is 6
So, 6×7 ÷ 2 = 42÷2 = 21
If last number is odd number..
Example 1+2+3+4+5+6+7
We pair
1+6 = 7
2+5 = 7
3+4 = 7
Plus the last number 7
Total = 4×7 =28
So we break it to 1+2+3+4+5+6 and +7
Or
7×8 ÷2 = 28
Example
1+2+3+4+3+.............+99
So working
1+2+3+4+.....+97+98 and +99
Working
98×99 ÷ 2 then +99
= 4851 +99
= 4950
Or
99×100 ÷ 2 = 4950
See 1 Answer
Example...
1 + 200 = 201
2 + 199 = 201
3 + 198 = 201
4 + 197 = 201
5 + 196 = 201
.
.
.
.
.
100 + 101 = 201 (last pair of number)
Total have 100 pair.
So, working = 100×201 = 20100.