Final answer:
Simplifying algebraic expressions involves reducing fractions by dividing both sides by common factors, using logical reasoning analogous to knowing that one half of one half is one quarter, and that a fraction like three thirds simplifies to one.
Step-by-step explanation:
The task is to simplify the expression. The expression given in the question can be interpreted in different parts as (a) ⅓a, (b) ⅔a, (c) ½ a, and (d) ⅓ a. To simplify these expressions, we can use the basic principles of fractions and eliminate terms wherever possible to reduce the expression to its simplest form.
For instance, let's simplify ⅔a (part b). Since one half of one-half is one quarter, and knowing that one half multiplied by two must be one, or that three thirds must be a whole 'one', we can apply this logical reasoning to simplify expressions. In the context of algebraic expressions, this involves dividing both sides by a common factor to reduce the fraction.