Instructor Manual: Peterson, John C.; Smith, Robert D.; and McGarry, Kathleen, Mathematics for Machine Technology, 9e, 2026,
9798214116457; Section 1: Common Fractions and Decimal Fractions
Instructor Manual
Peterson, John C.; Smith, Robert D.; and McGarry, Kathleen, Mathematics for
Machine Technology, 9e, 2026, 9798214116457; Section 1: Common Fractions and Decimal
Fractions
TABLE OF CONTENTS
Purpose and Perspective of the Section.......................................................................2
Section Objectives..........................................................................................................2
What’s New in This Section..........................................................................................4
Section Outline..............................................................................................................4
© 2026 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 1
accessible website, in whole or in part.
, Instructor Manual: Peterson, John C.; Smith, Robert D.; and McGarry, Kathleen, Mathematics for Machine Technology, 9e, 2026,
9798214116457; Section 1: Common Fractions and Decimal Fractions
PURPOSE AND PERSPECTIVE OF THE SECTION
The purpose of this section is to provide students with procedures for simplifying and performing
operations (addition, subtraction, multiplication, and division) on common fractions, mixed numbers, and
decimal fractions. Students will learn how to perform whole number exponentiation, extract roots for
positive numbers, and evaluate and approximate expressions involving numerical radical expressions.
Order of operations will be explained and applied to simplify numerical expressions. Students will learn
how to write decimal or fractional equivalents using tables of decimal equivalents. They will learn how to
perform the aforementioned sills and use them in the context of machine technology.
SECTION OBJECTIVES
By the end of this section, you should be able to:
Unit 1
Express fractions in lowest terms.
Express fractions as equivalent fractions.
Express mixed numbers as improper fractions.
Express improper fractions as mixed numbers.
Unit 2
Determine lowest common denominators.
Express fractions as equivalent fractions having lowest common denominators.
Add fractions and mixed numbers.
Unit 3
Subtract fractions.
Subtract mixed numbers.
Unit 4
Multiply fractions.
Multiply mixed numbers.
Divide by common factors (cancellation).
Unit 5
Divide fractions.
Divide mixed numbers.
Unit 6
Solve problems that involve combined operations of fractions and mixed numbers.
Solve complex fractions.
© 2026 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 2
accessible website, in whole or in part.
, Instructor Manual: Peterson, John C.; Smith, Robert D.; and McGarry, Kathleen, Mathematics for Machine Technology, 9e, 2026,
9798214116457; Section 1: Common Fractions and Decimal Fractions
Unit 7
Locate decimal fractions on a number line.
Express common fractions having denominators of powers of 10 as equivalent decimal fractions.
Write decimal numbers in word form.
Write numbers expressed in word form as decimal fractions.
Unit 8
Round decimal fractions to any required number of places.
Express common fractions as decimal fractions.
Express decimal fractions as common fractions.
Unit 9
Add decimal fractions.
Add combinations of decimals, mixed decimals, and whole numbers.
Subtract decimal fractions.
Subtract combinations of decimals, mixed decimals, and whole numbers.
Unit 10
Multiply decimal fractions.
Multiply combinations of decimals, mixed decimals, and whole numbers.
Unit 11
Divide decimal fractions.
Divide decimal fractions with whole numbers.
Divide decimal fractions with mixed decimals.
Unit 12
Raise numbers to indicated powers.
Solve problems that involve combinations of powers with other basic operations.
Unit 13
Extract whole number roots.
Solve problems that involve combinations of roots with other basic arithmetic operations.
Unit 14
Write decimal or fraction equivalents using a decimal equivalent table.
Determine nearer fraction equivalents of decimals by using the decimal equivalent table.
Solve problems consisting of combinations of operations by applying the order of operations.
Unit 15
Solve problems by applying the principles and methods covered in Units 1–14
[return to top]
WHAT’S NEW IN THIS SECTION
The following elements are improvements in this section from the previous edition:
© 2026 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 3
accessible website, in whole or in part.
, Instructor Manual: Peterson, John C.; Smith, Robert D.; and McGarry, Kathleen, Mathematics for Machine Technology, 9e, 2026,
9798214116457; Section 1: Common Fractions and Decimal Fractions
Removed unit: Computing with a Calculator: Fractions and Mixed Numbers
Removed unit: Computing with a Spreadsheet: Fractions and Mixed Numbers
Removed unit: Computing with a Calculator: Decimals
Removed unit: Computing with a Spreadsheet: Decimals
[return to top]
SECTION OUTLINE
The following outline provides an overview of the topics covered in this section organized by topic and
subtopic.
I. Unit 1: Introduction to Common Fractions and Mixed Numbers (PPT Slide 2)
i. Working with fractions is crucial for machinists. Precision is key in machining,
and many measurements are given in fractional units to ensure accuracy.
a. Fractional Parts
i. Fractions are a fundamental concept in mathematics and everyday measurements.
They help us understand and work with parts of a whole.
b. Definitions of Fractions
i. A fraction represents how many parts of a whole are being considered. Here are
the two components of a common fraction:
Numerator: The top number in a fraction, indicating how many parts are
taken.
Denominator: The bottom number, showing the total number of equal
parts the whole is divided into.
ii. Terminology:
A proper fraction has a numerator that is smaller than its denominator.
This means the value of the fraction is less than 1.
An improper fraction has a numerator that is larger than or equal to its
denominator. This means the value of the fraction is 1 or greater.
A mixed number combines a whole number with a proper fraction. This
format is useful for representing values greater than 1.
A complex fraction is a fraction where the numerator, the denominator,
or both are themselves fractions or mixed numbers.
c. Expressing Fractions as Equivalent Fractions
i. Equivalent fractions are fractions that represent the same value, even though they
may look different. You can create equivalent fractions by multiplying or
dividing both the numerator and the denominator by the same number.
ii. A fraction is in its lowest terms when the numerator and the denominator have no
common factors other than 1. This process is also known as simplifying or
reducing the fraction.
d. Expressing Mixed Numbers as Improper Fractions
i. To express a mixed number as an improper fraction
Multiply the whole number by the denominator.
Add the numerator to obtain the numerator of the improper fraction.
© 2026 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 4
accessible website, in whole or in part.
9798214116457; Section 1: Common Fractions and Decimal Fractions
Instructor Manual
Peterson, John C.; Smith, Robert D.; and McGarry, Kathleen, Mathematics for
Machine Technology, 9e, 2026, 9798214116457; Section 1: Common Fractions and Decimal
Fractions
TABLE OF CONTENTS
Purpose and Perspective of the Section.......................................................................2
Section Objectives..........................................................................................................2
What’s New in This Section..........................................................................................4
Section Outline..............................................................................................................4
© 2026 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 1
accessible website, in whole or in part.
, Instructor Manual: Peterson, John C.; Smith, Robert D.; and McGarry, Kathleen, Mathematics for Machine Technology, 9e, 2026,
9798214116457; Section 1: Common Fractions and Decimal Fractions
PURPOSE AND PERSPECTIVE OF THE SECTION
The purpose of this section is to provide students with procedures for simplifying and performing
operations (addition, subtraction, multiplication, and division) on common fractions, mixed numbers, and
decimal fractions. Students will learn how to perform whole number exponentiation, extract roots for
positive numbers, and evaluate and approximate expressions involving numerical radical expressions.
Order of operations will be explained and applied to simplify numerical expressions. Students will learn
how to write decimal or fractional equivalents using tables of decimal equivalents. They will learn how to
perform the aforementioned sills and use them in the context of machine technology.
SECTION OBJECTIVES
By the end of this section, you should be able to:
Unit 1
Express fractions in lowest terms.
Express fractions as equivalent fractions.
Express mixed numbers as improper fractions.
Express improper fractions as mixed numbers.
Unit 2
Determine lowest common denominators.
Express fractions as equivalent fractions having lowest common denominators.
Add fractions and mixed numbers.
Unit 3
Subtract fractions.
Subtract mixed numbers.
Unit 4
Multiply fractions.
Multiply mixed numbers.
Divide by common factors (cancellation).
Unit 5
Divide fractions.
Divide mixed numbers.
Unit 6
Solve problems that involve combined operations of fractions and mixed numbers.
Solve complex fractions.
© 2026 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 2
accessible website, in whole or in part.
, Instructor Manual: Peterson, John C.; Smith, Robert D.; and McGarry, Kathleen, Mathematics for Machine Technology, 9e, 2026,
9798214116457; Section 1: Common Fractions and Decimal Fractions
Unit 7
Locate decimal fractions on a number line.
Express common fractions having denominators of powers of 10 as equivalent decimal fractions.
Write decimal numbers in word form.
Write numbers expressed in word form as decimal fractions.
Unit 8
Round decimal fractions to any required number of places.
Express common fractions as decimal fractions.
Express decimal fractions as common fractions.
Unit 9
Add decimal fractions.
Add combinations of decimals, mixed decimals, and whole numbers.
Subtract decimal fractions.
Subtract combinations of decimals, mixed decimals, and whole numbers.
Unit 10
Multiply decimal fractions.
Multiply combinations of decimals, mixed decimals, and whole numbers.
Unit 11
Divide decimal fractions.
Divide decimal fractions with whole numbers.
Divide decimal fractions with mixed decimals.
Unit 12
Raise numbers to indicated powers.
Solve problems that involve combinations of powers with other basic operations.
Unit 13
Extract whole number roots.
Solve problems that involve combinations of roots with other basic arithmetic operations.
Unit 14
Write decimal or fraction equivalents using a decimal equivalent table.
Determine nearer fraction equivalents of decimals by using the decimal equivalent table.
Solve problems consisting of combinations of operations by applying the order of operations.
Unit 15
Solve problems by applying the principles and methods covered in Units 1–14
[return to top]
WHAT’S NEW IN THIS SECTION
The following elements are improvements in this section from the previous edition:
© 2026 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 3
accessible website, in whole or in part.
, Instructor Manual: Peterson, John C.; Smith, Robert D.; and McGarry, Kathleen, Mathematics for Machine Technology, 9e, 2026,
9798214116457; Section 1: Common Fractions and Decimal Fractions
Removed unit: Computing with a Calculator: Fractions and Mixed Numbers
Removed unit: Computing with a Spreadsheet: Fractions and Mixed Numbers
Removed unit: Computing with a Calculator: Decimals
Removed unit: Computing with a Spreadsheet: Decimals
[return to top]
SECTION OUTLINE
The following outline provides an overview of the topics covered in this section organized by topic and
subtopic.
I. Unit 1: Introduction to Common Fractions and Mixed Numbers (PPT Slide 2)
i. Working with fractions is crucial for machinists. Precision is key in machining,
and many measurements are given in fractional units to ensure accuracy.
a. Fractional Parts
i. Fractions are a fundamental concept in mathematics and everyday measurements.
They help us understand and work with parts of a whole.
b. Definitions of Fractions
i. A fraction represents how many parts of a whole are being considered. Here are
the two components of a common fraction:
Numerator: The top number in a fraction, indicating how many parts are
taken.
Denominator: The bottom number, showing the total number of equal
parts the whole is divided into.
ii. Terminology:
A proper fraction has a numerator that is smaller than its denominator.
This means the value of the fraction is less than 1.
An improper fraction has a numerator that is larger than or equal to its
denominator. This means the value of the fraction is 1 or greater.
A mixed number combines a whole number with a proper fraction. This
format is useful for representing values greater than 1.
A complex fraction is a fraction where the numerator, the denominator,
or both are themselves fractions or mixed numbers.
c. Expressing Fractions as Equivalent Fractions
i. Equivalent fractions are fractions that represent the same value, even though they
may look different. You can create equivalent fractions by multiplying or
dividing both the numerator and the denominator by the same number.
ii. A fraction is in its lowest terms when the numerator and the denominator have no
common factors other than 1. This process is also known as simplifying or
reducing the fraction.
d. Expressing Mixed Numbers as Improper Fractions
i. To express a mixed number as an improper fraction
Multiply the whole number by the denominator.
Add the numerator to obtain the numerator of the improper fraction.
© 2026 Cengage Learning, Inc. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly 4
accessible website, in whole or in part.
