What's 48 plus 36? Adults can figure out it's 84 in no time, even without a calculator. There's just one trick to it: split each number up by place, add each place separately, and whenever one place ends up holding more than it can fit, send the extra over to the next place.
48 splits into a 4 in the tens place and an 8 in the ones place. 36 splits into a 3 in the tens place and a 6 in the ones place. Let's add matching places together first. In the ones place, 8+6=14.
But there's a problem. In the number system we use, each place can only hold ten possible digits, 0 through 9. 14 is a two-digit number, so it can't just be written in the ones place as is.
So we split 14 into "one bundle of 10" and "4 leftover ones." The bundle of 10 gets carried over to the tens place next door, leaving just the 4 leftover ones in the ones place. Moving something over to the next place like this is called carrying.
Now let's look at the tens place. Add the original 4 and 3 to the 1 that got carried over, and 4+3+1=8. So the final answer is 84. Add each place separately, and send only the overflow to the next place — that's all carrying really is.
Subtraction runs into the opposite situation. Let's subtract 27 from 52. Looking at the ones place, you can't subtract 7 from 2, because 7 is bigger than 2.
When that happens, you borrow 10 from the tens place. That's fair, because one block in the tens place is worth exactly 10 blocks in the ones place. So you add 10 to the 2 in the ones place to make 12, and in exchange, the tens place drops from 5 down to 4.
12 minus 7 is 5, and 4 minus 2 is 2. So 52−27=25. Borrowing 10 from the next place over like this is called borrowing. What's fun about it is that the total amount doesn't change one bit, even after borrowing.
Carrying and borrowing are really two sides of the same idea: when a place ends up with more than 10, send the extra to the next place over, and when it doesn't have enough, borrow 10 from the next place over instead. This same idea shows up again later — in clock calculations (where the hour changes once the minutes pass 60) and in working with much larger numbers.
On our activity page, you can use sliders to change the two numbers yourself, and we'll show you in purple exactly how many blocks move over to the next place. Try it with different numbers and confirm for yourself that carrying and borrowing always happen by the exact same principle.