PRAXIS ELEMENTARY MATH 5003 150
CORE CURRICULUM SCENARIOS WITH
CORRECT VERIFIED ANSWERS and
HIGHLY DETAILED RATIONALES GRADE
A+ MASTERY BLUEPRINT | 100% PASS
GUARANTEE [INSTANT DOWNLOAD]
PRAXIS Mathematics Subtest (5003) Examination
1. Which of the following numbers satisfies both conditions:
it is a multiple of 6 and a factor of 84?
A) 14
B) 18
C) 28
D) 42
Correct Answer: D
Rationale: To be a multiple of 6, the number must be
divisible by 6. Testing the options, 42 divided by 6 equals
7 (a whole number). To be a factor of 84, 84 divided by
the number must equal a whole number. 84 divided by 42
equals 2. Thus, 42 fulfills both numerical conditions
perfectly.
2. A elementary teacher asks her students to find the value of
the expression 4 + 3 × (8 - 2)² ÷ 4. According to the
standard order of operations (PEMDAS), what is the
correct value?
A) 13
B) 31
C) 40
D) 63
Correct Answer: B
Rationale: First, evaluate parentheses: (8 - 2) = 6.
, Next, apply exponents: 6² = 36. Substitute back into the
expression: 4 + 3 × 36 ÷ 4. Perform multiplication and
division from left to right: 3 × 36 = 108, then 108 ÷ 4 =
27. Finally, perform addition: 4 + 27 = 31.
3. Which of the following property descriptions matches the
statement 5 × (4 + 9) = (5 × 4) + (5 × 9)?
A) Associative Property of Addition
B) Commutative Property of Multiplication
C) Distributive Property of Multiplication over Addition
D) Identity Property of Multiplication
Correct Answer: C
Rationale: The Distributive Property states that
multiplying a sum by a number is the same as
multiplying each addend by the number and then adding
the products together. The structural expression clearly
demonstrates the number 5 being distributed to both 4
and 9.
4. A student subtracts two fractions: \(\frac{7}{8} -
\frac{1}{3}\). What is the correct simplified value of this
difference?
A) \(\frac{6}{5}\)
B) \(\frac{13}{24}\)
C) \(\frac{2}{3}\)
D) \(\frac{17}{24}\)
Correct Answer: B
Rationale: To subtract fractions, find a common
denominator. The least common multiple of 8 and 3 is 24.
Convert both fractions: \(\frac{7}{8} = \frac{7 \times
3}{8 \times 3} = \frac{21}{24}\), and \(\frac{1}{3} =
\frac{1 \times 8}{3 \times 8} = \frac{8}{24}\). Subtract
the numerators over the common denominator:
\(\frac{21 - 8}{24} = \frac{13}{24}\).
,5. An educational assessment records a raw score of 0.375.
How is this decimal value correctly represented when
converted into its simplest fractional form?
A) \(\frac{3}{7}\)
B) \(\frac{37}{100}\)
C) \(\frac{3}{8}\)
D) \(\frac{375}{10}\)
Correct Answer: C
Rationale: The decimal 0.375 can be written as the
fraction \(\frac{375}{1000}\). To simplify to lowest
terms, divide both the numerator and denominator by
their greatest common factor, which is 125. 375 ÷ 125 = 3,
and 1000 ÷ 125 = 8. This yields the simplified fraction
\(\frac{3}{8}\).
6. If a classroom bookshelf contains x fiction books, and the
number of non-fiction books is 5 more than three times
the number of fiction books, which algebraic expression
represents the total number of books on the shelf?
A) 3x + 5
B) 4x + 5
C) 3(x + 5)
D) 4x - 5
Correct Answer: B
Rationale: The number of fiction books is x. The
number of non-fiction books is represented by the
expression 3x + 5. To find the total book count, combine
the two expressions together: Total = x + (3x + 5) = 4x +
5.
7. Solve the linear equation for the unknown variable y: 3(y -
4) = 2y + 5. What is the value of y?
A) y = 1
B) y = 9
C) y = 12
, D) y = 17
Correct Answer: D
Rationale: First, distribute the 3 on the left side of the
equation: 3y - 12 = 2y + 5. Next, isolate the variable y by
subtracting 2y from both sides: y - 12 = 5. Finally, add 12
to both sides to find the solution: y = 17.
8. A map utilizes a scale where 0.5 inches represents an
actual distance of 12 miles. If two towns are separated on
the map by a distance of 3.5 inches, what is the actual
physical distance between them in miles?
A) 42 miles
B) 70 miles
C) 84 miles
D) 96 miles
Correct Answer: C
Rationale: Set up a proportion where \(\frac{0.5 \text{
inches}}{12 \text{ miles}} = \frac{3.5 \text{ inches}}{M
\text{ miles}}\). Cross-multiply to solve for M: 0.5 × M =
12 × 3.5, which simplifies to 0.5M = 42. Divide both sides
by 0.5 to find M: M = 42 ÷ 0.5 = 84 miles.
9. A local electronic retail store slashes the original price of a
tablet by 20%. If a customer purchases the tablet on sale
for $160, what was the original retail price of the tablet
before the discount?
A) $192
B) $200
C) $240
D) $320
Correct Answer: B
Rationale: A 20% discount means the customer paid
80% of the original price. Let P represent the original
price. The scenario can be written as 0.80 × P = 160.
CORE CURRICULUM SCENARIOS WITH
CORRECT VERIFIED ANSWERS and
HIGHLY DETAILED RATIONALES GRADE
A+ MASTERY BLUEPRINT | 100% PASS
GUARANTEE [INSTANT DOWNLOAD]
PRAXIS Mathematics Subtest (5003) Examination
1. Which of the following numbers satisfies both conditions:
it is a multiple of 6 and a factor of 84?
A) 14
B) 18
C) 28
D) 42
Correct Answer: D
Rationale: To be a multiple of 6, the number must be
divisible by 6. Testing the options, 42 divided by 6 equals
7 (a whole number). To be a factor of 84, 84 divided by
the number must equal a whole number. 84 divided by 42
equals 2. Thus, 42 fulfills both numerical conditions
perfectly.
2. A elementary teacher asks her students to find the value of
the expression 4 + 3 × (8 - 2)² ÷ 4. According to the
standard order of operations (PEMDAS), what is the
correct value?
A) 13
B) 31
C) 40
D) 63
Correct Answer: B
Rationale: First, evaluate parentheses: (8 - 2) = 6.
, Next, apply exponents: 6² = 36. Substitute back into the
expression: 4 + 3 × 36 ÷ 4. Perform multiplication and
division from left to right: 3 × 36 = 108, then 108 ÷ 4 =
27. Finally, perform addition: 4 + 27 = 31.
3. Which of the following property descriptions matches the
statement 5 × (4 + 9) = (5 × 4) + (5 × 9)?
A) Associative Property of Addition
B) Commutative Property of Multiplication
C) Distributive Property of Multiplication over Addition
D) Identity Property of Multiplication
Correct Answer: C
Rationale: The Distributive Property states that
multiplying a sum by a number is the same as
multiplying each addend by the number and then adding
the products together. The structural expression clearly
demonstrates the number 5 being distributed to both 4
and 9.
4. A student subtracts two fractions: \(\frac{7}{8} -
\frac{1}{3}\). What is the correct simplified value of this
difference?
A) \(\frac{6}{5}\)
B) \(\frac{13}{24}\)
C) \(\frac{2}{3}\)
D) \(\frac{17}{24}\)
Correct Answer: B
Rationale: To subtract fractions, find a common
denominator. The least common multiple of 8 and 3 is 24.
Convert both fractions: \(\frac{7}{8} = \frac{7 \times
3}{8 \times 3} = \frac{21}{24}\), and \(\frac{1}{3} =
\frac{1 \times 8}{3 \times 8} = \frac{8}{24}\). Subtract
the numerators over the common denominator:
\(\frac{21 - 8}{24} = \frac{13}{24}\).
,5. An educational assessment records a raw score of 0.375.
How is this decimal value correctly represented when
converted into its simplest fractional form?
A) \(\frac{3}{7}\)
B) \(\frac{37}{100}\)
C) \(\frac{3}{8}\)
D) \(\frac{375}{10}\)
Correct Answer: C
Rationale: The decimal 0.375 can be written as the
fraction \(\frac{375}{1000}\). To simplify to lowest
terms, divide both the numerator and denominator by
their greatest common factor, which is 125. 375 ÷ 125 = 3,
and 1000 ÷ 125 = 8. This yields the simplified fraction
\(\frac{3}{8}\).
6. If a classroom bookshelf contains x fiction books, and the
number of non-fiction books is 5 more than three times
the number of fiction books, which algebraic expression
represents the total number of books on the shelf?
A) 3x + 5
B) 4x + 5
C) 3(x + 5)
D) 4x - 5
Correct Answer: B
Rationale: The number of fiction books is x. The
number of non-fiction books is represented by the
expression 3x + 5. To find the total book count, combine
the two expressions together: Total = x + (3x + 5) = 4x +
5.
7. Solve the linear equation for the unknown variable y: 3(y -
4) = 2y + 5. What is the value of y?
A) y = 1
B) y = 9
C) y = 12
, D) y = 17
Correct Answer: D
Rationale: First, distribute the 3 on the left side of the
equation: 3y - 12 = 2y + 5. Next, isolate the variable y by
subtracting 2y from both sides: y - 12 = 5. Finally, add 12
to both sides to find the solution: y = 17.
8. A map utilizes a scale where 0.5 inches represents an
actual distance of 12 miles. If two towns are separated on
the map by a distance of 3.5 inches, what is the actual
physical distance between them in miles?
A) 42 miles
B) 70 miles
C) 84 miles
D) 96 miles
Correct Answer: C
Rationale: Set up a proportion where \(\frac{0.5 \text{
inches}}{12 \text{ miles}} = \frac{3.5 \text{ inches}}{M
\text{ miles}}\). Cross-multiply to solve for M: 0.5 × M =
12 × 3.5, which simplifies to 0.5M = 42. Divide both sides
by 0.5 to find M: M = 42 ÷ 0.5 = 84 miles.
9. A local electronic retail store slashes the original price of a
tablet by 20%. If a customer purchases the tablet on sale
for $160, what was the original retail price of the tablet
before the discount?
A) $192
B) $200
C) $240
D) $320
Correct Answer: B
Rationale: A 20% discount means the customer paid
80% of the original price. Let P represent the original
price. The scenario can be written as 0.80 × P = 160.
