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### Multiplying Two-Digit Numbers

```
Date: 06/04/98 at 09:33:00
From: Rosalind
Subject: Times tables

I get stuck on multiplying 2-digit numbers like 39 x 98.
```

```
Date: 06/08/98 at 12:35:52
From: Doctor Fred
Subject: Re: Times tables

It can help if you think about what multiplication is. For instance,
2 x 3 means you have 2 groups of 3 things. 4 x 8 would mean you have 4
groups of 8 things each. So 39 x 98 means you have 39 groups of 98
things each.

We want to find out how many things (let's call them balls) we have.
Counting 39 groups of 98 balls each is the same thing as counting the
first 30 groups of 98 balls and then counting the other 9 groups of 98
balls.

Let's first look at the 9 groups of 98 balls. That would mean we need
to do 9 x 98. That is:

98
x 9
----

First find that 9 x 8 is 72, and then write down the 2 in the ones
place and carry the 7 to the tens place. This gives us:

7
98
x 9
----
2

Now, we do the tens place. 9 x 9 gives 81, plus the other 7 from the
first part. This gives us:

7
98
x 9
----
882

Now let's look at 30 x 98. You probably remember that multiplying a
number by 10 can be done by just adding a 0 at the end of the number,
for example, 10 x 13 = 130. The same thing works with 30 times
something. We can do it by just multiplying by 3 and then adding a 0
at the end of the answer. So:

98
x 3
----

First find that 3 x 8 is 24, and then write down the 4 in the ones
place and carry the 2 to the tens place:

2
98
x 3
----
4

Then, 3 x 9 = 27 plus the other 2 gives 29:

2
98
x 3
----
294

Then 30 x 98 = 2940. So our answer is 2940 + 882 = 3822.

Now let's do it again but all in one problem.

98
x 39
----

Again, 9 x 8 is 72. Put the 2 in the ones place and carry the 7 to the
tens place. This gives us:

7
98
x 39
----
2

Then 9 x 9 = 81 plus the 7 gives 88 or:

7
98
x 39
----
882

Doesn't this first part look familiar? Now let's recall that whatever
we get in the other part will get a zero put in at the end. Let's do
that now:

7
98
x 39
----
882
0

Now the 3 x 8 = 24, so write the 4 in the tens column since the ones
place is already filled. Then carry the 2 to the next column:

2
7
98
x 39
----
882
40

Then 3 x 9 is 27 plus the 2 gives 29:

2
7
98
x 39
----
882
2940

2
7
98
x 39
----
882
2940
----
3822

I hope this helps.

-Doctor Fred,  The Math Forum
Check out our web site! http://mathforum.org/dr.math/
```
Associated Topics:
Elementary Multiplication

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