Vertical Subtraction

Vertical subtraction is a way of writing a subtraction problem where the second number is written below the first number vertically and in the correct order - ones under ones, tens under tens, and so on.

Sometimes you'll encounter relatively complex subtraction exercises that look like this: $431-278=$
By writing them vertically we can easily solve them.

The First Rule - writing the problem in the correct order!

ones digits under ones digits, tens digits under tens digits, hundreds digits under hundreds digits, and thousands digits under thousands digits.
Pay attention! It is extremely important that the first number in the exercise is the first and top number.
For example: $87-54=$
We will write it as follows:

Write the (minus) – sign in order to indicate that this is a subtraction exercise.
Draw a line underneath to separate the exercise from the results line.
We'll start by subtracting the ones digits as follows:

$7-4=3$

Let's continue to subtract the tens digits to obtain the following :
$8-5=3$

We're done! The result is $33$.
Now let's learn the next rule using the following example:

The Second Rule -

When the upper digit is smaller than the lower digit - we borrow $1$ from the next digit.

Here's a more advanced exercise!
$45-29=$

Solution:

Given that we cannot subtract $5$ minus $9$ we need to borrow a digit from the next number!
That means:
$5$ will become $15$ given that we'll place one in front of it and $4$ will become $3$.

We will write it in the following way:

Now we can proceed to solve the problem:
$15-9=6$
$3-2=1$
As seen below:

The result is $16$!

What do we do when we need to subtract a number from the digit $0$? For example in the exercise
$40-29=$
Here too we'll need to borrow $1$ from the digit $4$ resulting in the exercise seen below.

We can proceed to solve the problem :
$10-9=1$
$3-2=1$
As seen below:

We're done! The result is $11$.
Now let's see what happens when we can't borrow from the next digit given that it's also $0$:
For example in the following exercise:
$500-365=$

The third rule -$0$ that cannot be borrowed from becomes $9$ until we reach a digit that is not $0$ from which we can borrow $1$.

Note! If there is a third $0$ immediately after, it becomes $8$, if there is a fourth $0$ immediately after, it becomes $7$ and so on..

Let's learn the following rule through an example:

We want to borrow $1$ for the first $0$ making it $10$.
The second $0$ will be $9$ because we can't borrow from it
and the digit $5$ will become $4$ given that we borrowed one from it.
As seen below:

We can proceed to solve the exercise:
$10-5=5$
$9-6=3$
$4-3=1$
Let's write the solution as follows:

We're done! The result is $135$
Now let's move on to a very advanced exercise!

Let's solve this problem together –
$5700-3786=$

Solution:
Let's write it correctly:

Let's begin to solve the problem:
$0$ The first will become $10$ since we borrow $1$.
$0$ The second will become $9$ because we can't borrow from it and the $7$ will become $6$ because we borrowed $1$ from it.
As seen below:

Hi! We've encountered a problem!
$6$ is less than $7$ thus we need to borrow $1$ .
So $6$ will become $16$ and $5$ will become 4 because already borrowed $1$from it. We'll obtain the following:

We're done! The result is $1914$.