f Multiplying in columns by a 2-digit number - Free lesson plan from HomeschoolMath.net
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The ideas in this lesson are taken from Multiplication Division 3 ebook. Only a few examples of each problem type are shown; you should make more problems of each kind for the student.


Multiplying in columns by a 2-digit number
Free lesson plan from HomeschoolMath.net

Multiplying a 2-digit number by a 2-digit number is again based on distributive property.

Let's look at 25 × 34.  To take 25 times a number we can find 20 times the number and 5 times the number, and then add those two, just like 25 times a carrot would be the same as 20 times a carrot AND 5 times a carrot. So 25 × 34 = 20 × 34  +  5 × 34.

You know how to find 5 × 34 - multiply in columns.

Since 20 is 2 × 10, we find that  20 × 34 can be broken down as 10 × 2 × 34.
You know how to find 2 × 34, and 20 × 34 is just 10 times as much - you just tag a zero to the end of the result!

Below is a simplified method for finding 25 × 34.
  

First multiply  5 × 34 Then find 20 × 34. Then add.

2  
34
×   5

170

 
34
×  2

68

Since you really need the result
for 20 × 34, you need to add
an extra zero to the result - 
which is therefore 680.

170
+  680

850


Alternatively you can find 20 × 34 this way:

First put down
that extra zero
that goes
to the end.

34
×   20

0

Then multiply as if you were
doing 2 × 34 (go 2 × 4, 
then 2 × 3). The digits just get
scooted one place because
the zero is already there.

34
×  20

680

 
Another example: 30 × 58.
First put down
that extra zero
that goes
to the end.

58
×   30

0

Then multiply as if you were
doing 3 × 58 (go 3 × 8, carry, 
then 3 × 5 + 2).

2     
58
×  30

1740



Study more examples.  Note you have three separate calculations to do.

34 × 16

First do
4 × 16.
Then do 30 × 16.
Don't forget
the extra zero.
Then add.

2  
16
×  4

64

 

1  2   
16
×  30

480

 
64
+  480

544


The traditional form of the algorithm

The way presented above takes three separate calculations on paper.  In the usual, traditional way all three calculations appear together.

67 × 54

2   
54
×  67

378

  

3   2   
54
×  67

378
3350

 

54
×  67

378
+  3350

3728

Then add.

First multiply  7 × 54
(Pretend the 6 of 
the 67 is not there.)
Then multiply  60 × 54 - but put
the result digits on the line
underneath the 378. Place the
extra zero at the end.  Then
multiply by 6 (pretending 
the 7 is not there).

Study these examples, too.  Note the extra zero placed at the end of the second line!

First do
5 × 34
Then do
20 × 34.
Then add.

2  
34
×  25

170

 
34

×  25

170
680

 
34
×  25

170
+  680

850



Example problems

1.  Multiply.

53
×  12

  

 

 

 

11
×  35

     

 

 

 

38
×  13

 

 

 

 

25
×  38

  

 

 

 

17
×  52

    

 

 

 

44
×  14

 

 

 

 

43
×  18

  

 

 

 

22
×  37

    

62
×  15

 



2.  Word problems.  Write a mathematical sentence for each one.

a.  How many eggs is 15 dozen eggs?

 

b.  The school has 455 pupils.  They all were going to a zoo by buses, and one bus could seat 39 passengers.  Was 11 buses enough to take them all? (Use multiplication!)

 

g.  Andrew saves of his earnings 15 dollars each month.  How much does he have saved at the end of the year?

 

h.  If he wants to by a radio that costs 78 dollars, how many months does he have to save for that?

 

 

3.  Times eleven!  Eleven is 10 + 1.  So using distributive property, anything times eleven is easy.

28 × 11 = 28 × 10 28 × 1

=

280 28 = 308.
45 × 11 = 45 × 10 45 × 1

=

+


4.  Try if you can multiply these in your head (mentally).

 a.  45 × 11 = d.  35 × 11 =
 
e.  20 × 45 = h.  20 × 33 =

 

5.  What is the missing factor?  Be careful with the zeros.

7 × __ = 560

40 × __ = 200

40 × __ = 2000

30 × __ = 360

30 × __ = 3600

40 × __ = 320

10 × __ = 560

100 × __ = 5000

8 × __ = 160

200 × __ = 1600

 

Multiplying a two-digit number by a two-digit number can be broken down into four parts using distributive property:

26 × 89  is first of all 6 × 89 and 20 × 89.

6 × 89 is 6 × 80 and 6 × 9.     20 × 89 is 20 × 80 and 20 × 9.

So all total, 26 × 89 is...  20 × 80 and  20 × 9 and 6 × 80 and 6 × 9  - four parts.

The area of a rectangle is side times side. Where are those four parts represented in this picture?  Can you explain why?

 

 
26
 
←-------- this whole side is 89 --------→
    
   

 

Multiply in Columns

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