NES ELEMENTARY EDUCATION
COMPREHENSIVE EXAM 2026 QUESTIONS
AND ANSWERS 100% CORRECT
◉ Whole natural numbers together with zero. Answer: W = {0, 1, 2, 3,
4, 5, 6, . . . }
◉ Every whole number has a unique opposite or negative whose sum
with it is 0. For example,. Answer: 2 + (-2) = 0
◉ The set of integers consists of the whole numbers and their opposites.
Answer: Z = {. . ., -3, -2, -1, 0, 1, 2, 3, . . . }
◉ Every nonzero integer has a unique reciprocal whose product with it
is one. For example,. Answer: 2 × 1/2 = 1
◉ The ratio or fraction of one integer to a nonzero integer is the product
of the first integer with the reciprocal of the second. For example, the
ratio of 2 to 3 is. Answer: 2/3 = 2 × 1/3
◉ not every rational number is an integer. For example, 1/2 is a rational
number that is not an integer. Answer: 1/2 = 0.5
,◉ There are three basic properties of addition:. Answer: commutativity,
associativity and identity.
◉ Commutative property. Answer: When adding two numbers, the sum
is the same regardless of the order in which the numbers are added.
2+3=3+2
◉ Associative property. Answer: When adding three or more numbers,
the sum is the same regardless of the way in which the numbers are
grouped.
2 + (3 + 5) = (2 + 3) + 5
◉ Identity property. Answer: Adding zero to a number does not change
it.
2+0=2
◉ There are three basic properties of multiplication:. Answer:
commutativity, associativity and identity.
, ◉ Distributive property. Answer: The product of a number with a sum
equals the sum of the products of the number with each term of the sum.
2 × (3 + 5) = (2 × 3) + (2 × 5)
◉ Exponentiation. Answer: Exponentiation is repeated multiplication.
An exponent is often called a power. For example, the third power of 2
is
2³ = 2 × 2 × 2 = 8
◉ We define the zero power of any nonzero number to be 1. For
example,. Answer: (-3)0 = 1
◉ A negative exponent indicates a reciprocal. For example,. Answer: 2
(-3rd power) = (3rd power) =
◉ The first power of any number is itself. For example,. Answer: 2 (to
the 1st power) = 2
◉ To multiply like bases with exponents, add the exponents. For
example,. Answer: 2 (to the 3rd) x 2 (to the 5th) = 2 (to the eighth)
◉ To exponentiate a power, multiply the exponents. For example,.
Answer: (2 to the 3rd) to the 5th = 2 to the 15th
COMPREHENSIVE EXAM 2026 QUESTIONS
AND ANSWERS 100% CORRECT
◉ Whole natural numbers together with zero. Answer: W = {0, 1, 2, 3,
4, 5, 6, . . . }
◉ Every whole number has a unique opposite or negative whose sum
with it is 0. For example,. Answer: 2 + (-2) = 0
◉ The set of integers consists of the whole numbers and their opposites.
Answer: Z = {. . ., -3, -2, -1, 0, 1, 2, 3, . . . }
◉ Every nonzero integer has a unique reciprocal whose product with it
is one. For example,. Answer: 2 × 1/2 = 1
◉ The ratio or fraction of one integer to a nonzero integer is the product
of the first integer with the reciprocal of the second. For example, the
ratio of 2 to 3 is. Answer: 2/3 = 2 × 1/3
◉ not every rational number is an integer. For example, 1/2 is a rational
number that is not an integer. Answer: 1/2 = 0.5
,◉ There are three basic properties of addition:. Answer: commutativity,
associativity and identity.
◉ Commutative property. Answer: When adding two numbers, the sum
is the same regardless of the order in which the numbers are added.
2+3=3+2
◉ Associative property. Answer: When adding three or more numbers,
the sum is the same regardless of the way in which the numbers are
grouped.
2 + (3 + 5) = (2 + 3) + 5
◉ Identity property. Answer: Adding zero to a number does not change
it.
2+0=2
◉ There are three basic properties of multiplication:. Answer:
commutativity, associativity and identity.
, ◉ Distributive property. Answer: The product of a number with a sum
equals the sum of the products of the number with each term of the sum.
2 × (3 + 5) = (2 × 3) + (2 × 5)
◉ Exponentiation. Answer: Exponentiation is repeated multiplication.
An exponent is often called a power. For example, the third power of 2
is
2³ = 2 × 2 × 2 = 8
◉ We define the zero power of any nonzero number to be 1. For
example,. Answer: (-3)0 = 1
◉ A negative exponent indicates a reciprocal. For example,. Answer: 2
(-3rd power) = (3rd power) =
◉ The first power of any number is itself. For example,. Answer: 2 (to
the 1st power) = 2
◉ To multiply like bases with exponents, add the exponents. For
example,. Answer: 2 (to the 3rd) x 2 (to the 5th) = 2 (to the eighth)
◉ To exponentiate a power, multiply the exponents. For example,.
Answer: (2 to the 3rd) to the 5th = 2 to the 15th
