Working with numbers in the thousands is one thing, but what about when you get into lakhs and crores? The good news is that the rules you know for addition and subtraction don't change. The process just gets a little longer.

Let's add two large numbers: 4,75,321 and 3,98,789. We'll set it up vertically, aligning the place values, just as you would with smaller numbers.

Subtraction works the same way, using regrouping when the top digit in a column is smaller than the bottom one. In subtraction, the number being subtracted from is the minuend, and the number you are subtracting is the subtrahend.

To check your subtraction, you can use the inverse operation: addition. Just add the result (the difference) to the subtrahend. If you get the minuend, your calculation is correct. For example, if $9,45,100 - 1,50,000 = 7,95,100$, then $7,95,100 + 1,50,000$ should equal $9,45,100$.

When you multiply a large number, like a 4-digit multiplicand by a 2 or 3-digit number, you are essentially doing a series of simpler multiplications and then adding the results. This method is often called long multiplication.

Let's try multiplying 3,467 by 52. First, we multiply 3,467 by 2 (the ones digit of 52). Then we multiply 3,467 by 50 (the tens digit of 52). Finally, we add these two partial products together.

For a 3-digit multiplier, you would simply have a third partial product, shifted two places to the left, before adding everything up.

Long division helps us divide large numbers, especially when the division isn't perfect. Sometimes, after dividing, you have a number left over. This is called the remainder .

Imagine you have to divide 4,525 by 15. We work from left to right.

So, 4,525 divided by 15 is 301 with a remainder of 10. Just like with subtraction, we can check our answer using the inverse operation, multiplication. Multiply the quotient by the divisor and add the remainder: $(301 \times 15) + 10$. If this equals the original dividend (4,525), our work is correct.

The key to solving word problems is to identify what is being asked. Are you combining amounts (addition)? Finding the difference (subtraction)? Calculating a total from equal groups (multiplication)? Or splitting an amount into equal groups (division)?

Let’s try one. A factory produced 1,25,500 cricket bats in a year. They packed them into boxes, with 25 bats in each box. They sold each box for ₹5,000. How much money did the factory earn that year?

Before doing a precise calculation, it's often useful to estimate the answer. This helps you check if your final result is reasonable.

For example, to estimate the product of $3,845 \times 49$, you could round the numbers to the nearest convenient place. Round 3,845 to 4,000 and 49 to 50. Now the problem is much simpler: $4,000 \times 50 = 2,00,000$. The actual answer is $1,88,405$, which is close to our estimate. This gives us confidence in our calculation.

Practicing these operations with large numbers builds a strong foundation for all kinds of mathematical and real-world challenges.