8/3/2019 Tabulate Multiplication Products To Evalute Generalisation ( Odd Numbers )

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Seeking for new generalisationto evaluate the products.

CoffeeMathMethods, Tips & Tricks

Multiplication ofOdd Numbers3, 7 & 9

8/3/2019 Tabulate Multiplication Products To Evalute Generalisation ( Odd Numbers )

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X 3

1 =

2 =3 =4 =5 =6 =

7 =8 =9 =10 =

03

0609121518

2124

2730

The Even Multiplication Table Of 3

Tabulate the

Products as

shown above

Erase the first

digit (black)

andretain thelast digit (red)

03 06 09

12 15 18

21 24 27

3 6 9

2 5 8

1 4 7

8/3/2019 Tabulate Multiplication Products To Evalute Generalisation ( Odd Numbers )

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X 7

1 =

2 =3 =4 =5 =6 =

7 =8 =9 =10 =

07

1421283542

4956

6370

The Even Multiplication Table Of 7

Tabulate the

Product as

shown above

Erase the first

digit (black)

andretain thelast digit (red)

07 14 21

28 35 42

49 56 63

7 4 1

8 5 2

9 6 3

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The Even Multiplication Table Of 9

X 9

1 =

2 =3 =4 =5 =6 =

7 =8 =9 =10 =

09

1827364554

6372

8190

Tabulate the

Product as

shown above

Erase the first

digit (black)

andretain thelast digit (red)

09 18 27

36 45 54

63 72 81

9 8 7

6 5 4

3 2 1

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Time

sTableof3

TimesTableof7

TimesTable

of9

Here are the tabularized last digits of products.

Lets us examine the similarities of the number patterns

3 6 9

2 5 8

1 4 7

7 4 1

8 5 2

9 6 3

9 8 7

6 5 4

3 2 1

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Time

sTableof3

TimesTableof7

TimesTable

of9

Here are the tabularized last digits of products.

Lets us examine the similarities of the number patterns

3 6 9

2 5 8

1 4 7

7 4 1

8 5 2

9 6 3

9 8 7

6 5 4

3 2 1

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Time

sTableof3

TimesTableof7

TimesTable

of9

Here are the tabularized last digits of products.

Lets us examine the similarities of the number patterns

3 6 9

2 5 8

1 4 7

7 4 1

8 5 2

9 6 3

9 8 7

6 5 4

3 2 1

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Here are the tabularized last digits of products.

Lets us examine the similarities of the number patterns

3 6 9

2 5 8

1 4 7

9 8 7

6 5 4

3 2 1

7 4 1

8 5 2

9 6 3Time

sTableof3

TimesTableof7

TimesTable

of9

8/3/2019 Tabulate Multiplication Products To Evalute Generalisation ( Odd Numbers )

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3 6 9

2 5 8

1 4 7

9 8 7

6 5 4

3 2 1

7 4 1

8 5 2

9 6 3Time

sTableof3

TimesTableof7

TimesTable

of9

Lets us rotate the Table of 7 and 9

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Time

sTableof3

TimesTableof7

TimesTable

of9

Lets us rotate every the number ofTable of 7 and 9.

6

7

3

4

5 82

1

9

741

852

963

3 6 9

2 5 8

1 4 7

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Times Table of3

Times Table of9

Times Table of7

Final Result fulfills with

3 6 9

2 5 8

1 4 7

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Now we use this generalisation

to evaluate the products.

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Multiplication of 3

3 6 9

2 5 8

1 4 7

X3

0 0 0

1 1 1

2 2 2

Menu

X 3

X 7

X 9

Click any link

FINISH

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3 6 9

2 5 8

1 4 7

X7

6 5 4

4 3 2

2 1 0

Multiplication of 7

Menu

X 3

X 7

X 9

Click any link

FINISH

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3 6 9

2 5 8

1 4 7

X9

6 3 0

7 4 1

8 5 2

Multiplication of 9

Menu

X 3

X 7

X 9

Click any link

FINISH

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Thanks