### Subtraction

Subtraction means "finding the difference" between two numbers. When working with natural numbers, understanding it as "taking away" does not change the result in practice.

## 3 - 2

If I subtract,  ( take away ) , 2 apples from 3 apples, 1 apple remains.

# Difference Meaning:

The difference between 3 apples and 2 apples is 1 apple. (The thing that is in 3 apples but not in 2 apples is 1 apple.)

# Classic Subtraction Operation

Just like in addition, in subtraction, I also need to write the same digits under each other to perform the operation.

Write the numbers under each other according to their place values.

The reason we write the digits aligned to the right under each other is so that we can subtract the units from the units, the tens from the tens, and the hundreds from the hundreds exct..

## Example:

I subtract 3 units from 6 units,  remaining 3 units, and I write it in the ones place.

I subtract one 10-unit from two 10-units, leaving one 10-unit remaining. I wrote the one 10-unit in the tens place.

I subtracted two 100-units from three 100-units, leaving one 100-unit remaining.

I don't have any 1000-units to subtract from the four 1000-units, so I write them as they are. You can think of it as subtracting zero 1000-units from four 1000-units. In the end, I still have four 1000-units.

# Subtraction with Borrowing ( Regrouping)

In elementary school, your teacher taught you to "borrow 1" from the neighbor. So why do we borrow 1 from the neighbor, and what does "borrowing 1" actually mean?
Indeed, this isn't really borrowing, because we're not giving it back.

### The accurate term is "exchanging."

We are breaking down larger place values into smaller ones. For example, we go to the cashier and give 10 dollars and receive 10 one-dollar bills in exchange.

# 263 - 85

We can model 263 in this way. From 263, I need to subtract 85, which means 8 tens and 5 ones.The problem here is that I don't have 5 ones or 8 tens. What should I do?

I'll exchange one of the tens and add it to the other ones.

Now I have 13 units, and I can subtract 5 units. When I do, I'm left with 8 units.

But we don't have 8 tens. I go to the hundreds and exchange 1 hundred (1 hundred makes 10 tens) and add it to the tens I already have.

I now have 15 tens, and I can subtract 8 tens. If I subtract 8 tens, I'm left with 7 tens.

## My result is 178.

Let's do this with subtraction operation.

I'm starting the subtraction from the units place, and I need to subtract 5 units from 3 units, but I can't subtract 5 from 3. What should I do?

I go to the neighbor and borrow 1. The neighbor's place is the tens place, and I see 6, which actually represents 6 tens (60). I take 1 ten from the neighbor and add it to the units.
Now I have 13 units, and since 1 ten was broken down from the tens, 5 tens remain out of 6 tens.

Subtract 5 units from 13 units and write it in the ones place.

Subtract 5 units from 13 units and write it in the ones place.

Now it's the tens' turn. I need to subtract 8 tens from 5 tens, but again it won't work, so I go to the neighbor in the hundreds place and take 1 hundred and break it down into tens. 1 hundred makes 10 tens, so my total tens become 15.

I subtract 8 tens from 15 tens, leaving 7 tens. I write 7 in the tens place.

I don't have any hundreds to subtract from 1 hundred, so I bring down the 1 hundred and write it in the hundreds place, or you can think of it as subtracting 0 hundreds from 1 hundred, leaving 1 hundred.

# 5000 - 276

In modeling, shapes and their meanings.

In modeling, shapes and their meanings can be used to represent mathematical concepts or quantities.We generally use cubes to represent 1000, squares for 100, rectangles for 10, and small squares for the units in modeling.

We can represent 5000 in this way,

I need to take out 2 hundreds, 7 tens, and 6 ones from here. But the problem is, I don't have any of them! I only have thousands. What should I do?

The nice thing about our place value system is that each place is made up of 10 times the value of the place to its right, so even though I don't have any hundreds, tens, or ones, I have thousands. I can create all of these by breaking down ( exchanging ) my thousands.

(The shapes have not been drawn to scale.)

I have 5 thousands, I break one of the thousands into 10 hundreds, and I am left with 4 thousands.
I break one of the 10 hundreds into 10 tens, so I am left with 9 hundreds.
I break one of the 10 tens into 10 ones, so I am left with 9 tens.

### As a result , I have 4 thousands, 9 hundreds, 9 tens, and 10 ones.

Now I can take out 2 hundreds, 7 tens, and 6 ones.

### Result : 4 thousands, 7 hundreds, 2 tens, 4 ones =  4724

Let's do this using the standard subtraction method.