Subtracting Large Numbers Mentally

 

This video features subtraction of larger numbers. A basic understanding of subtraction of numbers from 1 – 9 forms our basis for solving larger subtraction problems. This can be explained by taking the following example:

5 – 2 = 3 is same as 50 – 20 = 30, reason being that 0 here in 50, 20 and 30 is at the tens place hence it can also be understood as

5* 10 = 50
2* 10 = 20
3* 10 = 30

Subtraction of digits where the tens place are the same is equivalent of subtraction of the digits themselves!

Having understood that we can now easily perform the same operation on the number line. 50 – 20 on the number line would mean moving five places forward on the number line marked with intervals of 10. Next, move two places backward, the number so obtained is the answer to the question here being 30.

Taking another example, 76 – 20, the digits on the unit place is 6 while for digit at the tens place we need to subtract 2 from 7 giving the answer as 56.

Further examples would make it more clear. Say 43 – 19, here the trick is to convert 19 into 20 to make the subtraction easier. That would result in 23 and to correct the -1 subtracted in the previous stage we can simply +1 to the number in this stage and the result is the same, i.e; 24. Similarly for 52 – 29, one can subtract 30 from 52 resulting in 22 and then add 1 to the result making it 23.

Now, using this concept on the number line. Let us first use the example of 43 – 19. Visualize the numbers marked on the number line. The first number after 19 is 20. The difference between them is 1. The number closest to 43 with zero at the tens place is 40, the difference between them is 3. The reason why we take numbers like 20 and 40 for this subtraction is that they are very easy to subtract with possibility of an error. Having done this we now subtract 20 from 40, result being 20Now add up all the differences, i.e; 1 + 20 + 3 = 24, which is the answer to this question.

Likewise for 52 – 29, the number nearest to 52 with zero in tens place is 50 (the difference between them being 2) while for 29 is 30 (difference 1) and the difference between 50 and 30 is 20. Adding up the differences we get, 1 + 20 + 2 = 23, the answer to this question.

Hence these are some alternate approaches of looking at subtraction which can be helpful in various competitive exams.

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