NES Elementary Education Subtest 2
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1. Natural Numbers N = {1, 2, 3, 4, 5, 6, . . . }
2. Whole natural numbers W = {0, 1, 2, 3, 4, 5, 6, . . . }
together with zero.
3. Every whole number 2 + (-2) = 0
has a unique opposite
or negative whose sum
with it is 0. For example,
4. The set of integers con- Z = {. . ., -3, -2, -1, 0, 1, 2, 3, . . . }
sists of the whole num-
bers and their oppo-
sites.
5. Every nonzero integer 2 × 1/2 = 1
has a unique reciprocal
whose product with it is
one. For example,
6. The ratio or fraction of 2/3 = 2 × 1/3
one integer to a nonze-
ro integer is the prod-
uct of the first integer
with the reciprocal of
the second. For exam-
ple, the ratio of 2 to 3 is
7. not every rational num- 1/2 = 0.5
ber is an integer. For ex-
ample, 1/2 is a rational
number that is not an
integer.
, NES Elementary Education Subtest 2
Study online at https://quizlet.com/_f42g2
8. There are three basic commutativity, associativity and identity.
properties of addition:
9. Commutative property. When adding two numbers, the sum is the same regardless of the order
in which the numbers are added.
2+3=3+2
10. Associative property. 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
11. Identity property. Adding zero to a number does not change it.
2+0=2
12. There are three basic commutativity, associativity and identity.
properties of multiplica-
tion:
13. Distributive property. 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)
14. Exponentiation Exponentiation is repeated multiplication. An exponent is often called a
power. For example, the third power of 2 is
2³ = 2 × 2 × 2 = 8
15. We define the zero pow- (-3)0 = 1
er of any nonzero num-
ber to be 1. For exam-
ple,
, NES Elementary Education Subtest 2
Study online at https://quizlet.com/_f42g2
16. A negative exponent in- 2 (-3rd power) = (3rd power) =
dicates a reciprocal. For
example,
17. The first power of any 2 (to the 1st power) = 2
number is itself. For ex-
ample,
18. To multiply like bases 2 (to the 3rd) x 2 (to the 5th) = 2 (to the eighth)
with exponents, add the
exponents. For exam-
ple,
19. To exponentiate a pow- (2 to the 3rd) to the 5th = 2 to the 15th
er, multiply the expo-
nents. For example,
20. 10 to the 0 power 1
21. 10 to the 1 power 10
22. 10 to the -2 power to the 2 power or
23. 10 to the 2 power x 10 to 10 to the 5 power
the 3 power
24. Identifying Place Value 2045 = (2 x 10 to the 3 power) + (0 x 10 to the 2 power) + (4 x 10 to the
in Numbers 1 power) + 5 x 10 to the 0 power)
2045
25. Digits to the right of 23.405 = (2 x 10 to the 1 power) + (3 x 10 to the 0 power) + (4 x 10 to
a decimal point corre- the -1 power) + (0 x 10 to the -2 power) + (5 x 10 to the -3 power)
spond to negative pow-
ers of ten. For example,
Study online at https://quizlet.com/_f42g2
1. Natural Numbers N = {1, 2, 3, 4, 5, 6, . . . }
2. Whole natural numbers W = {0, 1, 2, 3, 4, 5, 6, . . . }
together with zero.
3. Every whole number 2 + (-2) = 0
has a unique opposite
or negative whose sum
with it is 0. For example,
4. The set of integers con- Z = {. . ., -3, -2, -1, 0, 1, 2, 3, . . . }
sists of the whole num-
bers and their oppo-
sites.
5. Every nonzero integer 2 × 1/2 = 1
has a unique reciprocal
whose product with it is
one. For example,
6. The ratio or fraction of 2/3 = 2 × 1/3
one integer to a nonze-
ro integer is the prod-
uct of the first integer
with the reciprocal of
the second. For exam-
ple, the ratio of 2 to 3 is
7. not every rational num- 1/2 = 0.5
ber is an integer. For ex-
ample, 1/2 is a rational
number that is not an
integer.
, NES Elementary Education Subtest 2
Study online at https://quizlet.com/_f42g2
8. There are three basic commutativity, associativity and identity.
properties of addition:
9. Commutative property. When adding two numbers, the sum is the same regardless of the order
in which the numbers are added.
2+3=3+2
10. Associative property. 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
11. Identity property. Adding zero to a number does not change it.
2+0=2
12. There are three basic commutativity, associativity and identity.
properties of multiplica-
tion:
13. Distributive property. 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)
14. Exponentiation Exponentiation is repeated multiplication. An exponent is often called a
power. For example, the third power of 2 is
2³ = 2 × 2 × 2 = 8
15. We define the zero pow- (-3)0 = 1
er of any nonzero num-
ber to be 1. For exam-
ple,
, NES Elementary Education Subtest 2
Study online at https://quizlet.com/_f42g2
16. A negative exponent in- 2 (-3rd power) = (3rd power) =
dicates a reciprocal. For
example,
17. The first power of any 2 (to the 1st power) = 2
number is itself. For ex-
ample,
18. To multiply like bases 2 (to the 3rd) x 2 (to the 5th) = 2 (to the eighth)
with exponents, add the
exponents. For exam-
ple,
19. To exponentiate a pow- (2 to the 3rd) to the 5th = 2 to the 15th
er, multiply the expo-
nents. For example,
20. 10 to the 0 power 1
21. 10 to the 1 power 10
22. 10 to the -2 power to the 2 power or
23. 10 to the 2 power x 10 to 10 to the 5 power
the 3 power
24. Identifying Place Value 2045 = (2 x 10 to the 3 power) + (0 x 10 to the 2 power) + (4 x 10 to the
in Numbers 1 power) + 5 x 10 to the 0 power)
2045
25. Digits to the right of 23.405 = (2 x 10 to the 1 power) + (3 x 10 to the 0 power) + (4 x 10 to
a decimal point corre- the -1 power) + (0 x 10 to the -2 power) + (5 x 10 to the -3 power)
spond to negative pow-
ers of ten. For example,
