Addition is fun

Addition is one of the most common mathematical operations, which even a layman uses frequently. Whether you go for shopping or purchasing your grocery, books, or other daily used commodities you need to calculate your expenditure and here the addition technique comes handy.

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Have you ever visited a bank? I’m sure you have. Now my question is-how does the cashier add the cashbook account so fast? The answer is very simple, he uses some tricks or adopts some methods which comes with practice and develops a method of his own to calculate fast. You must have noticed the greengrocer mentally adding the cost of objects purchased. A more astonishing fact, which you will not believe is that some of them haven’t been to school but are equally efficient at calculations.

I shall focus on some of the unconventional methods and tricks which will help you calculate faster than the method you use and many a times you will see that you can compete with a calculator.

Addition of 5 Consecutive Numbers

Addition of 5 consecutive numbers can be done by various methods but the simplest one is to multiply the highest number by 5 and subtract 10 from the result obtained.

Example: 13 + 14 + 15 + 16 + 17 =?

Solution:- Here the highest number is 17 Multiply it by 5: 17 × 5 = 85; Subtract 10: 85 – 10 = 75

Example:- 66 + 67 + 68 + 69 + 70 =?

Solution:- Here the highest number is 70 Multiply it by 5: 70 × 5 = 350; Subtract 10: 350 – 10 = 340

Now the question you may ask: If there are more consecutive numbers then what strategy shall you use to find the total? I am giving here some points and expect you to generalise  a rule to add consecutive numbers on your own.

n If there are 4 consecutive numbers; multiply the highest by 4 and subtract 6 (1½ × 4)

n If there are 5 consecutive numbers; multiply the highest by 5 and subtract 10 (2 × 5)

n If there are 6 consecutive numbers; multiply the highest by 6 and subtract 15 (2½ × 6)

n If there are 7 consecutive numbers; multiply the highest by 7 and subtract 21 (3 × 7)

n If there are 8 consecutive numbers; multiply the highest by 8 and subtract 28 (3½ × 8)

You can add consecutive numbers more smartly if you understand the two cases.

Case 1:- If there are odd numbers of consecutive terms.

Rule:- Multiply the middle term by the number of terms.

Example:- 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20

Solution:- Since there are 9 terms so the middle term = 16 Multiply it by 9 = 16 × 9 = 144

Case 2:- If there are even  numbers  of  consecutive terms.

Rule:- Take the mean of the two middle terms and multiply it with the number of terms.

Example:- 23 + 24 + 25 + 26 + 27 + 28 + 29 + 30 = ?

Solution:- You can see that  there  are  8  consecutive  numbers to be added. The two middle numbers are obviously 26 and 27

Take the mean of the two = 26.5

Multiply it with the number of terms = 26.5 × 8 = 212