Real Numbers and Monomials for General Studies
Learn about the mathematical applications of Real Numbers, and manipulating Monomials in this free online course.Publisher: ADU
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This course is the second in a series of algebra topics in mathematics. It explains more about mathematical concepts of real numbers and monomials. The free online course begins by introducing you to rational numbers. It gives you an insight into the standard definition of a rational number, the properties of rational numbers and types. There are two types of rational numbers which you will learn about their differences with the aid of examples. Interval notation is a way to describe continuous sets of real numbers by the numbers that bound them. Sometimes it is more convenient to write sets of numbers using interval notations rather than using inequality statements. This course gives you a summary of the possible inequality and interval notations. Square roots can be confusing when working with because most times the learner does the mistake of multiplying that number by 2 or by the power. Also, it gets more confusing when it deals with more than one variable. You will learn about the most commonly used roots and cube roots.
The course then introduces you to the various operations with radicals. These operations will be valid for square roots, cube roots, fourth roots, etc. Simplifying radicals is one of the easiest yet confusing aspects of algebra, the course outlines a gradual process of taking you through this with the aid of examples. An algebraic expression containing only one term is called a monomial. You will learn about the various definitions and vocabularies of words associated with monomials so as to help you have a better understanding of each concept. Not all algebraic expressions are monomials. By the end of this course, you should be able to differentiate between monomial expressions and non-monomial expressions. Monomials have a certain characteristic that makes them monomial, you will learn about the different parts of the characteristics and what they mean. Addition and subtraction of monomials can be performed by using the Distributive Property and then adding or subtracting their coefficients. "what is the distributive property?". This course outlines the various properties and definitions of each operator and how they work.
Furthermore, this course analyzes non-positive exponents in algebra. The exponents of a monomial can be negative integers or zero, as well as positive integers. You will learn about the different properties of non-positive exponents with the aid of examples. Rational exponents (also called fractional exponents) are expressions with exponents that are rational numbers (as opposed to integers). While all the standard rules of exponents apply, it is helpful to think about rational exponents carefully. How do you express numbers that are too large or small to be conveniently written? Scientific notation is particularly useful in dealing with extremely large or extremely small numbers. It allows a person to write or compute these extreme numbers more easily, which you will learn about in this course. Solving equations with rational exponents can be a bit difficult when you don't follow the rules and regulations associated with working with notations which you will learn about in this course. The learning content in this course is crucial and will be of great interest to students, researchers, analysts, and mathematicians. So, register for this course and start your learning today.
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The Real Numbers
The Real Numbers - Learning Outcomes
Real Numbers and Interval Notations
The Real Numbers - Lesson Summary
Monomials and Laws for Exponents
Monomials and Laws for Exponents - Learning Outcomes
Monomials and Laws for Exponents
Monomials and Laws for Exponents - Lesson Summary
Upon the successful completion of this course, you should be able to:
- Differentiate between rational and irrational numbers.
- Outline the definitions and vocabulary associated with monomials.
- Explain the addition and subtraction of monomials.
- Describe how to convert rational numbers to and from decimals.
- Identify how to use radicals in problem-solving.
- Describe the rules for the multiplication of monomials.
- Identify irrational numbers and their properties.
- Analyze non-positive exponents in algebra.
- Recall the law for the quotient power of the same base.
- Explain how to approximate square roots.
- Explain how to solve equations with rational exponents.
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