Show that the commutative property of whole number addition

Show that the commutative property of whole number addition holds for the following examples in other bases by using a different number line for each base.

Solution

a) yes , since

lhs is 7 mod 5 =2

rhs is 7 mod 5 = 2

therefore lhs = rhs hence property holds

b) 12 mod 9 = 3 is lhs

12 mod 9 =3 rhs

therefore lhs = rhs hence property holds