David O’Bryan, Ph.D., CPA, CMA, CFM, CFE

Becky Casey, MBA, CPA

Cynthia Woodburn, Ph.D.

The purpose of this teaching note is to provide a formal linkage between the algebra of the accounting equation and the double entry system utilizing debit and credit rules. Instructors may find this material useful in helping their students understand the logical and mathematical foundation for the debit and credit rules. This material is especially helpful for students who want to understand “why” – not just “how.”

**The Algebra
Underlying Account Rules: A Teaching
Note:**

David O’Bryan,
Ph.D., CPA, CMA, CFM, CFE*

Associate
Professor and Chairperson

Department of
Accounting, Kelce College of Business

Pittsburg State
University, Pittsburg, Kansas 66762

Email:
obryan@pittstate.edu Voice: (620)
235-4566 Fax: (620) 235-4558

Becky Casey,
MBA, CPA

Instructor

Pittsburg State
University

Cynthia
Woodburn, Ph.D.

Associate
Professor

Pittsburg State University

*Contact
Author

** **

One of the most
awkward points in teaching financial or intermediate accounting is
transitioning to the double entry system utilizing debit and credit rules. User oriented financial accounting textbooks
commonly use an algebraic approach by recording increases and decreases with
pluses and minuses. At some point, if
not in financial accounting, certainly in intermediate accounting, the
instructor needs to transition to the debit and credit approach used by
practitioners.

For an instructor, this can be frustrating. Some students who were doing very well using the algebraic approach become quite confused by the debit and credit approach. These students fail to see the equivalency of the two approaches. Instead, they view the debit and credit approach as an entirely new method of recording transactions.

This should not
be surprising. The equivalency of the
two approaches is not transparent.
Textbooks generally begin with the accounting equation, followed by the
t-accounts and debit and credit rules.
A formal and explicit linkage between the accounting equation and the
debit and credit rules is not found in any published introductory or
intermediate financial accounting textbook.
In the absence of a formal connection,
students memorize account rules but may fail to realize the underlying reason
for them.

The purpose of
this short teaching note is to provide instructors a concise linkage between
the accounting equation and the debit and credit account rules. In four short steps an instructor can
demonstrate to students that the debit and credit account rules are a direct
derivation of the algebra of the accounting equation. This material provides an instructor with a mathematical
foundation for the account rules rather than the ad hoc, leap-of-faith approach
provided in textbooks. In addition,
students can use the approach to derive the account rules rather than memorize
them. For instructors who stress
understanding over memorization, this approach may be attractive.

This
section describes a method to link the accounting equation to the debit and
credit account rules. First, start with
the basic accounting equation:

+ A = + L + E (1)

where
A = assets, L = liabilities, and E = stockholders’ equity.

Second, allow
for either an increase or a decrease in each element:

+ A - A = + L - L + E - E (2)

Third, rearrange the terms by putting all terms to the left of the equals sign. From basic algebra, remember to switch the sign of elements being moved from the right to the left side. Arrange the terms so that the positive-signed component of each element is listed first followed by its respective negative-signed component:

+ A - A + L - L + E - E = 0 (3)

Now, visualize a “t-account” beneath each element of the accounting equation, with the positive-signed component appearing on the left-hand side of the t-account and the negative-signed component appearing in the right-hand side of the t-account:

The
mathematical connection between the accounting equation and the double-entry
system is now apparent from equation (4).
The left-hand, or debit, side of the t-account is simply for the terms with positive signs
in equation (4). Likewise,
the right-hand, or credit, side of the t-account is for the terms with negative
signs in equation (4).

An alternative
approach is to begin with equation (3) and group like-signed terms together.
Then visualize two columns beneath this equation; a column for the
positive-signed terms and a column for the negative-signed terms:

Equation (5) complements equation (4) and reinforces the concept that the
algebraic sign of each term determines whether it is a debit or credit.
That is, the account rules flow directly from the underlying algebra
of the accounting equation.

This teaching approach may be attractive to instructors who want their students to understand the logic of the account rules. In fact, it is an open question how many practitioners truly understand the mathematical foundation for the debit and credit rules. Students and practitioners can no doubt survive and prosper without understanding this linkage. However, the account rules are so fundamental to our profession that it seems as though we would want to understand “why” – not just “how.”