Math:  Multiplication - Tutorial
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4 written 3 times      4 + 4 + 4  = 12

                            or

3 written 4 times      3 + 3 + 3 + 3 = 12
(factor)
(factor)
(product)
  4
x 3   12
The commutative property says that changing the order of the factors in a multiplication sentence does not change the product. 

So,




Commutative Property
A multiplication sentence can be written horizontally or vertically as shown below:
4 x 3 = 12
(factor)
(factor)
(product)
  4
x 3 
and
(factor)
(factor)
(product)
  3
x 4
Annexing Zeroes
(factor)
(factor)
(product)
Annexing zeros is a quick way of multiplying by 10, 100, 1,000, and so on. Count the number of  zeros in the first factor. Then place that amount of zeros at the end of the product. 

For example:     
Multiples are the products of multiplication facts. 

For example:

To find the multiples of 4, multiply 4 times all of the numbers from 1 to 9

Find the multiples of 4:





Therefore,   1 x 4 = 4      2 x 4 = 8 
    3 x 4 = 12   4 x 4 = 16  and so on.

Multiples
Multiplying Single and Double Digit  Factors 
Example 1: Multiply two single digit factors.
5 x 4 = 20     Write the zero. Carry or regroup the 2 to the                        tens place.


4 x 2 + 2 = 10    Write 10 in the hundreds place.
The product is 20.
Example 2: Multiply a double digit and a single digit factor. 
The first partial product is 100.
5 x 4 = 20
Multiplication is a short way of adding or counting numbers. 
Flashcards: click here

Timed Multiplication Drill:  click here
Just for Practice
A Closer Look
Mutliplication Facts Printout: click here

Extra Study Help:  click here

Lessons:  click here

Math Homepage:  click here


Some Helpful Tools
12
12
Step 2:
2 x 5 = 10    Write the 0. Carry or regroup the 1 to the                            tens place and place it above the 2. 
2 x 2 + 1 = 5    Write the 5 in the hundreds place.
The product is 600.
The product is 100.


Example 3: Multiply two double digit factors.
5 x 4 = 20     Write the zero. Carry or regroup the 2 to the                        tens place.


4 x 2 + 2 = 10    Write 10 in the hundreds place.
Step 1:
Step 3:   Add both partial products 100 and 50 together.
The second partial product is 50.
The last zero in the first partial product 100 is written in the ones
place because 4 is in the ones place.

The last zero in the second partial product 50 is written in the tens place
because 2 in the tens place.

If we were multiplying triple-digit factors, the last digit in the third partial product would be written in the hundreds place, and so on.
Hint: