Operations on Larger Numbers

Example 1:
If A = 48,497, B = 7,328, and C = 1,33,224.
Find: 
(i) A + B 
 4 8, 4 9 7
+  7, 3 2 8
  5 5, 8 2 5

(ii) B + C 
         7, 3 2 8
+ 1,3 3, 2 2 4
   1, 4 0, 5 5 2

Example 2:
The weight of one bag of wheat is 98 kg 450 g and the weight of another bag of wheat is 106 kg 928 g. What is the total weight of both the bags?

Solution:
             Weight of one bag of wheat = 98 kg 450 g
and, weight of another bag of wheat = 106 kg 928 g
 ∴        Total weight of both the bags = 204 kg 1378 g
Since 1378 g = 1 kg 378 g

 Therefore, the total weight of both bags = 205 kg 378 g

Example 3:
Three different tanks contain 54,937 liters, 49,328 liters, and 1,07,244 litre of water.
What is the total quantity of water in the three tanks?

Solution:
                    Water in one tank = 54,937 liters.
            water in another tank = 49,328 liters
                 water in third tank = 1,07,244 litre

 ∴Water In all the three tanks = 2, 11 ,509 litre 

Example 1:
If A = 48,497, B = 7,328, and C = 1,33,224.
Find: 
(i) C –  A
1, 3 3, 2 2 4
 – 4 8, 4 9 7
    8 4, 7 2 7 

Example 2:
The sales receipt of a company during a certain year was ₹ 8,73,540. In the following year, it was decreased by ₹ 84,670. What was the sales receipt of the company during the second year?

Solution:
The sale receipt of the company during second year
= ₹ 8,73,540 – ₹ 84,670 = ₹ 8,73,540                                     

  8, 7 3, 5 4 0
   − 8 4, 7 2 7 
   7, 8 8, 8 7 0

Example 1:
The Cost of one article is  ₹57,390. What will be the cost of 275 such articles

Solution:
Cost of one article =  ₹ 57,390
Cost of 275 such articles = 275 × ₹57,390 = ₹1,57,82,250 

Example 2:
In an examination, a student multiplied 40,327 by 46 instead of 64. By how much was his answer greater than or less than the correct answer?

Solution:
The student's answer = 40,327 × 46
                                  = 40,327
                                         × 46
                                    241962
                                + 161308
                                18,55,042

Correct answer = 40,327 × 64
                         =         40,327
                                        × 64
                                   161308
                                + 241962
                               25,80,928

The incorrect answer is less than the correct answer

by 25,80,928 − 18,55,042 = 25,80,928
                                          − 18,55,042
                                               7,25,886 

₹ 82,804 is divided equally among 326 pupils. How much will each get? 
          254
`326")"overline(82804)`
        –  652       (326 × 2)
          1760
    –    1630      (326 × 5)
          1304
     –   1304    (326 × 4)
             ×          
Each will get ₹ 82,804 ÷ 326 = ₹ 254 

• Align digits by place value for all operations.

• Carry over and borrow carefully in addition and subtraction.

• Check multiplication and division with estimation or reverse calculation.

• Always interpret answers in context (e.g., convert grams to kilograms if needed).