Operations on Large Numbers

Step 1: Arrange the numbers in columns.
 1 5 4 0 3 2
+ 4 2 1 7 4 6

Step 2: Add the digits in ones place. 2 + 6 = 8, we write 8 in the ones place of the result.
 1 5 4 0 3 2
+ 4 2 1 7 4 6
      8

Step 3: Add the digits in tens place. 3 + 4 = 7, we write 7 in the tens place of the result.
 1 5 4 0 3 2
+ 4 2 1 7 4 6
    7 8

Step 4: Add the digits in hundreds place. 0 + 7 = 7, we write 7 in the hundreds place of the result.
 1 5 4 0 3 2
+ 4 2 1 7 4 6
   7 7 8

Step 5: Add the digits in thousands place. 4 + 1 = 5, we write 5 in the thousands place of the result.
 1 5 4 0 3 2
+ 4 2 1 7 4 6
   5 7 7 8

Step 6: Add the digits in ten-thousands place. 5 + 2 = 7, we write 7 in the ten-thousands place of the result.
 1 5 4 0 3 2
+ 4 2 1 7 4 6
  7 5 7 7 8

Step 7: Add the digits in lakhs place. 1 + 4 = 5, we write 5 in the lakhs place of the result.
 1 5 4 0 3 2
+ 4 2 1 7 4 6
 5 7 5 7 7 8

1,54,032 + 4,21,746 = 5,75,778

Step 1: Arrange the numbers in columns.
 3 5 2 9 0 8
+ 4 7 9 8 5 6

Step 2: Add the digits in ones place. 8 + 6 = 14, we write 4 in the ones place of the result and 1 in the tens place as a carry over.
    1
 3 5 2 9 0 8
+ 4 7 9 8 5 6
      4

Step 3: Add the digits in tens place. 1 + 0 + 5 = 6, we write 6 in the tens place of the result.
    1
 3 5 2 9 0 8
+ 4 7 9 8 5 6
    6 4

Step 4: Add the digits in hundreds place. 9 + 8 = 17, we write 7 in the hundreds place of the result and 1 in the thousands place as a carry over.
   1
 3 5 2 9 0 8
+ 4 7 9 8 5 6
    7 6 4

Step 5: Add the digits in thousands place. 1 + 2 + 9 = 12, we write 2 in the thousands place of the result and 1 in the ten-thousands place as a carry over.
  1
 3 5 2 9 0 8
+ 4 7 9 8 5 6
   2 7 6 4

Step 6: Add the digits in ten-thousands place. 1 + 5 + 7 = 13, we write 3 in the ten-thousands place of the result and 1 in the lakhs place as a carry over.
 1
 3 5 2 9 0 8
+ 4 7 9 8 5 6
  3 2 7 6 4

Step 7: Add the digits in lakhs place. 1 + 3 + 4 = 8, we write 8 in the lakhs place of the result.
 1
 3 5 2 9 0 8
+ 4 7 9 8 5 6
 8 3 2 7 6 4

3,52,908 + 4,79,856 = 8,32,764

Step 1: Arrange the numbers in columns.
 9 5 8 3 4 7
- 7 2 5 0 1 3

Step 2: Subtract the digits in ones place. 7 - 3 = 4, we write 4 in the ones place of the result.
 9 5 8 3 4 7
- 7 2 5 0 1 3
     4

Step 3: Subtract the digits in tens place. 4 - 1 = 3, we write 3 in the tens place of the result.
 9 5 8 3 4 7
- 7 2 5 0 1 3
    3 4

Step 4: Subtract the digits in hundreds place. 3 - 0 = 3, we write 3 in the hundreds place of the result.
 9 5 8 3 4 7
- 7 2 5 0 1 3
   3 3 4

Step 5: Subtract the digits in thousands place. 8 - 5 = 3, we write 3 in the thousands place of the result.
 9 5 8 3 4 7
- 7 2 5 0 1 3
   3 3 3 4

Step 6: Subtract the digits in ten-thousands place. 5 - 2 = 3, we write 3 in the ten-thousands place of the result.
 9 5 8 3 4 7
- 7 2 5 0 1 3
  3 3 3 3 4

Step 7: Subtract the digits in lakhs place. 9 - 7 = 2, we write 2 in the lakhs place of the result.
 9 5 8 3 4 7
- 7 2 5 0 1 3
 2 3 3 3 3 4

958347 - 725013 = 233334

Step 1: Arrange the numbers in columns.
 4 5 2 1 5 3
- 2 3 9 8 5 6

Step 2: Subtract the digits in ones place. 3 - 6 is not possible, so we regroup the digit in tens place.
5 tens = 4 tens + 10 ones, we add 10 ones to 3 ones. Now the digit at ones place is 13. Now subtract. 13 - 6 = 7, we write 7 in the ones place of the result.
    4 13
 4 5 2 1 5 3
- 2 3 9 8 5 6
     7

Step 3: Subtract the digits in tens place. 4 - 5 is not possible, so we regroup the digit in hundreds place.
1 hundred = 10 tens, we add 10 tens to 4 tens. Now the digit at tens place is 14. Now subtract. 14 - 5 = 9, we write 9 in the tens place of the result.
    0 14
 4 5 2 1 5 3
- 2 3 9 8 5 6
    9 7

Step 4: Subtract the digits in hundreds place. 0 - 8 is not possible, so we regroup the digit in thousands place.
2 thousands = 1 thousands + 10 hundreds, we add 10 hundreds to 0 hundreds. Now the digit at hundreds place is 10. Now subtract. 10 - 8 = 2, we write 2 in the hundreds place of the result.
   1 10
 4 5 2 1 5 3
- 2 3 9 8 5 6
    2 9 7

Step 5: Subtract the digits in thousands place. 1 - 9 is not possible, so we regroup the digit in ten-thousands place.
5 ten-thousands = 4 ten-thousands + 10 thousands, we add 10 thousands to 1 thousands. Now the digit at thousands place is 11. Now subtract. 11 - 9 = 2, we write 2 in the thousands place of the result.
  4 11
 4 5 2 1 5 3
- 2 3 9 8 5 6
   2 2 9 7

Step 6: Subtract the digits in ten-thousands place. 4 - 3 = 1, we write 1 in the ten-thousands place of the result.
   4
 4 5 2 1 5 3
- 2 3 9 8 5 6
  1 2 2 9 7

Step 7: Subtract the digits in lakhs place. 4 - 2 = 2, we write 2 in the lakhs place of the result.
 4 5 2 1 5 3
- 2 3 9 8 5 6
 2 1 2 2 9 7
2,39,856 - 4,52,153 = 2,12,297

Step 1: Find 7,53,028 + 1,81,734.
  7 5 3 0 2 8
+ 1 8 1 7 3 4
  9 3 4 7 6 2

Step 1: Now we subtract 5,17,316 from the sum got in step 1.
  9 3 4 7 6 2
-  5 1 7 3 1 6
  4 1 7 4 4 6

7,53,028 + 1,81,734 - 5,17,316 = 4,17,446
When addition and subtraction are coming together, start the operations one-by-one from the left.

Step 1: Write the numbers as below.
 2 1 2 0 6
x    2 4

Step 2: We know 24 = 20 + 4, We will multiply 21,206 by 4 and 24 separately and write the partial products as below.
(To multiply with 20, we just multiplied with 2 and put a zero to the right)
 2 1 2 0 6
x   2 4
  8 4 8 2 4
4 2 4 1 2 0

Step 3: Add the sub products to get the final product.
 2 1 2 0 6
x   2 4
  8 4 8 2 4
4 2 4 1 2 0
5 0 8 9 4 4

Step 1: Write the numbers as below.
 2 5 1 4
x  1 2 6

Step 2: We know 126 = 100 + 20 + 6, We will multiply 21,206 by 6, 20 and 100 separately and write the partial products as below.
(To multiply with 20, we just multiplied with 2 and put a zero to the right.
To multiply with 100, we just put two zeroes to the right.)
  2 5 1 4
x  1 2 6
  1 5 0 8 4
  5 0 2 8 0
2 5 1 4 0 0

Step 3: Add the sub products to get the final product.
  2 5 1 4
x  1 2 6
  1 5 0 8 4
  5 0 2 8 0
2 5 1 4 0 0
3 1 6 7 6 4

Terms associated with Division:
1. Dividend: The number to be divided is called the dividend.
2. Divisor: The number by which we divide the dividend is called the divisor.
3. Quotient: The number that we get after division is called the quotient.
4. Remainder: The number which is left over after division is called the remainder.
5. dividend = divisor x quotient + remainder.
6. The symbol of division is ÷

Step 1: Write the numbers as below.

7  4 8 7 0 6 7

Step 2:
(i) Identify the number that starting from left of the dividend (4,87,067) which is divisible by 7.
4 is not divisible by 7, so we will consider 48.
We know, 7 x 6 = 42 and 7 x 7 = 49,
(ii) so we write 6 in the quatient place and 42 under 48.
(iii) subtract 42 from 48 and write the difference below.

  6
7  4 8 7 0 6 7
  4 2   
  6

Step 3: Bring down the next digit (7). Divide 67 by 7. Continue the steps mentioned in Step 2.

  6 9
7  4 8 7 0 6 7
  4 2 ↓   
  6 7
    6 3  
    4

Step 4:
  6 9 5
7  4 8 7 0 6 7
  4 2 ↓ ↓  
  6 7 ↓
    6 3 ↓  
    4 0
    3 5  
    5
Step 5:
  6 9 5 8
7  4 8 7 0 6 7
  4 2 ↓ ↓ ↓  
  6 7 ↓ ↓
    6 3 ↓ ↓  
    4 0 ↓
    3 5 ↓  
    5 6
    5 6  
     0
Step 6:
  6 9 5 8 1
7  4 8 7 0 6 7
  4 2 ↓ ↓ ↓ ↓  
  6 7 ↓ ↓ ↓
    6 3 ↓ ↓ ↓  
    4 0 ↓ ↓
    3 5 ↓ ↓  
    5 6 ↓
    5 6 ↓  
     0 7
     7  
     0

4,87,067 ÷ 7 = 69,581

   2 5
10  2 5 4
  2 0 ↓  
   5 4
    5 0
   4

We can see that, when a number is divided by 10, the quotient is obtained by removing the digit in the ones place of the dividend. and the removed digit is the remainder.