Test Bank for Elementary & Intermediate Algebra: Concepts and Applications | 200+ Practice Questions with Verified Answers & Rationales | Real Numbers, Linear Equations & Inequalities, Graphing, Systems of Equations, Exponents & Polynomials, Factoring, Ra

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**TEST BANK – ELEMENTARY &
INTERMEDIATE ALGEBRA: CONCEPTS AND
APPLICATIONS (200+ QUESTIONS WITH
RATIONALES)**



# SECTION 1: REAL NUMBERS AND BASIC OPERATIONS
(Questions 1–20)


**1.** Simplify: \( |-8| - | -3 | \)
A) 5
B) 11
C) -5
D) -11


**Correct Answer:** A – 5
**Rationale:** The absolute value of -8 is 8, and the absolute value of -
3 is 3. Thus, \( 8 - 3 = 5 \).


**2.** Evaluate: \( 3^2 + 4 \times 2 - 5 \)
A) 12
B) 14
C) 20

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D) 21


**Correct Answer:** A – 12
**Rationale:** Follow order of operations (PEMDAS). First, \( 3^2 = 9
\). Then multiplication: \( 4 \times 2 = 8 \). So \( 9 + 8 - 5 = 12 \).


**3.** Simplify: \( \frac{3}{4} + \frac{2}{3} \)
A) \( \frac{5}{7} \)
B) \( \frac{17}{12} \)
C) \( \frac{6}{12} \)
D) \( \frac{1}{2} \)


**Correct Answer:** B – \( \frac{17}{12} \)
**Rationale:** Find common denominator 12. \( \frac{3}{4} =
\frac{9}{12} \), \( \frac{2}{3} = \frac{8}{12} \). \( \frac{9}{12} +
\frac{8}{12} = \frac{17}{12} \).


**4.** Simplify: \( \frac{5}{6} \times \frac{2}{3} \)
A) \( \frac{10}{18} \)
B) \( \frac{5}{9} \)
C) \( \frac{7}{9} \)
D) \( \frac{10}{9} \)

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**Correct Answer:** B – \( \frac{5}{9} \)
**Rationale:** Multiply numerators: \( 5 \times 2 = 10 \). Multiply
denominators: \( 6 \times 3 = 18 \). Reduce: \( \frac{10}{18} =
\frac{5}{9} \).


**5.** Simplify: \( \frac{7}{8} \div \frac{3}{4} \)
A) \( \frac{21}{32} \)
B) \( \frac{28}{24} \)
C) \( \frac{7}{6} \)
D) \( \frac{21}{8} \)


**Correct Answer:** C – \( \frac{7}{6} \)
**Rationale:** Dividing by \( \frac{3}{4} \) is multiplying by its
reciprocal \( \frac{4}{3} \). \( \frac{7}{8} \times \frac{4}{3} =
\frac{28}{24} = \frac{7}{6} \).


**6.** What is the value of \( \frac{5}{8} \) as a decimal and percent?
A) 0.625, 62.5%
B) 0.625, 6.25%
C) 0.625, 0.625%
D) 0.625, 625%


**Correct Answer:** A – 0.625, 62.5%

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**Rationale:** \( \frac{5}{8} = 0.625 \). To convert to percent, multiply
by 100: \( 0.625 \times 100 = 62.5\% \).


**7.** Simplify: \( (-4) + (-7) \)
A) 11
B) -11
C) 3
D) -3


**Correct Answer:** B – -11
**Rationale:** Adding two negative numbers: keep the negative sign
and add absolute values. \( 4 + 7 = 11 \), so result is -11.


**8.** Simplify: \( -5 - (-9) \)
A) -14
B) 4
C) -4
D) 14


**Correct Answer:** B – 4
**Rationale:** Subtracting a negative is adding a positive: \( -5 - (-9) =
-5 + 9 = 4 \).