You've already mastered adding and subtracting smaller numbers. Now, let's tackle bigger problems. When we work with numbers in the hundreds, we sometimes need a special technique called regrouping, also known as carrying over. This happens when the sum of digits in any column is 10 or more.

Imagine you run a toy store. At the start of the week, you have 158 teddy bears. A new shipment arrives with 274 more. To find the total, you add 158 + 274. Let's line up the numbers by their place value: ones, tens, and hundreds.

First, add the ones column: $8 + 4 = 12$. Since 12 is a two-digit number, we can't just write it in the ones place. We write the 2 in the ones place of our answer and 'carry' the 1 (which represents one ten) over to the top of the tens column.

Next, add the tens column, including the 1 we carried over: $1 + 5 + 7 = 13$. Again, we have a two-digit number. We write the 3 in the tens place of our answer and carry the 1 over to the hundreds column.

Finally, add the hundreds column: $1 + 1 + 2 = 4$. We write the 4 in the hundreds place. You now have a total of 432 teddy bears.

Subtraction gets interesting when a digit on top is smaller than the digit directly below it. This is where borrowing comes in. It's the reverse of carrying over.

Let's say you start with $432 and spend $185 on a new bike. How much money do you have left? We need to solve 432 - 185.

Looking at the ones column, we can't subtract 5 from 2. So, we need to 'borrow' from the tens column. We take one ten from the 3 (leaving 2 tens) and add it to the ones column. That one ten is equal to 10 ones, so our 2 ones become 12 ones. Now we can subtract: $12 - 5 = 7$.

Now for the tens column. We have a 2 on top (since we borrowed from the 3) and an 8 on the bottom. We can't do $2 - 8$. So, we borrow again, this time from the hundreds column. We take one hundred from the 4 (leaving 3 hundreds) and add it to the tens column. That one hundred is equal to 10 tens, so our 2 tens become 12 tens. Now we can subtract: $12 - 8 = 4$.

Finally, the hundreds column is simple: $3 - 1 = 2$. You have $247 left.

Whether you're adding or subtracting, understanding place value is the most important skill. Every digit in a number has a value based on its position. In the number 789, the 9 is in the ones place, the 8 is in the tens place (meaning 80), and the 7 is in the hundreds place (meaning 700). Breaking a number down like this is called expanded form: $700 + 80 + 9$.

When you carry a '1' in addition, you're really carrying a '10' or a '100'. When you borrow a '1' in subtraction, you're really borrowing a '10' or a '100'. Mastering this concept makes multi-digit math much less intimidating.

Time to practice what you've learned.

Well done. Keep practicing these skills, and you'll be able to solve even bigger problems with confidence.