NES Elementary Education Subtest 2
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Natural Numbers - ANS N = {1, 2, 3, 4, 5, 6, . . . }
Whole natural numbers together with zero. - ANS 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, -
ANS 2 + (-2) = 0
The set of integers consists of the whole numbers and their opposites. - ANS Z = {. . ., -3, -2,
-1, 0, 1, 2, 3, . . . }
Every nonzero integer has a unique reciprocal whose product with it is one. For example, -
ANS 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 - ANS 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. - ANS 1/2 = 0.5
There are three basic properties of addition: - ANS commutativity, associativity and identity.
Commutative property. - ANS 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. - ANS 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. - ANS Adding zero to a number does not change it.
2+0=2
, There are three basic properties of multiplication: - ANS commutativity, associativity and
identity.
Distributive property. - ANS 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 - ANS 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, - ANS (-3)0 = 1
A negative exponent indicates a reciprocal. For example, - ANS 2 (-3rd power) = (3rd
power) =
The first power of any number is itself. For example, - ANS 2 (to the 1st power) = 2
To multiply like bases with exponents, add the exponents. For example, - ANS 2 (to the 3rd) x 2
(to the 5th) = 2 (to the eighth)
To exponentiate a power, multiply the exponents. For example, - ANS (2 to the 3rd) to the 5th =
2 to the 15th
10 to the 0 power - ANS 1
10 to the 1 power - ANS 10
10 to the -2 power - ANS to the 2 power or
10 to the 2 power x 10 to the 3 power - ANS 10 to the 5 power
Identifying Place Value in Numbers
2045 - ANS 2045 = (2 x 10 to the 3 power) + (0 x 10 to the 2 power) + (4 x 10 to the 1 power) +
5 x 10 to the 0 power)
Digits to the right of a decimal point correspond to negative powers of ten. For example,
23.405 - ANS 23.405 = (2 x 10 to the 1 power) + (3 x 10 to the 0 power) + (4 x 10 to the -1
power) + (0 x 10 to the -2 power) + (5 x 10 to the -3 power)
Converting a fraction to a decimal. For example 3/8 - ANS 3 divided by 8 = 0.375
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Natural Numbers - ANS N = {1, 2, 3, 4, 5, 6, . . . }
Whole natural numbers together with zero. - ANS 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, -
ANS 2 + (-2) = 0
The set of integers consists of the whole numbers and their opposites. - ANS Z = {. . ., -3, -2,
-1, 0, 1, 2, 3, . . . }
Every nonzero integer has a unique reciprocal whose product with it is one. For example, -
ANS 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 - ANS 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. - ANS 1/2 = 0.5
There are three basic properties of addition: - ANS commutativity, associativity and identity.
Commutative property. - ANS 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. - ANS 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. - ANS Adding zero to a number does not change it.
2+0=2
, There are three basic properties of multiplication: - ANS commutativity, associativity and
identity.
Distributive property. - ANS 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 - ANS 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, - ANS (-3)0 = 1
A negative exponent indicates a reciprocal. For example, - ANS 2 (-3rd power) = (3rd
power) =
The first power of any number is itself. For example, - ANS 2 (to the 1st power) = 2
To multiply like bases with exponents, add the exponents. For example, - ANS 2 (to the 3rd) x 2
(to the 5th) = 2 (to the eighth)
To exponentiate a power, multiply the exponents. For example, - ANS (2 to the 3rd) to the 5th =
2 to the 15th
10 to the 0 power - ANS 1
10 to the 1 power - ANS 10
10 to the -2 power - ANS to the 2 power or
10 to the 2 power x 10 to the 3 power - ANS 10 to the 5 power
Identifying Place Value in Numbers
2045 - ANS 2045 = (2 x 10 to the 3 power) + (0 x 10 to the 2 power) + (4 x 10 to the 1 power) +
5 x 10 to the 0 power)
Digits to the right of a decimal point correspond to negative powers of ten. For example,
23.405 - ANS 23.405 = (2 x 10 to the 1 power) + (3 x 10 to the 0 power) + (4 x 10 to the -1
power) + (0 x 10 to the -2 power) + (5 x 10 to the -3 power)
Converting a fraction to a decimal. For example 3/8 - ANS 3 divided by 8 = 0.375
