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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

Now add:

    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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