find the sum by using short method ;
a) 19782+9999
Answers
Answer:
29781 is a correct answer
Given operation is,
19782 + 9999
If we do it in a normal way, it will carry too many steps and will take more time, it may went in vain.
In normal method, from right to left,
2 + 9 = 11 => 1 (1 is borrowed to left)
8 + 9 + '1' = 18 => 8 (1 is borrowed to left)
7 + 9 + '1' = 17 => 7 (1 is borrowed to left)
9 + 9 + '1' = 19 => 9 (1 is borrowed to left)
1 + '1' = 2
Now we get the result - 29781.
But there's no need to such a time wasting method, we may just use some short tricks for some mathematical operations, and some of them are even hidden in the questions too!!!
Observe the given sum. 19782 + 9999
Is it wrong to express 9999 as 10000 - 1 ?!
So, isn't adding 9999 to 19782 the same as adding 10000 to it and then subtracting 1 from it ?!
Adding 10000 makes only one change that the ten thousands digit will be increased by 1.
Subtracting 1 from the resultant sum makes change which is none other that the deduction of the ones digit by 1.
So doesn't adding 9999 to a number bring these two changes simultaneously?! Means addition of the ten thousands digit by 1 and the subtraction of 1 from the ones digit at the same time?!
Algebraically and decimally, we write,
a/b/c/d/e + 9999 = (a + 1)/b/c/d/(e - 1)
[Keep in mind that the slash is used to split the digit, not to divide.]
Hence we simply write,