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Mathematical Reasoning

 

Knowing Multiplication  Patterns
                                            can help you find the product.

 Remember:
Multiplying is just like 'counting by groups'
(ex: Multiplying by 3 is like counting by 3's= 3, 6, 9, 12, etc.)

 

  Examples:

                                Input Multiplying Machine
        Input          X                        =        Output

5              x 

25

4              x 

20

3             x

15

In order to get the answers we got in the Output,
the Input Machine must be x5

This would be an example of a 
                  x5 Multiplying Pattern because                                

5 x 5= 25     (5, 10, 15, 20, 25)  count by 5, five times
4 x 5= 20     (5, 10, 15, 20)        count by 5, four times
3 x 5= 15     (5, 10, 15)              count by 5, three times
          


  Input Multiplying Machine
Input         X                       =       Output

2              x 

4

5              x 

10

8             x 

16

In order to get the answers we got in the Output here,
the Input Machine must be x2

This would be an example of a 
                  x2 Multiplying Pattern because                                

2 x 2= 4     (2, 4)                                  count by 2, two times
5 x 2= 10   (2, 4, 6, 8, 10)                    count by 2, five times
8 x 2= 16   (2, 4, 6, 8, 10, 12, 14, 16)  count by 2, eight times
          

Don't Forget:
Multiplying is just like 'counting by groups'
(ex: Multiplying by 3 is like counting by 3's= 3, 6, 9, 12, etc.)

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