Shop Essentials (Applied Mathematics)

Math: Fractions and Decimals 111

This class describes the methods used to perform basic mathematical operations using fractions, decimals, and percentages. Concepts like addition, subtraction, multiplication, and division with fractions and decimals are a large part of manufacturing processes and operations. This class also discusses conversions between fractions, decimals, mixed numbers, and improper fractions.

Almost all manufacturing prints use fractions and decimals in their measurements. Knowing how to manage these mathematical concepts and convert between these types of numbers is an essential part of the basic skills needed to work in a manufacturing environment.

  • Difficulty Beginner

  • Format Online

  • Number of Lessons 25

  • Language English


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Course Outline
  • Fractions
  • Parts of a Fraction
  • Reducing Fractions
  • Adding Fractions
  • Subtracting Fractions
  • Multiplying Fractions
  • Dividing Fractions
  • Fraction Calculations Review
  • Improper Fractions and Mixed Numbers
  • Converting Improper Fractions and Mixed Numbers
  • Adding Mixed Numbers
  • Subtracting Mixed Numbers
  • Multiplying Mixed Numbers
  • Dividing Mixed Numbers
  • Mixed Numbers and Improper Fractions Review
  • Decimals
  • Rounding Decimals
  • Adding and Subtracting Decimals
  • Multiplying Decimals
  • Dividing Decimals
  • Math Operations with Decimals Review
  • Converting Fractions and Decimals
  • Percentages
  • Determining Percentages
  • Determining Percentages Review
  • Define a fraction.
  • Distinguish between the two parts of a fraction.
  • Explain how to reduce a fraction to its lowest terms.
  • Solve an addition problem using fractions.
  • Solve a subtraction problem using fractions.
  • Solve a multiplication problem using fractions.
  • Solve a division problem using fractions.
  • Contrast improper fractions and mixed numbers.
  • Explain how to convert improper fractions and mixed numbers.
  • Solve addition problems using mixed numbers.
  • Solve subtraction problems using mixed numbers.
  • Solve multiplication problems using mixed numbers.
  • Solve division problems using mixed numbers.
  • Define a decimal.
  • Explain how to round a decimal.
  • Solve addition problems using decimals. Solve subtraction problems using decimals.
  • Solve a multiplication problem using decimals.
  • Solve a division problem using decimals.
  • Explain how to convert a fraction to a decimal and a decimal to a fraction.
  • Define percentage. Explain how to convert a percentage to a decimal and a decimal to a percentage.
  • Calculate a percentage.
Vocabulary Term


To take an amount from the whole number in a mixed number and add it to the fraction. Borrowing changes the way the number is expressed but does not change its value.

common factor

o A factor that is shared by two or more numbers. For example, 4 is a common factor of 8 and 12 because 4 divides 8 and 12 evenly (8/4 = 2, 12/4 = 3).


A type of fraction in which the denominator is 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.

decimal point

The period between whole numbers and decimals. The higher the number of places to the right of the decimal point, the more precise the value.


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 that a number is divided into. The dividend is in the numerator of a fraction.


The quantity that divides a number. The divisor is in the denominator of a fraction.


A number that evenly divides another number. For example, 3 is a factor of 12 because 12 can be divided by 3 with no remainder (12/3 = 4).


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.

greatest common factor

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.


To switch the locations of the numerator and denominator. Invert the second fraction when dividing with fractions, and then multiply.

lowest common denominator

The smallest possible denominator that can be shared by two fractions. The lowest common denominator is used when adding or subtracting fractions with different denominators.

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.


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


A mathematical action or process such as addition or subtraction. A mathematical equation can consist of multiple operations.


A number that indicates part of a whole out of 100. Percentages are fractions in which the denominator is 100.

place value

The numerical value of a digit as determined by 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.


Having a constant amount in relation to another quantity. For two numbers to be proportional, as one number increases, the other should increase by an equal factor.


The value left after division. When converting improper fractions, remainders become the numerator of the fraction in the mixed number.


A method used to shorten numbers. Rounding simplifies numbers but sacrifices precision.


An acceptable deviation from a desired dimension that meets specifications. Parts outside of a required tolerance must be discarded or reworked.

whole number

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