When we are familiar with the treatment of quantities by equations, we may ignore the units and deal solely with numbers; and (ii.) (a) and (ii.) (b) may then, by the commutative law for multiplication, be regarded as identical.

This is due to the fact that there are really two kinds of subtraction, respectively involving counting forwards (complementary addition) and counting backwards (ordinary subtraction); and it suggests that it may be wise not to use the one symbol - to represent the result of both operations until the commutative law for addition has been fully grasped.

May be regarded as resulting from the commutative law for addition and subtraction.

View more

Division.-From the commutative law for multiplication, which shows that 3 X 4d.