TExES Core Subjects EC-6 (291) – MATH || with True
Solutions.
Integer correct answers a whole number that includes all positive numbers, negative numbers,
and 0; does not include decimals or fractions
Natural number correct answers all positive or nonnegative integers, including 0; does not
include negative numbers, decimals, or fractions
Rational number correct answers a number that can be expressed as a ratio or quotient of two
nonzero integers
How can rational numbers be expressed? correct answers As common fractions or decimals
Irrational numbers correct answers A number that cannot be expressed as an exact ratio of two
integers
What is a characteristic of an irrational number in decimal form? correct answers The decimal
will never terminate and never repeat
Define divisor and dividend correct answers Divsor = number doing the dividing Dividend =
number being divided
Homogeneous fraction correct answers fractions with the same denominator
common denominator correct answers number that is a multiple of the original denominators
How do you multiply fractions? correct answers Multiply the numerators and denominators
horizontally and then simplify the remaining product
Reciprocal fraction correct answers a fraction with the numerator and denominator switched
How do you divide fractions? correct answers take the reciprocal of the second fraction (the one
doing the dividing) and multiply them together
What does a negative exponent indicate? correct answers A reciprocal fraction
Expanded form correct answers shows the place value of each digit; example 542 = 500 + 40 +
2, which is equal to 5 hundreds, 4 tens, and 2 ones
Prime numbers correct answers natural numbers greater than 1 that are divisible only by 1 and
themselves (2, 3, 5, 7, 11, 13, 17, 19...)
, Composite numbers correct answers natural numbers greater than zero that are divisible by at
least one other number besides 1 and themselves; they have at least 3 factors, such as 9 having 1,
3, and 9
prime factorization correct answers writing the product of prime numbers that make up the
number
How do you perform prime factorization? correct answers Factor a known prime number into the
given number; repeat on all factors until no more factorization can take place
Greatest common divisor correct answers the largest positive integer that divides into the
numbers without producing a remainder
Commutative property correct answers The order of the addends (terms being added) or factors
(in multiplication) do not change the result;
addition ex. a + b = b + a
multiplication ex. a × b = b × a
Associative property of multiplication and division correct answers The order of the addends or
factors will not change the sum or the product;
addition ex. (a+b) + c = a + (b+c)
multiplication ex. (a × b) × c = a × (b × c)
Property of Zero correct answers The sum of a number and zero is the number itself; the product
of a number and zero is zero
Distributive property correct answers everything within the parentheses needs to be multiplied by
the number on the outside
a(b+c) = a x (b+c)
8(5+2) = 8x7 = 56
a(b+c) = (a x b) + (a x c)
8(5 +2) = (8 x 5) + (8 x 2) = 56
What is the order of operations? correct answers Parentheses - simplify everything within
grouping symbols starting with the innermost
Exponents - complete all powers and roots
Multiplication/Division - complete all from left to right
Addition/Subtraction - complete all from left to right
What does the graph of a linear function look like? correct answers A straight line
algebraic expressoin correct answers a mathematical phrase that is written by using one or more
variables and constants, but does not contain a relation symbol (ex. 5y + 8)
Variable correct answers a letter that stands in for a number in an algebraic expression
Solutions.
Integer correct answers a whole number that includes all positive numbers, negative numbers,
and 0; does not include decimals or fractions
Natural number correct answers all positive or nonnegative integers, including 0; does not
include negative numbers, decimals, or fractions
Rational number correct answers a number that can be expressed as a ratio or quotient of two
nonzero integers
How can rational numbers be expressed? correct answers As common fractions or decimals
Irrational numbers correct answers A number that cannot be expressed as an exact ratio of two
integers
What is a characteristic of an irrational number in decimal form? correct answers The decimal
will never terminate and never repeat
Define divisor and dividend correct answers Divsor = number doing the dividing Dividend =
number being divided
Homogeneous fraction correct answers fractions with the same denominator
common denominator correct answers number that is a multiple of the original denominators
How do you multiply fractions? correct answers Multiply the numerators and denominators
horizontally and then simplify the remaining product
Reciprocal fraction correct answers a fraction with the numerator and denominator switched
How do you divide fractions? correct answers take the reciprocal of the second fraction (the one
doing the dividing) and multiply them together
What does a negative exponent indicate? correct answers A reciprocal fraction
Expanded form correct answers shows the place value of each digit; example 542 = 500 + 40 +
2, which is equal to 5 hundreds, 4 tens, and 2 ones
Prime numbers correct answers natural numbers greater than 1 that are divisible only by 1 and
themselves (2, 3, 5, 7, 11, 13, 17, 19...)
, Composite numbers correct answers natural numbers greater than zero that are divisible by at
least one other number besides 1 and themselves; they have at least 3 factors, such as 9 having 1,
3, and 9
prime factorization correct answers writing the product of prime numbers that make up the
number
How do you perform prime factorization? correct answers Factor a known prime number into the
given number; repeat on all factors until no more factorization can take place
Greatest common divisor correct answers the largest positive integer that divides into the
numbers without producing a remainder
Commutative property correct answers The order of the addends (terms being added) or factors
(in multiplication) do not change the result;
addition ex. a + b = b + a
multiplication ex. a × b = b × a
Associative property of multiplication and division correct answers The order of the addends or
factors will not change the sum or the product;
addition ex. (a+b) + c = a + (b+c)
multiplication ex. (a × b) × c = a × (b × c)
Property of Zero correct answers The sum of a number and zero is the number itself; the product
of a number and zero is zero
Distributive property correct answers everything within the parentheses needs to be multiplied by
the number on the outside
a(b+c) = a x (b+c)
8(5+2) = 8x7 = 56
a(b+c) = (a x b) + (a x c)
8(5 +2) = (8 x 5) + (8 x 2) = 56
What is the order of operations? correct answers Parentheses - simplify everything within
grouping symbols starting with the innermost
Exponents - complete all powers and roots
Multiplication/Division - complete all from left to right
Addition/Subtraction - complete all from left to right
What does the graph of a linear function look like? correct answers A straight line
algebraic expressoin correct answers a mathematical phrase that is written by using one or more
variables and constants, but does not contain a relation symbol (ex. 5y + 8)
Variable correct answers a letter that stands in for a number in an algebraic expression
