Let us arrange numbers in elementary shapes made up of dots.

Every number can be arranged as a line

The number 2 is shown as

The number 6 can be shown as a rectangle

Similarly , patterns can be observed in numerical representation too.

Observation of patterns can guide you in simplifying processes. Following are examples of how we can simplify and solve addition, subtraction problems:

(a) 117 + 9 = 117 + 10 – 1 = 127 – 1 = 126

(b) 117 – 9 = 117 – 10 + 1 = 107 + 1 = 108

(c) 117 + 99 = 117 + 100 – 1 = 217 – 1 = 216

(d) 117 – 99 = 117 – 100 + 1 = 17 + 1 = 18