NES Elementary Education Subtest 2 Exam Questions with Complete Solutions

NES Elementary Education Subtest 2 Exam Questions with Complete Solutions Natural Numbers - ANSWER N = {1, 2, 3, 4, 5, 6, . . . } 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) =1 / 2 (3rd power) = 1 / 8 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 10 to the 0 power - ANSWER 1 10 to the 1 power - ANSWER 10 10 to the -2 power - ANSWER 1 / 10 to the 2 power or 1 / 100 10 to the 2 power x 10 to the 3 power - ANSWER 10 to the 5 power Identifying Place Value in Numbers 2045 - ANSWER 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 - ANSWER 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 - ANSWER 3 divided by 8 = 0.375