Test Bank For Elementary & Intermediate Algebra 4th Edition
By Michael Sullivan III; Katherine R. Struve; Janet Mazzarella
9780134556079 Chapter 1-16 Complete Guide
What is Algebra? - ANSWER: It is essentially a way to reduce a math problem down to a small set of
symbols.
The term algebra is derived from the Persian ______________. - ANSWER: Aljabr
What is a literal number and a variable? - ANSWER: Both are a letter that stands for a number.
What is an equation? - ANSWER: A mathematical statement that two quantities are equal.
What is the solution? - ANSWER: It is the number or numbers which, when used as the value of a
variable or variables, makes the statement true.
The variable must be ________________on one side of the equation. - ANSWER: isolated.
How is a variable isolated in an equation? - ANSWER: Apply any inverse operations to both sides of
the equation until the variable is isolated. Make sure to use the same operation on each side of the
equation or the balance of the equation will be destroyed and the solution of the equation will be
incorrect.
What is a directed or signed number? - ANSWER: A number that has negative or positive sign.
What is the absolute value of a number? - ANSWER: It is the unsigned or undirected value of a
number.
What are the rules of adding signed numbers and subtracting signed numbers? - ANSWER: If you are
adding:
If they both have like signs, then add their absolute values and use the sign common to both.
If they both have opposite signs, subtract their absolute values and keep the sign of the largest
numerical value.
If you are subtracting:
Change the sign of the subtrahend (the number being subtracted) and then use the rules for adding.
What are the rules of multiplying and dividing signed numbers? - ANSWER: 1. If the two numbers
have like signs, their product or quotient is always positive.
2. If the two numbers have unlike signs, their product or quotient is always negative.
When dealing with negative numbers, what is an easy way to determine the sign of the product? This
follows from what logic? - ANSWER: An even number of minus signs multiplied will result in a positive
product while an odd number of minus signs will result in a negative product. This follows from the
logic that negative numbers can be paired up to give positive results and a negative number times a
positive number results in a negative product.
What is an algebraic expression? - ANSWER: A collection of numbers and variables separated by
normal operators; addition, subtraction, multiplication, and division. This collection of numbers and
variables represents the value of something.
, What do algebraic expressions allow us to do? - ANSWER: They allow us to communicate ideas and
generalize (simplify) big ideas.
What is a term? - ANSWER: An algebraic expression connected only by the operations of
multiplication and division.
Since terms are formed using only multiplication and division, plus and minus signs _____________
terms and make expressions with more than one term. - ANSWER: separate
What is a monomial? - ANSWER: An algebraic expression with only one term
What is a binomial? - ANSWER: An algebraic expression with only two terms separated by plus or
minus signs.
What is a trinomial? - ANSWER: An algebraic expression with only three terms separated by plus or
minus signs.
What is a polynomial? - ANSWER: Any algebraic expression with more than one term(monomial).
What are similar or like terms? - ANSWER: Terms that are similar or like because they are both
constant terms or they have the same literal factors raised to the same powers.
When adding algebraic expressions, only ____ terms can be combined. - ANSWER: like or similar.
What are rational numbers? - ANSWER: Fractions where the numerator and denominator are integers
as long as the bottom integer (divisor) is not 0.
What are natural numbers? - ANSWER: 1 through 9. Excluding 0.
What is the roster method? - ANSWER: The method of writing a set by listing its elements. It uses
brackets to group the elements:
What is a set? - ANSWER: An organized collection of objects, such as numbers.
What is set builder notation? - ANSWER: Another method of writing a set of elements where the
vertical line is read as "such that".
What is an irrational number? - ANSWER: A number that when written in decimal form, does not have
a terminating decimal or block of repeating digits. There are endless non-repeating digits. Irrational
numbers can written as decimals such as these but not as fractions. They are also often the result of
taking the square root of a number.
What are real numbers? - ANSWER: All the natural numbers, whole numbers, integers, and rational,
and irrational numbers combined.
Real numbers are a part of a larger system of numbers called what? - ANSWER: complex numbers
Why is it particularly important to read the symbol -x as "the opposite of x," and not "negative x"? -
ANSWER: Because -x is not always necessarily a negative number.
What is a numerical expression? - ANSWER: Any combination of numbers and operations.
Describe the order of operations - ANSWER: 1. Perform operations within grouping symbols
performing the ones within the inner most grouping symbols first.
2. Perform operations involving exponents and square roots.
3. Perform operations of multiplication and division from left to right.
4. Perform operations of addition and subtraction from left to right.
By Michael Sullivan III; Katherine R. Struve; Janet Mazzarella
9780134556079 Chapter 1-16 Complete Guide
What is Algebra? - ANSWER: It is essentially a way to reduce a math problem down to a small set of
symbols.
The term algebra is derived from the Persian ______________. - ANSWER: Aljabr
What is a literal number and a variable? - ANSWER: Both are a letter that stands for a number.
What is an equation? - ANSWER: A mathematical statement that two quantities are equal.
What is the solution? - ANSWER: It is the number or numbers which, when used as the value of a
variable or variables, makes the statement true.
The variable must be ________________on one side of the equation. - ANSWER: isolated.
How is a variable isolated in an equation? - ANSWER: Apply any inverse operations to both sides of
the equation until the variable is isolated. Make sure to use the same operation on each side of the
equation or the balance of the equation will be destroyed and the solution of the equation will be
incorrect.
What is a directed or signed number? - ANSWER: A number that has negative or positive sign.
What is the absolute value of a number? - ANSWER: It is the unsigned or undirected value of a
number.
What are the rules of adding signed numbers and subtracting signed numbers? - ANSWER: If you are
adding:
If they both have like signs, then add their absolute values and use the sign common to both.
If they both have opposite signs, subtract their absolute values and keep the sign of the largest
numerical value.
If you are subtracting:
Change the sign of the subtrahend (the number being subtracted) and then use the rules for adding.
What are the rules of multiplying and dividing signed numbers? - ANSWER: 1. If the two numbers
have like signs, their product or quotient is always positive.
2. If the two numbers have unlike signs, their product or quotient is always negative.
When dealing with negative numbers, what is an easy way to determine the sign of the product? This
follows from what logic? - ANSWER: An even number of minus signs multiplied will result in a positive
product while an odd number of minus signs will result in a negative product. This follows from the
logic that negative numbers can be paired up to give positive results and a negative number times a
positive number results in a negative product.
What is an algebraic expression? - ANSWER: A collection of numbers and variables separated by
normal operators; addition, subtraction, multiplication, and division. This collection of numbers and
variables represents the value of something.
, What do algebraic expressions allow us to do? - ANSWER: They allow us to communicate ideas and
generalize (simplify) big ideas.
What is a term? - ANSWER: An algebraic expression connected only by the operations of
multiplication and division.
Since terms are formed using only multiplication and division, plus and minus signs _____________
terms and make expressions with more than one term. - ANSWER: separate
What is a monomial? - ANSWER: An algebraic expression with only one term
What is a binomial? - ANSWER: An algebraic expression with only two terms separated by plus or
minus signs.
What is a trinomial? - ANSWER: An algebraic expression with only three terms separated by plus or
minus signs.
What is a polynomial? - ANSWER: Any algebraic expression with more than one term(monomial).
What are similar or like terms? - ANSWER: Terms that are similar or like because they are both
constant terms or they have the same literal factors raised to the same powers.
When adding algebraic expressions, only ____ terms can be combined. - ANSWER: like or similar.
What are rational numbers? - ANSWER: Fractions where the numerator and denominator are integers
as long as the bottom integer (divisor) is not 0.
What are natural numbers? - ANSWER: 1 through 9. Excluding 0.
What is the roster method? - ANSWER: The method of writing a set by listing its elements. It uses
brackets to group the elements:
What is a set? - ANSWER: An organized collection of objects, such as numbers.
What is set builder notation? - ANSWER: Another method of writing a set of elements where the
vertical line is read as "such that".
What is an irrational number? - ANSWER: A number that when written in decimal form, does not have
a terminating decimal or block of repeating digits. There are endless non-repeating digits. Irrational
numbers can written as decimals such as these but not as fractions. They are also often the result of
taking the square root of a number.
What are real numbers? - ANSWER: All the natural numbers, whole numbers, integers, and rational,
and irrational numbers combined.
Real numbers are a part of a larger system of numbers called what? - ANSWER: complex numbers
Why is it particularly important to read the symbol -x as "the opposite of x," and not "negative x"? -
ANSWER: Because -x is not always necessarily a negative number.
What is a numerical expression? - ANSWER: Any combination of numbers and operations.
Describe the order of operations - ANSWER: 1. Perform operations within grouping symbols
performing the ones within the inner most grouping symbols first.
2. Perform operations involving exponents and square roots.
3. Perform operations of multiplication and division from left to right.
4. Perform operations of addition and subtraction from left to right.
