CLASSROOM EXAMPLE
SOLUTIONS
BEVERLY FUSFIELD
COLLEGE ALGEBRA
THIRTEENTH EDITION
Margaret L. Lial
American River College
John Hornsby
University of New Orleans
David I. Schneider
University of Maryland
Callie J. Daniels
St. Charles Community College
ISBN-13: 978-0-13-597882-5
ISBN-10: 0-13-597882-3
,taxation.---### Overview of Business Entities#### 1. Types of Business EntitiesBusiness
entities can be categorized based on ownership structure and tax treatment. Understanding
these types is crucial for determining tax obligations and benefits.- **Sole Proprietorships**:
- Owned by a single individual, this is the simplest form of business entity. Income is reported
on the owner’s personal tax return (Form 1040, Schedule C), which simplifies tax filing but
also means personal liability for debts and obligations.- **Partnerships**: - Consisting of
two or more individuals, partnerships do not pay federal income taxes. Instead, they are
considered pass-through entities, meaning income is taxed at the partners' individual rates.
Form 1065 is used to report partnership income, while partners receive Schedule K-1 to
report their share on their returns.- **Corporations**: - Corporations are separate legal
entities that provide limited liability protection to their owners (shareholders). C-
Corporations face double taxation: once at the corporate level on profits and again at the Classroom Example 4 (page 4)
individual level when dividends are distributed. S-Corporations, on the other hand, are pass-
through entities but have restrictions on ownership and number of shareholders.- **Limited
Liability Companies (LLCs)**: - LLCs combine the flexibility of partnerships with the
liability protection of corporations. An LLC can choose to be taxed as a sole proprietorship,
partnership, or corporation, allowing for strategic tax planning. ### 2. Tax Implications of
Each Entity TypeUnderstanding the tax implications of each entity type is critical for effective
business planning.- **Sole Proprietorships**: - Income is taxed at the owner’s individual tax
rate. All profits and losses are reported on the owner’s tax return. This simplicity, however,
can expose owners to significant personal risk.- **Partnerships**: - Each partner reports
their share of income and losses on their personal returns, allowing for loss deductions.
Partners are also subject to self-employment taxes on their share of the income, which can
significantly impact tax liability.- **Corporations**: - C-Corporations are taxed at the
corporate tax rate (currently 21%). Dividends are taxed again at the shareholder level. S-
Corporations avoid double taxation, but there are restrictions on the number and type of
shareholders.- **Limited Liability Companies (LLCs)**: - By default, single-member LLCs
are treated as sole proprietorships for tax purposes, while multi-member LLCs are treated as
partnerships. However, they can elect to be taxed as a corporation if beneficial.### Key Tax
Concepts#### 1. Income RecognitionIncome recognition is a fundamental principle in
taxation, determining when income must be reported.- **Cash vs. Accrual Accounting**: -
Businesses can choose between cash and accrual methods. Cash accounting recognizes income
when received and expenses when paid, making it straightforward. Accrual accounting
recognizes income when earned and expenses when incurred, aligning revenue with the
period it relates to, but can complicate cash flow management.#### 2. DeductionsDeductions
reduce taxable income, directly impacting tax liability.- **Ordinary and Necessary
Expenses**: - The IRS allows deductions for expenses that are ordinary (common in the
industry) and necessary (helpful and appropriate for the business). Common deductions
include rent, utilities, salaries, and professional fees.- **Limits on Deductions**: - Certain
expenses, such as meals and entertainment, have specific limits (e.g., meals are typically only
50% deductible). Understanding these limits is vital for effective tax planning.#### 3. Tax
CreditsTax credits directly reduce the tax liability, providing a dollar-for-dollar reduction of
taxes owed.- **Types of Tax Credits**: - Examples include the Research and Development
(R&D) tax credit, which encourages innovation, and the Work Opportunity Tax Credit
(WOTC) for hiring individuals from certain target groups.### Specific Business Entity
Taxation#### 1. PartnershipsPartnerships are a popular choice for many businesses due to
their flexible structure.- **Pass-Through Taxation**: - Income is reported on individual
partners’ returns, preventing double taxation. However, partners must pay self-employment
taxes on their earnings.- **Distributions and Basis**: - When a partner receives a
distribution, it is generally tax-free to the extent of their basis in the partnership.
Understanding how basis is calculated
Chapter R
Review of Basic Concepts
Section R.1 Fractions, Decimals, and
Percents 5 18 5 18 Multiply numerators.
=
9 25 9 25 Multiply denominators.
Classroom Example 1 (page 2)
90
12 3 4 3 4 3 3 = Multiply.
(a) = = = 1= 225
20 5 4 5 4 5 5 2 45 The greatest common factor
=
5 45 of 90 and 225 is 45.
8 1 8 1 1 2
(b) = = 1= = 2 45 2 2
48 6 8 6 6 5 5 45 5 5
90 5 18 5 18 5 5
(c) = = = 1= Classroom Example 5 (page 4)
162 9 18 9 18 9 9
Another strategy is to choose any common 9 3 9 5 Multiply by 53 , the
(a) =
factor and work in stages. 10 5 10 3 reciprocal of 53 .
90 10 9 5 2 9 5 5 9 5 Multiply numerators.
= = = 1= =
162 18 9 9 2 9 9 9 10 3 Multiply denominators.
45
Classroom Example 2 (page 3) =
30
To write 37
as a mixed number, divide the 3 15 The greatest common factor
10 = 2 15
of 45 and 30 is 15.
numerator by the denominator.
7 → Quotient = 3 or 1 1
Denominator → 8 59 → Numerator 2 2
56 3 1 11 10 Write the mixed numbers
(b) 2 3 =
3 → Remainder 4 3 4 3 as improper fractions.
37 7 11 3 Multiply by 3 , the
=3 Classro
Example 3 (page 3)
10 10
om
,To write 3 4 as an improper fraction, multiply the = 10
10
5
4 10 reciprocal of 3
.
11 3
= Multiply.
4 10
33
= Lowest terms
denominator of the fraction by the natural number, 40
and then add the numerator to obtain the numerator Classroom Example 6 (page 5)
of the improper fraction: 5 3 = 15 and 15 + 4 = 19
The denominator of the improper fraction is the same 1 5 1+ 5 Add numerators.
(a) + =
as the denominator in the mixed number, 5. 9 9 9 Keep same denominator.
4 5 3 + 4 19 6
3 = = =
5 5 5 9
2
= Write in lowest terms.
3
Copyright © 2021 Pearson Education, Inc. 1
, 2
30 3 = 90 and 42.830
7 2 7 3 2 2
(b) + = + 45 2 = 90, so the 71.000
30 45 30 3 45 2 LCD = 90. + 3.074
Write equivalent 116.904
21 4 fractions with the
= + 32.50
90 90 common
denominator. (b) – 21.72
25 Add numerators 10.78
= Keep the same
90 denominator. Classroom Example 9 (page 8)
5 Write in lowest (a) 30.2 has one decimal place, and 0.052 has
= three decimal places, so the product has four
18 terms.
decimal places.
10 2 = 20 and
3 1 3 2 1 5 30.2
(c) – = – 4 5 = 20, so the
10 4 10 2 4 5 0.052
LCD = 20.
604
Write equivalent
1510
6 5 fractions with the
= – 1.5704
20 20 common
denominator. (b) 0.06 has two decimal places, and 0.12 has two
Subtract numerators decimal places, so the product has four
1
= Keep the same decimal places.
20
denominator. 0.06
Write each mixed
0.12
3 1 27 3 12
(d) 3 –1 = – number as an
8 2 8 2 6
improper fraction.
27 3 4 0.0072
= – The LCD is 8.
8 2 4
(c) 0.37 5.476
Write equivalent
27 12 Move each decimal point two places to the
= – fractions with the
8 8 common right.
denominator. 14.8
15
= Subtract. Write as a 37 547.6
8 mixed number. 37
177
Classroom Example 7 (page 7) 148
15 29 6
(a) 0.15 =
29 6
100
0
9
(b) 0.009 =
1000 (d) 3.1 3.76
5 25 Move each decimal point one place to the
(c) 2.5 = 2 = right.
10 10
1.21
Classroom Example 8 (page 7) 31 37.60
(a) 42.83 + 71 + 3.074 31
Place the digits of the decimal numbers in 66
columns by place value. Attach zeros as 62
placeholders. 40
31
9
(continued on next page)
