RBQE - Relationships Between Quantities and Expressions (Overview)

Relationships Between Quantities and Expressions

Introduction

Imagine you are a builder and you working on a new home. You are trying to save money so you skip the foundation and start on the walls. Can you picture what would happen? The home you are building would fall in before you could even get the roof on! Algebra is similar in that you must have a solid foundation in order to build on your knowledge. This module will help to solidify your math foundation and prepare you for all of the new topics you will encounter. You will interpret units of measure, learn about and manipulate polynomials, and finally simplify radical expressions. All of these skills will be beneficial to you as you continue to grow in your math journey!

Essential Questions

How do I choose and interpret units of measure?
What does each part of an expression represent in the context of the problem?
How are polynomial operations related to operations in the real number system?
How can polynomials be used to express realistic situations?
How do I simplify radical expressions?
What type of number will result from the addition or multiplication of two rational numbers, one rational and one irrational number, or two irrational numbers?

Key Terms

The following key terms will help you understand the content in this module.

Algebra - The branch of mathematics that deals with relationships between numbers, utilizing letters and other symbols to represent specific sets of numbers, or to describe a pattern of relationships between numbers.

Binomial Expression - An algebraic expression with two unlike terms.

Capacity - The greatest volume that a container can hold.

Circumference - The distance around a circle.

Coefficient - A number multiplied by a variable.

Constant Term - A quantity that does not change its value.

Expression - A mathematical phrase involving at least one variable and sometimes numbers and operation symbols.

Factor - When two or more integers are multiplied, each integer is a factor of the product. "To factor" means to write the number or term as a product of its factors.

Integer - The set of numbers ..., –3, –2, –1,0,1,2,3,...

Irrational Number - A number whose decimal form is nonterminating and nonrepeating. Irrational numbers cannot be written in the form a/b, where a and b are integers (b cannot be zero). So all numbers that are not rational are irrational.

Monomial Expression - An algebraic expression with one term.

Perimeter - The sum of the lengths of the sides of a polygon.

Polynomial Function - A polynomial function is defined as a function, $LaTeX: f\left(x\right)=a_0x^n+a_1x^{n-1}+a_2x^{n-2}+...+a_{n-2}x^2+a_{n-1}x+a_n$ $f\left(x\right)=a_0x^n+a_1x^{n-1}+a_2x^{n-2}+...+a_{n-2}x^2+a_{n-1}x+a_n$ where the coefficients are real numbers.

Pythagorean Theorem - It is a theorem that states a relationship that exists in any right triangle. If the lengths of the legs in the right triangle are a and b and the length of the hypotenuse is c, we can write the theorem as the following equation a^2+b^2=c^2 Radical The symbol,√(b&a), which is read "the bth root of a," is called a radical.

Radical - The symbol √.

Radicand - The number underneath the root symbol. So, in $LaTeX: \sqrt[2]{b}=a$ $\sqrt[2]{b}=a$ , the b is called the radicand.

Rational Number - A number expressible in the form a/b or –a/b for some fraction a/b. The rational numbers include the integers.

Standard Form of a Polynomial - To express a polynomial by putting the terms in descending exponent order.

Term - A number, a variable, or a product of numbers and variables.

Trinomial - An algebraic expression with three unlike terms.

Variable - A letter or symbol used to represent a number.

Volume - The amount of space occupied by an object.

Whole Numbers - The numbers 0, 1, 2, 3, ....

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