Page 13 - Revised Maths Wisdom Class - 6

Patterns in Mathematics 11

(iv) Pattern by adding even numbers
No. of even numbers
2 + 4 = 6 ⇒ 2 × 3 = 6
Successor of the number of even numbers
2 + 4 + 6 = 12 ⇒ 3 × 4 = 12
2 + 4 + 6 + 8 = 20 ⇒ 4 × 5 = 20

2 + 4 + 6 + 8 + 10 = 30 ⇒ 5 × 6 = 30

Here, the sum of given even numbers is equal to the number of even numbers multiplied by the consecutive
number to it.
Thus, sum of first 11 even numbers = 11 × 12 = 132

2. Patterns in Multiplication
While all multiples of any number form a pattern, there are more interesting patterns as shown below:

1 × 1 = 1
11 × 11 = 121

111 × 111 = 12321
1111 × 1111 = 1234321

3. Patterns in Division
Observe the following patterns.

› 14 ÷ 7 = 2 › 11 ÷ 11 = 1
140 ÷ 7 = 20 121 ÷ 11 = 11
1400 ÷ 7 = 200 1221 ÷ 11 = 111
14000 ÷ 7 = 2000 12221 ÷ 11 = 1111
140000 ÷ 7 = 20000 122221 ÷ 11 = 11111

4. Patterns in Square Numbers
Observe the following,
1 × 1 = 1; 2 × 2 = 4; 3 × 3 = 9; 4 × 4 = 16

A number when multiplied by itself is called a squared number. Geometrically, these numbers form a square as
shown here.
4

3

4

2 3

2

1 dot 4 dots 9 dots 16 dots