Hello friends! I hope you all had a great and relaxed vacation. I am very glad to be in touch with you once again. Let us start with something interesting. When somebody asks you to choose a number to do a few calculations, which number will you choose? I will choose 10, because almost all calculations are easily done with 10.
Do you agree? Shall we call 10 our number friend? However, all numbers can become our friends. Let us see how.
Let us consider the first set of single-digit numbers, 1 to 9, we can see that 1 and 9 make 10, as do 2 and 8, 3 and 7, 4 and 6, 5 and 5. This combining of numbers makes calculation easier. These sets of numbers are called complements. Two numbers whose sum is 10 are called complements, or we can call them number friends. We came across the same concept in the Ten Point circle last year.
Let us recall how we used this to add numbers. If you have to add 5+2+9+2+8+1, immediately combine 9 & 1, and 8 & 2, so that you are ready with two 10s. Then the remaining numbers to be added are 5 and 2 which make 7. So the total is 27.
If you have 4+6+7+1+4+2, 4 & 6 make 10. Then you can combine 7, 1 & 2 to make another 10. The remaining 1 & 4 make 5. So the total is 25. This combining of numbers can be practised to make calculations easier.
Next I am going to tell you an easy method to add a set of consecutive numbers. We have come across the formula to add numbers from 1 to n: n(n+1)/2. To be more precise, say you want to add the numbers from 1 to 10. Here your n is 10. So the answer can be easily obtained by putting substituting10 for n in the above formula.
10 x (10+1)) /2
(10 x 11)/2
= 55
This formula can be used only if the numbers start from 1. Today I am going to give you an easy method to add any set of consecutive numbers. Suppose we need to add the numbers from 22 to 30, a total of nine numbers.
First add the smallest and the largest numbers. 22 + 30 = 52.
Next multiply that by 9 (because 22 to 30 has nine numerals). 52 x 9 = 418.
Divide the answer by 2. 418 / 2 = 209.
209 is the answer.
Summing up:
1. Add the first and last numbers in the given series.
2. Multiply the answer by the number of numerals in the series.
3. Divide the answer by 2.
Can we try this method for a bigger set of numbers? Let’s try 201 to 208.
1. 201 + 208 = 409.
2. There are eight numbers in our series, so 409 x 8 = 3272.
3. Divide 3272 by 2 = 1636.
1636 is the answer.