# Math Concepts

## Math Concepts Courses Duration: 0.25 Hrs

Course Level: Intermediate
Languages: English
Capability: Audio, Video

This course begins with the definition of exponents and then discusses scientific and engineering notation as well as multiplying exponents. The course concludes by illustrating binary, decimal, and hexadecimal number systems.

#### Learning Objectives

• Describe the purpose of exponents
• Identify the terms in exponential expressions
• Apply exponent rules to simplify exponential expressions
• Evaluate exponential expressions
• Convert numbers to Scientific and Engineering Notation

Duration: 0.25 Hrs

Course Level: Intermediate
Languages: English
Capability: Audio, Video

This course discusses the definition of percent and fraction, how to change between numbers and percentages, how to properly write a fraction, as well as how to multiply, divide, add, and subtract fractions.

#### Learning Objectives

This module will cover the following topics:

• Definition of percent and fraction
• Changing between numbers and percentages
• How to properly write a fraction
• Fraction multiplication, division, addition, and subtraction

Duration: 0.25 Hrs

Course Level: Intermediate
Languages: English
Capability: Audio, Video

Distance measuring units include the U.S. standard, (inch, feet, yard), decimal-inch (tenth, hundredth, thousandth, ten-thousandth), or the metric (millimeter, centimeter, meter). Being able to measure distance or determining if something is square are integral parts of many projects. This can include weekend do-it-yourself jobs to major landscaping and construction projects. While measuring cannot be done without some variation, errors can be reduced by following basic principles covered in this course.

#### Learning Objectives

• Describe the difference between errors and mistakes as they relate to measuring
• List ways to increase measuring accuracy
• Describe the parallax error
• Identify basic unit measurements for U.S. Standard, Decimal-Inch, and International System of Units, or SI (metric)
• Describe how to measure an angle
• Differentiate between the architectural and engineering scales
• Describe how to determine if something is square

Duration: 2.00 Hrs

Course Level: Intermediate
Languages: English
Capability: Audio, Video

This course is designed to introduce participants to the basic principles of addition, subtraction, multiplication, and division. After completing this course, participants should be able to describe how to add, subtract, and multiply numbers in vertical columns, and to explain how short division and long division is done. They should also be able to explain powers of numbers and roots of numbers, and they should be able to describe shortcuts for multiplying and dividing with multiples of ten.

#### Learning Objectives

• Define number line.
• Describe the basic principles of addition and subtraction.
• Describe the base 10 number system.
• Describe how to add and subtract numbers in vertical columns.
• Describe the basic principles of multiplication.
• Explain how to use a multiplication table.
• Describe how to multiply numbers in vertical columns.
• Describe a shortcut for multiplying with multiples of ten.
• Explain powers of numbers.
• Explain roots of numbers.
• Describe the basic principles of division.
• Explain how short division is done.
• Explain how long division is done.
• Describe a shortcut for dividing with multiples of ten.
• Describe a shortcut for dividing with powers of numbers.

Duration: 2.00 Hrs

Course Level: Intermediate
Languages: English
Capability: Audio, Video

This course is designed to familiarize participants with basic mathematical operations involving signed numbers, averaging, rates, fractions, decimals, and conversions. After completing this course, participants should be able to perform basic mathematical operations with signed numbers, perform combined operations in the proper order, find the average of a group of numbers, and calculate rates. They should also be able to add, subtract, multiply, and divide with fractions and decimals. Finally, participants should be able to convert between fractions, decimals, and percents; write numbers using scientific notation; and use conversion tables.

#### Learning Objectives

• Explain how to do basic math operations with signed numbers.
• Define grouping symbols.
• Explain the order in which combined operations are performed.
• Explain how to calculate averages and rates.
• Explain what a fraction is, and how to add and subtract them.
• Describe how to get common denominators, and what a lowest common denominator is.
• Explain how to multiply and divide fractions.
• Explain how to express a fraction in simplest terms.
• Explain what a mixed number is, and how to convert whole and mixed numbers to fractions.
• Define the term “decimal.”
• Describe basic math operations involving decimals.
• Describe how to convert between fractions and decimals.
• Describe how to write numbers using scientific notation.
• Explain what percents are.
• List how to convert between fractions, decimals, and percents.
• Describe the following conversion tables: factor-type and equivalents-type.

Duration: 2.00 Hrs

Course Level: Intermediate
Languages: English

This course is designed to familiarize participants with basic mathematical applications that can be used on the job. After completing this course, participants should be able to interpret measurements that include fractions and decimal values, measurements in English and metric units, and perform mathematical applications involving fractions and decimals. They should also be able to calculate dimensions associated with rectangles, triangles, and circles.

#### Learning Objectives

• Interpret measurements that include fractions.
• Add and subtract fractional measurements.
• Multiply and divide fractional measurements.
• Convert a fraction to a decimal, and a decimal to a fraction.
• Convert a decimal to a percent, and a percent to a decimal.
• Perform mathematical operations with decimal numbers.
• Use a calculator to perform mathematical operations.
• Round off a decimal to a specific number of places.
• Interpret measurements in metric units.
• Explain what an angle is, and how angles are measured.
• Explain what a rectangle is, and define the terms “length” and “width.”
• Explain what a triangle is, and define the terms “base” and “height.”
• Explain what a circle is, and define the terms “diameter” and “radius.”
• Calculate the perimeter of a rectangle.
• Calculate the length of the hypotenuse of a right angle.
• Calculate the circumference of a circle.
• Calculate the area of a rectangle, a right triangle, and a circle.
• Calculate the volume of a rectangular solid.
• Calculate the volume of a cylinder.

Duration: 2.00 Hrs

Course Level: Intermediate
Languages: English
Capability: Audio, Video

This course is designed to familiarize participants with the basic concepts of algebra. After completing this course, participants should be able to define terms commonly associated with the use of algebra, isolate an unknown in an equation, and use the processes of distribution and factoring. They should also be able to explain what ratios and proportions are and to explain the difference between a direct proportion and an inverse proportion. Finally, participants should be able to use a calculator to solve math problems.

#### Learning Objectives

• State the difference between arithmetic and algebraic operations.
• Define the terms “constant,” “unknown,” “variable,” and “equation.”
• Describe how equations are used to solve an arithmetic or algebraic problem.
• Explain how to maintain an equation’s balance.
• Describe how the unknown in an equation can be isolated.
• Describe the operation of distribution.
• Describe the operation of factoring.
• Explain what a ratio is and how ratios can be expressed.
• Explain the difference between a direct proportion and an inverse proportion.
• Explain how to use a calculator.

Duration: 2.00 Hrs

Course Level: Intermediate
Languages: English
Capability: Audio, Video

This course is designed to familiarize participants with the basic principles associated with using formulas, reading and interpreting graphs, and detecting and analyzing trends. After completing this course, participants should be able to explain what a formula is and use formulas to find areas, volumes, and volumetric flow rates. They should also be able to describe how graphs and charts can provide information about process variables. In addition, participants should be able to describe basic procedures for detecting and analyzing trends.

#### Learning Objectives

• Define the term “formula.”
• Describe how formulas can be used to find areas.
• Describe how formulas can be used to find volumes.
• Define the term “flow rate.”
• Describe how to use volumetric flow rate formulas.
• Describe how graphs can provide information about process variables.
• Describe how charts can provide information about process variables.
• Describe what a trend is and explain the difference between expected trends and unexpected trends.
• Describe some basic procedures for detecting a trend.
• Describe some basic procedures for analyzing a trend.

Duration: 1.00 Hr

Course Level: Intermediate
Languages: English
Capability: Audio, Video

Boolean algebra, also known as Boolean logic, is a way of calculating truth values based on 0 and 1, or false and true. This system of logic, illustrated by Boolean logic gates, is applied to the construction, inputs, and outputs of applications such as circuitry and computer function. This course outlines the basics of Boolean functions and laws, instructions on writing out truth tables in order to illustrate each of the logic gates and all their possible outputs, instructions on converting these tables into Boolean expressions, how to use Boolean algebra to simplify combinational logic circuits, and how to convert Boolean expressions into Karnaugh maps.

#### Learning Objectives

• Describe the operation of the five basic gates.
• Identify the diagram symbol for the five basic gates.
• Identify Boolean algebra laws and rules for simplifying combinational logic circuits.

Duration: 1.00 Hr

Course Level: Intermediate
Languages: English
Capability: Audio, Video

Boolean algebra, also known as Boolean logic, is a way of calculating truth values based on 0 and 1, or false and true. This system of logic, illustrated by Boolean logic gates, is applied to the construction, inputs, and outputs of applications such as circuitry and computer function. This course outlines the basics of Boolean functions and laws, instructions on writing out truth tables in order to illustrate each of the logic gates and all their possible outputs, instructions on converting these tables into Boolean expressions, how to use Boolean algebra to simplify combinational logic circuits, and how to convert Boolean expressions into Karnaugh maps.

#### Learning Objectives

• Describe DeMorgan’s Theorems.
• Utilize Boolean algebra laws and rules for simplifying combinational logic circuits.
• Demonstrate the ability to convert a truth table into a Boolean expression.

Duration: 1.00 Hr

Course Level: Intermediate
Languages: English
Capability: Audio, Video

Boolean algebra, also known as Boolean logic, is a way of calculating truth values based on 0 and 1, or false and true. This system of logic, illustrated by Boolean logic gates, is applied to the construction, inputs, and outputs of applications such as circuitry and computer function. This course outlines the basics of Boolean functions and laws, instructions on writing out truth tables in order to illustrate each of the logic gates and all their possible outputs, instructions on converting these tables into Boolean expressions, how to use Boolean algebra to simplify combinational logic circuits, and how to convert Boolean expressions into Karnaugh maps.

#### Learning Objectives

• Discuss products-of-sums expressions.
• Discuss Karnaugh mapping and how it is performed.
• Demonstrate Boolean reduction using Karnaugh mapping.