Math Fundamentals for Welding 161

This class covers basic arithmetic operations used in welding, such as addition, subtraction, multiplication, and division. Decimals and fractions are used for welding calculations and measurements, and welders should be able to round decimals, convert fractions and decimals, and perform basic arithmetic with both fractions and decimals.

Knowledge of basic math concepts is integral to understanding welding measurements and reading specifications and prints. After taking this course, users will know the foundations of arithmetic and conversions related to welding processes.

  • Difficulty Beginner

  • Format Online

  • Number of Lessons 21

  • Language English


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Course Outline
  • Math for Welding
  • Measurement and Math Tools
  • Whole Numbers, Place Values, and Decimals
  • Rounding Decimals
  • Place Value and Rounding Review
  • Addition
  • Subtraction
  • Adding and Subtracting Decimals
  • Multiplication
  • Division
  • Remainders
  • Dividing Decimals
  • Math Operations Review
  • Fractions
  • Reducing Fractions
  • Improper Fractions and Mixed Numbers
  • Converting Fractions and Decimals
  • Adding and Subtracting Fractions
  • Multiplying and Dividing Fractions
  • Conversions for Measurement
  • Final Review
  • Describe how math is used in welding.
  • Describe measurement tools and calculators for welding.
  • Describe whole numbers, place values, and decimals.
  • Demonstrate how to round decimals.
  • Solve addition problems.
  • Solve subtraction problems.
  • Solve addition problems using decimals. Solve subtraction problems using decimals.
  • Solve multiplication problems.
  • Describe division.
  • Solve division problems with remainders and decimals.
  • Solve division problems using decimals.
  • Define fractions. Identify the components of fractions.
  • Demonstrate how to reduce fractions.
  • Explain how to convert between improper fractions and mixed numbers.
  • Demonstrate how to convert fractions and decimals.
  • Solve addition and subtraction problems using fractions.
  • Solve multiplication and division problems using fractions.
  • Calculate conversions for common measurement fractions.
Vocabulary Term


A mathematical operation that unites two separate quantities into one sum. 2 + 2 = 4 is an example of addition.

bevel protractors

An instrument with a pivoting blade and dial for measuring angles. Bevel protractors are commonly used for measuring workpiece and weld angles.


To take a value away from one column and move it to a column on the right in order to be able to solve an equation. Borrowing may be necessary in subtraction when the top number is smaller than the bottom number.


A small electronic device or application within another electronic device used to compute mathematical operations. Calculators can reduce mathematical errors.


A measuring instrument that includes one or more sets of jaws and a scale marked with unit divisions. Calipers often include one set of jaws to measure outer diameters and another set of jaws to measure internal diameters.


To transfer a digit from one column to the next column on the left in order to solve an equation. Carrying may be necessary in addition when adding numbers with two or more place values.


cm. A small unit of linear measurement in the metric system. One centimeter is equal to 0.01 of a meter metric and 0.394 of an inch U.S. customary.

decimal point

The period between whole numbers and decimals. The more digits to the right of a decimal point, the smaller the decimal's value.


A type of fraction in which the denominator is always a power of ten and the numerator is indicated by values placed to the right of a decimal point. Decimals include 2.7, 0.41, and so on.


The number on the bottom of a fraction. The denominator expresses the total quantity of parts into which the whole number has been divided.


The quantity being divided in a division problem. The dividend is in the numerator of a fraction.


A mathematical operation that indicates how many equal quantities add up to a specific number. 8 ÷ 4 = 2 is an example of division.


The quantity by which a number is divided in a division problem. The divisor is in the denominator of a fraction.


A mathematical calculation or formula that includes numbers and/or variables using mathematical operations. Expressions do not include an equals sign, but equations do.


ft. A unit of linear measurement in the U.S. customary system. One foot equals 12 inches and 30.48 centimeters metric.


A number that indicates parts of a whole number. Fractions appear as one number over the other with a slash or horizontal line between them.


The branch of mathematics that involves the measurements, properties, and relationships of all shapes and sizes of things. Geometry combines simple shapes such as circles, triangles, and squares to create more complex shapes.

greatest common factor

GCF. The highest number that can evenly divide into two numbers. Finding the greatest common factor of the numerator and the denominator is the first step to reducing a fraction.

improper fraction

A fraction in which the numerator is larger than the denominator. Improper fractions equal amounts greater than one.


in. A small unit of linear measurement in the U.S. customary system. One inch equals approximately 2.54 centimeters metric.


The meeting point where two materials are joined together. Welding creates a permanent joint.

lowest common denominator

The smallest number into which two numbers can both be divided. The lowest common denominator is used when adding or subtracting fractions to make them share a denominator.


m. A unit of linear measurement in the metric system. One meter is equal to 100 centimeters metric and 3.281 feet U.S. customary.

metric system

A standard system of measurement based on the gram, liter, and meter. The metric system is widely recognized as the standard measurement system internationally.


A measuring instrument with a threaded spindle that slowly advances toward a small anvil. Micrometers are available in numerous types for measuring a variety of dimensions and features.


mm. A small unit of linear measurement in the metric system. One millimeter is equal to 0.1 of a centimeter metric and 0.039 of an inch U.S. customary.

mixed number

A whole number combined with a fraction. Mixed numbers can be converted to improper fractions, and improper fractions can be converted to mixed numbers.


A mathematical operation that indicates how many times a number is added to itself. 2 x 4 = 8 is an example of multiplication.


The number on the top of a fraction. The numerator indicates the number of parts of a whole that are present.

place value

The numerical value of a digit, based on its position in a number. Place values are equal to multiples of ten.


The dispersion of measurements or fineness of readings. More decimals in measurements indicate a need for higher precision.


A document containing all the information necessary to manufacture and inspect a part. Prints include measurements and other important details.


The answer in a division problem. In the problem 18 divided by 9, the quotient is 2.


Any left-over value that does not divide evenly into the dividend when performing division. Remainders can be indicated by using decimals or the letter R.

repeating decimal

A decimal in which one or more digits repeat endlessly. Dividing 1 by 3 results in the repeating decimal 0.333....


Shortening the number of digits in a number to express an approximately equivalent value. Rounding involves either increasing the value of a digit or dropping one or more digits.

steel rules

A simple measuring instrument consisting of a long, thin metal strip with a marked scale of unit divisions. Steel rules can come in many sizes and forms and are rigid.


A mathematical operation that takes away a quantity from a larger whole. 4 - 2 = 2 is an example of subtraction.

tape measures

A piece of flexible and retractable metal with a marked scale of unit divisions for measurement. Tape measures are commonly used for linear measurement in welding.


An acceptable deviation from a desired dimension that still meets part specifications. Tolerances indicate the allowable difference between a physical feature and its intended design.


A branch of mathematics that addresses the measurements and relationships of a triangle and its parts. Trigonometry involves calculating the angles and sides of triangles.

U.S. customary system

A standard system of measurements based on the inch, ounce, and pound. The U.S. customary system is based on the English and Imperial systems and is most common in the U.S.


A joining process that permanently bonds two separate components together. Welding uses heat, pressure, or a combination of the two to make one new part.

welding procedure specifications

WPSs. A formal, written document detailing specifications for a welding procedure. Welding procedure specifications contain guidelines and recommendations for welding procedures.

whole numbers

Any number that has not been divided into fractions or decimals. Whole numbers include 1, 2, 3, 10, 15, 23, and so on.


Welding procedure specifications. A formal, written document detailing specifications for a welding procedure. WPSs contain guidelines and recommendations for welding procedures.