Operations on Large Numbers

# Operations on Large Numbers

## Addition of Large Numbers

Addition of 7- and 8-digit numbers is also done in the same way as the addition of 4-, 5- and 6-digit numbers.
We start adding from the ones place, and if the sum of any number is greater than 10, we regroup it with the next column.
For example, if the sum in the ones column is 16, regroup it as 1 ten and 6 ones. Write 6 in the ones column and carry over one to the tens column.

Example 1: Add 57,86,335 and 34,95,768.
Solution:
We need to arrange the numbers in correct columns, before we start adding.

 TL L TTh Th H T O 5 7 8 6 3 3 5 + 3 4 9 5 7 6 8 9 2 8 2 1 0 3

Example 2: Add 2,41,84,356; 42,86,894 and 3,35,93,547.
Solution:
We need to arrange the numbers in correct columns, before we start adding.

 C TL L TTH Th H T O 2 4 1 8 4 3 5 6 4 2 8 6 8 9 4 + 3 3 5 9 3 5 4 7 6 2 0 6 4 7 9 7

## Subtraction of Large Numbers

Subtraction of 7- and 8-digit numbers is also done in the same way as the subtraction of 4-, 5- and 6-digit numbers.

Example 1: Subtract 35,98,568 from 72,65,621.
Solution:
We need to place the numbers in correct columns before we start subtracting.

 TL L TTh Th H T O 7 2 6 5 6 2 1 – 3 5 9 8 5 6 8 3 6 6 7 0 5 3

Example 2: Subtract 5,67,82,738 from 8,63,78,423.
Solution:
We need to place the numbers in correct columns to start subtracting.

 C TL L TTH Th H T O 8 6 3 7 8 4 2 3 – 5 6 7 8 2 7 3 8 2 9 5 9 5 6 8 5

## Multiplication of Large Numbers

Let us discuss the steps involved in the multiplication of 4-digit numbers by a 3-digit or a 4-digit number.

Example 1: Multiply 2657 by 364.
Here, 2657 is the multiplicand and 364 is the multiplier.
Solution:

 L TTh Th H T O 2 6 5 7 x 3 6 4 1 0 6 2 8 1 5 9 4 2 0 + 7 9 7 1 0 0 9 6 7 1 4 8

Example 2: Multiply 2476 by 1264.
Here, 2476 is the multiplicand and 1264 is the multiplier.
Solution:

 TL L TTh Th H T O 2 4 7 6 x 1 2 6 4 9 9 0 4 1 4 8 5 6 0 4 9 5 2 0 0 +2 4 7 6 0 0 0 3 1 2 9 6 6 4

## Multiplication of a Number by 100, 1000 and 10000

v While multiplying a number by 100, insert two zeros to the right of the number.
Example: 32 × 100 = 3200; 250 × 100 = 25,000; 2456 × 100 = 2,45,600

v While multiplying a number by 1000, insert three zeros to the right of the number.
Example: 54 × 1000 = 54,000; 453 × 1000 = 4,53,000; 730 × 1000 = 7,30,000

v While multiplying a number by 10,000, insert four zeros to the right of the number.

Example: 85 × 10,000 = 8,50,000; 64 × 10,000 = 6,40,000; 47 × 10,000 = 4,70,000

## Division of Large Numbers

Example: Divide 4932 by 38.
Solution:
Step 1: 38 is a 2-digit number. So, consider the number formed by the thousands and hundreds place in the dividend.
49 > 38, so divide 49 by 38.

Step 2: Bring down the next digit and divide.
Step 3: Bring down the last digit and divide.
Step 4: No more digits are left to bring down.
Therefore, quotient is 129 and remainder is 30.

### Checking Division

You can check your division by using the following formula.
Quotient × Divisor + Remainder = Dividend
129 × 38 + 30 = 4932
Thus, our division is correct.

## Division by 10, 100 and 1000

v If a number is divided by 10, then the digit at ones place becomes the remainder and the remaining digits form the quotient.

Example 1: Divide 7285 by 10.
Solution: Here, Quotient = 728 and Remainder = 5
Example 2: Divide 37252 by 10.
Solution: Here, Quotient = 3725 and Remainder = 2

v If a number is divided by 100, then the digits at ones and tens places together form the remainder and the rest of the digits form the quotient.

Example 1: Divide 87546 by 100.
Solution:   Here, Quotient = 875 and Remainder = 46
Example 2: Divide 7853 by 100.
Solution: Here, Quotient = 78 and Remainder = 53

v If a number is divided by 1000, then the digits at ones, tens and hundreds places together form the remainder and the rest of the digits form the quotient.

Example 1: Divide 89253 by 1000.
Solution:   Here, Quotient = 89 and Remainder = 253
Example 2: Divide 83243 by 1000.
Solution: Here, Quotient = 83 and Remainder = 243
Example 3: Divide 97283 by 1000.

Solution: Here, Quotient = 97 and Remainder = 283

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