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Patterns in Whole Numbers

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notes

Patterns in Whole Numbers:

1. Every number can be arranged as a line;

The number 2 is shown as 

The number 3 is shown as 

2. Some numbers can be shown also as rectangles.

For example, number 6 can be shown as a rectangle.

Note there are 2 rows and 3 columns.

3. Some numbers like 4 or 9 can also be arranged as squares;

 

4. Some numbers can also be arranged as triangles.

For example,




Patterns with numbers are not only interesting but are useful especially for verbal calculations and help us to understand the properties of numbers better.

Add or subtract numbers of the form 9, 99, 999,…

117 + 99 = 117 + 100 – 1 = 217 – 1 = 216
117 – 99 = 117 – 100 + 1 = 17 + 1 = 18

Multiply a number by numbers of the form 9, 99, 999,…

84 × 9 = 84 × (10 – 1)
84 × 99 = 84 × (100 – 1)
84 × 999 = 84 × (1000 - 1)

Multiplying a number by 5 or 25 or 125.

96 × 5 = 96 × `10/2 = 960/2` = 480
96 × 25 = 96 × `(100)/4 = (9600)/4` = 2400
96 × 125 = 96 × `(1000)/8 = (96000)/8` = 12000......

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