Addition of Large Numbers 

Addition is one of the four basic operations of arithmetic, the others being subtraction, multiplication and division. Till now we have read addition of numbers which are very small and could be added just by counting. 

For example, Ron had 5 oranges and Sam gave him 7 oranges more. 

Total Oranges with Ron = 5 + 7 = 12 oranges 

This could be calculated simply by counting till 12.  

But what if numbers are so large that counting becomes impractical?  

Let’s say one market sold 2,891 oranges while another market sold 3,698 oranges. If we ask how many oranges were sold in total, it would be impossible to add the numbers by counting. In such case, we calculate the sum of the two.  

But how do we do that?  

To find the sum, we arrange the two numbers one over the another such that the place value of the two numbers are in perfect correspondence. Then we add two digits at a time starting with the units place. 

Let us find how many oranges were sold in total by the two markets- 

Here as we add starting with units place but as we move to the tens place we see 

At tens place, 9 + 9 = 18  

But we do not write 18 in the tens place as we cannot keep two digits in a single place.  

Then how do we proceed?  

We know, 10 × 10 = 1 × 100 

So, we write ‘8’ in the tens place and carry the ‘1’ to the next place i.e. the hundreds place. We do this every time we run out of capacity of any particular place.  

Similarly, in hundreds place, 1 + 8 + 6 = 15 

So, we write ‘5’ in the hundreds place and carry the ‘1’ to the next place i.e. the thousands place. 

Thus, the total number of oranges sold by both the markets were 6,589 oranges. 

In real life, we may have to deal with large numbers that are in lakhs or at times even beyond that.  

Let us look at an example on addition of large numbers- 

Example: Add5,12,97,165 and 1,67,78,374 

Solution: 

Let us add the two numbers using the place value chart 

Thus, 5,12,97,165 + 1,67,78,374 = 6,80,75,539 

Now, as we know how to add large numbers, let us look at a problem of how we use addition of large numbers in real life- 

Example: In a country, there are 4,13,14,175 men; 2,75,11,850 women and 75,90,100 children. Find the total population of the country. 

Solution: 

Let us find the total population of the country using the place value chart 

So, the total population of the country is 7,64,16,125. 

Subtraction of Large Numbers 

Subtraction is an arithmetic operation in which one number is taken away from another to find the difference. Till now we have learned subtraction of small numbers which can be found by backward counting or add 

For example, there were 16 bees in a garden out of which 5 bees died. So, to find how many bees are left in the garden we simply find a number that should be added to 5 to get 16 or we do backwards counting from 16 till 5 steps. 

We find, 16 – 5 = 11 bees 

So, we can say 11 bees were left. 

But how do we find the difference when the numbers are large?  

Similar to addition, to find the difference between two large numbers, we arrange the given numbers in columns in correspondence to their place values. In subtraction, order of the numbers matters a lot. We write the larger of the two numbers first followed by the smaller number. Then we subtract two digits at a time starting with the unit place borrowing if needed from the next column to the left, till the largest place value of digit. 

Let us look at an example- 

Example- There were 1,961 trees in a jungle. 1,237 trees were cut down. How many trees were left? 

To find the number of trees left, we need to find the difference between the two numbers. Let us first arrange the numbers as per their place value. 

As we can see in the above table, starting with the units place, it is not possible to subtract 7 from 1. So, we borrow a ten from the tens place and add it to 1 in the ones place. Then we subtract 7 from 11 to get 4. Now, we are left with 5 tens at tens place from which we subtract 3 tens to get 2 tens.  

Similarly, we subtract the remaining places to find the difference. 

Here we can see, 724 trees were left in the forest. 

This is subtraction by regrouping method where we borrow from the next place in case of shortage to find the difference between the numbers. Many a times we come across numbers that are in thousands, lakhs, crores or beyond. We find the difference between these large numbers using subtraction by regrouping method which we learnt above. 

Let us look at an example of subtraction of two large numbers 

Example: Subtract 4,22,79,845 and 8,61,28,354 

Solution: 

Let us subtract the two numbers using the place value chart 

Now, as we know how to subtract large numbers, let us look at a problem of how we use subtraction of large numbers in real life- 

Example: The total population of a country is 7,92,55,000. If the number of women is 4,67,29,175 find the number of men in the country. 

Solution: 

Let us find the number of men in the country using the place value chart 

So, the number of men in the country is 3,25,25,825. 

Relation between Addition & Subtraction 

We can easily check subtraction by adding the difference to the smaller number. 

Example- 

Subtract 3,28,941 from 6,75,834 and verify your answer. 

Solution: 

Let us subtract and then verify our answer. 

As we can see from the above tables, when we add the difference of the two numbers to the smaller number, we get the larger number. 

So, we can say that subtraction or the difference between two numbers is nothing but the number which is to be added to the smaller number to get the larger number.  

This method can be used to verify our subtraction also as shown above.