Long Division

When starting division, you may be given
simple division problems
that you can do in your head, using mental math.
Those problems would look like this:

You would think to yourself, what number times 9 gives me 27? And your answer would
be 3. However, eventually you will encounter bigger division problems that you cannot
do using mental math. In these cases, you will have to use long division.

For example, you might have a problem that looks like this:

You would re-write the problem so that it looks like this:

In this case, 5 is the divisor (the number we’re dividing by) and it goes on the
outside of the division bar, as shown. 125 is the dividend (the number we’re dividing)
and it goes on the inside of the division bar. The quotient (answer) will eventually
sit on top of the division bar, when we’re done. Right now, the top of the division
bar should be blank because we have not started yet.

Now, we can start our long division. There are four steps of long division; they
are: divide, multiply, subtract, and bring down. Each step will be explained and
shown in a different color in the step-by-step image.

Our first step of long division is to divide. In this step,
we have to ask ourselves how many times the divisor goes into the first number of
the dividend; or, in this case, we ask ourselves how many times we can put 5 into
1. You will notice that we cannot put 5 into 1, because 5 is bigger than one; thus,
our first division results in 0. We write this number on top of the division bar,
above the number we used (in this case, 1). Your problem so far looks like this:

Our next step of long division is to multiply. In this
step, we multiply the divisor (5) by the answer we got to our division (in this
case, 0). We multiply the two numbers together like this: 5 x 0 = 0. We write this
number below the dividend, lining it up with the number we divided.

Our next step of long division is to subtract. In this
step, we subtract our product (answer) from multiplication from the original number
in the dividend. In this case, our problem would be 1 – 0 = 1. We would write the
answer in the column we’ve now made (see diagram below).

Now we move on to our last step, which is to bring down.
In order to bring down, we have to look at the next number in the dividend that
we haven’t worked with yet; in this case, it’s 2. In order to bring down, we draw
an arrow from the number in the dividend down to where we just ended our subtraction,
and we write this number (2) next to the answer from our subtraction (1) to form
a new number (12). This is shown in the diagram below.

Once you bring down the next number, you start this entire process over with division!
In the image below, you’ll see the next set of steps performed, starting with this
division question: how many times can we put 5 into 12? Follow along with the diagrams:

That was a complete step (division, multiplication,
subtraction, and bringing down)
that we just went through! We keep repeating the process until there are no more
numbers to bring down. In this problem, we have one more complete step to go through
before we get our answer. Here’s how to go through the last step:

Notice that when you went to bring down, there were no other numbers after the 5,
so you had nothing to bring down. This means you are done! Your answer is the number
that you have written on top of the division bar. For this problem, our answer is
25, and it is written in red on top of our division bar.

Some people like to have a way to remember the steps to long division, so they’ve
come up with a saying to help you remember the order. The order is:
, Multiply,
, Bring down. The
saying is: Does McDonald’s Sell Burgers? The first letters of this saying match
up with the first letters of the order of long division: DMSB.
If this helps you, feel free to use it to remember; if it confuses you, then don’t
use it—just memorize the steps for long division.

Long Division Examples

Let’s go through one more example like this before we move on. Our new example is:

Let’s re-write the problem using the long division bar, and then follow the steps
to long division (dividemultiplysubtractbring down). Re-read
the steps to the first problem if you’re still having trouble. Here’s the problem
worked out:

Once again, our answer (quotient) is written above the division bar. Ours is written
in red. Both of these problems had quotients of 25, but this will not always be
the case! You could have any number as your quotient for a division problem.

When we have an answer for our division problem, it is easy to go back and check
it. In order to check a division problem, you multiply the quotient (answer) by
the divisor, and your product (answer to the multiplication problem) should be the
same as the dividend.

Here’s the work for checking the last division problem:

We can see that our product, 100, is the same as the dividend, so we know we did
our division correctly.

Now, here’s one for you to try to make sure you get the hang of it!

Long Division Steps

Here’s the problem:

What do we do first?

Bring Down

The correct answer here would be B.

We always start with division, looking at how many times we can put the divisor
into the first digit (or first two digits, if it won’t go into the first digit)
of division.

Our division looks like this:

What do we do next?

Bring Down

The correct answer here would be A.

We always follow division with multiplication, multiplying the divisor by the number
we put at the top of our division problem. In this case, it would be 7 x 1, which
is 7, so we would write 7 underneath the 11.

Now our problem looks like this:

What do we do next?

Bring Down

The correct answer here would be D.

We always follow multiplication with subtraction, so we would subtract 11 – 7.

Now, our problem looks like this:

What do we do next?

Bring Down

The correct answer here would be C.

We always follow subtraction by bringing down the next digit of the dividend, so
we would bring down the 2. Now, the problem looks like this:

Now, we can start over again with division, seeing how many times we can put 7 into
42. The rest of the division is shown here:

Thus, your final answer is 16.

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