Module 2: Fractions, Decimals, & Percentages Complete
Math Guide (2025/2026)
Document Content
➢ 2.01 Learning Objectives
➢ 2.02 Introduction to Fractions
➢ 2.03 Identify Equivalent Fractions
➢ 2.03.1 Reducing Fractions
➢ 2.03.2 The Butterfly Method: Identifying Equivalent Fractions
➢ 2.04 Multiples and the Least Common Multiple
➢ 2.05 Least Common Denominators
➢ 2.06 Fractions: Addition & Subtraction
➢ 2.07.1 Multiplying Fractions and Mixed Numbers
➢ 2.07.2 Dividing Fractions and Mixed Numbers
➢ 2.08 Decimals
➢ 2.09 Rounding
➢ 2.10 Decimals: Addition and Subtraction
➢ 2.11 Decimals: Multiplication and Division
➢ 2,12 Percentages
➢ 2.13 Proportions and Unknown Quantity
➢ 2.14 Convert Decimals, Fractions, and Percentages
➢ 2.15 Unit Conversions
➢ 2.17 Review Game: Fractions, Decimals, & Percentages
Module 2: Fractions, Decimals, & Percentages
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2.01 Learning Objectives
Module 2: Learning Objectives
After completing this module, you should be able to:
1. Identify equivalent fractions
2. Identify the Least Common Denominator of two fractions
3. Apply the mathematical operations of addition, subtraction, multiplication, and division to fractions
4. Identify place values for a given decimal number
5. Apply a given rounding algorithm for decimal numbers
6. Apply the mathematical operations of addition, subtraction, multiplication, and division to decimals
7. Apply the mathematical operations of addition, subtraction, multiplication, and division to percentage values
8. Solve for an unknown quantity using ratios in the context of a proportion
9. Convert between decimals, fractions, and percentages
10. Apply basic unit conversions for household and metric measures
,2.02 Introduction to Fractions
Introduction to Fractions
Whole Number Refresher
Whole Number Review
Whole numbers are numbers whose values are "whole," such as 1 or 2. These numbers represent whole units, or multiple whole units.
For example, let's use these numbers to talk about pie. If you have 1 pie, this number represents 1 whole pie. If you have 2 pies, this
number represents 2 whole pies. What about the situation where you only have part of a pie?
Proper Fractions
In a proper fraction, the numerator is less than the denominator, and therefore, the value is less than 1. We can read these
fractions as four-fifths, one-half, and seven-eighths.
Improper Fractions
In an improper fraction, the numerator is greater than the denominator, and therefore, the value is greater than 1 (except if the
fraction is negative, which we will discuss later). We can read these fractions as seven over four, six over one, and five over
two.
Mixed Numbers
A mixed number consists of a whole number and a proper fraction. Note that a negative sign in front applies to both parts of the
mixed number.
1
-8
14
We can read these mixed numbers as:
One and one-third
Negative eight and two-fifths
Fourteen and one-half
Changing Improper Fractions and Mixed Numbers
Improper fractions can be converted to mixed numbers by following these steps:
, 1. Write division problem with numerator divided by denominator.
2. Divide to determine quotient and remainder.
3. Write mixed number with the quotient as the whole number and the remainder as the numerator over the same denominator.
Example: Changing an Improper Fraction to a Mixed Number
Change from a fraction to a mixed number.
Step 1: Write the fraction as a division problem: 9 divided by 5. 5 goes into 9 one time with a remainder of 4.
Step 3: Write the answer using the quotient, 1, followed by a fraction whose
numerator is the remainder, 4, and whose denominator is the
Step 2: Solve by dividing numerator 9 by denominator 5.
denominator from the original fraction, 5.
Changing Mixed Numbers Into Improper Fractions
Mixed numbers can also be converted to improper fractions by following these steps:
1. Multiply the whole number by the denominator of the fraction.
2. To the product given by step 1, add the number of the numerator.
3. Write the result of step 2 as the numerator of the improper fraction. The denominator of the improper fraction should be the
denominator of the original fraction.
4. Simplify the improper fraction by diving the numerator and denominator by all common factors.
Example: Changing a Mixed Number to an Improper Fraction
Change 1 from a mixed number to an improper fraction.
Step 1: Multiply the whole number by the fraction's denominator.
1×5=5
Step 2: Add that product to the numerator of the fraction.
5+4=9
Step 3: The answer from step 2 now becomes the numerator of the improper fraction. Rewrite the answer as an improper fraction.
Step 4: Reduce the fraction.
No reduction is necessary.
Here is the same example from above in a more graphical presentation:
Math Guide (2025/2026)
Document Content
➢ 2.01 Learning Objectives
➢ 2.02 Introduction to Fractions
➢ 2.03 Identify Equivalent Fractions
➢ 2.03.1 Reducing Fractions
➢ 2.03.2 The Butterfly Method: Identifying Equivalent Fractions
➢ 2.04 Multiples and the Least Common Multiple
➢ 2.05 Least Common Denominators
➢ 2.06 Fractions: Addition & Subtraction
➢ 2.07.1 Multiplying Fractions and Mixed Numbers
➢ 2.07.2 Dividing Fractions and Mixed Numbers
➢ 2.08 Decimals
➢ 2.09 Rounding
➢ 2.10 Decimals: Addition and Subtraction
➢ 2.11 Decimals: Multiplication and Division
➢ 2,12 Percentages
➢ 2.13 Proportions and Unknown Quantity
➢ 2.14 Convert Decimals, Fractions, and Percentages
➢ 2.15 Unit Conversions
➢ 2.17 Review Game: Fractions, Decimals, & Percentages
Module 2: Fractions, Decimals, & Percentages
,Course Support Community
WGU has partnered with WGU Connect to provide a Course Support Community for students in this course. Join the WGU Connect community
to begin asking your questions and engaging with course instructors and your peers!
Launch course community
2.01 Learning Objectives
Module 2: Learning Objectives
After completing this module, you should be able to:
1. Identify equivalent fractions
2. Identify the Least Common Denominator of two fractions
3. Apply the mathematical operations of addition, subtraction, multiplication, and division to fractions
4. Identify place values for a given decimal number
5. Apply a given rounding algorithm for decimal numbers
6. Apply the mathematical operations of addition, subtraction, multiplication, and division to decimals
7. Apply the mathematical operations of addition, subtraction, multiplication, and division to percentage values
8. Solve for an unknown quantity using ratios in the context of a proportion
9. Convert between decimals, fractions, and percentages
10. Apply basic unit conversions for household and metric measures
,2.02 Introduction to Fractions
Introduction to Fractions
Whole Number Refresher
Whole Number Review
Whole numbers are numbers whose values are "whole," such as 1 or 2. These numbers represent whole units, or multiple whole units.
For example, let's use these numbers to talk about pie. If you have 1 pie, this number represents 1 whole pie. If you have 2 pies, this
number represents 2 whole pies. What about the situation where you only have part of a pie?
Proper Fractions
In a proper fraction, the numerator is less than the denominator, and therefore, the value is less than 1. We can read these
fractions as four-fifths, one-half, and seven-eighths.
Improper Fractions
In an improper fraction, the numerator is greater than the denominator, and therefore, the value is greater than 1 (except if the
fraction is negative, which we will discuss later). We can read these fractions as seven over four, six over one, and five over
two.
Mixed Numbers
A mixed number consists of a whole number and a proper fraction. Note that a negative sign in front applies to both parts of the
mixed number.
1
-8
14
We can read these mixed numbers as:
One and one-third
Negative eight and two-fifths
Fourteen and one-half
Changing Improper Fractions and Mixed Numbers
Improper fractions can be converted to mixed numbers by following these steps:
, 1. Write division problem with numerator divided by denominator.
2. Divide to determine quotient and remainder.
3. Write mixed number with the quotient as the whole number and the remainder as the numerator over the same denominator.
Example: Changing an Improper Fraction to a Mixed Number
Change from a fraction to a mixed number.
Step 1: Write the fraction as a division problem: 9 divided by 5. 5 goes into 9 one time with a remainder of 4.
Step 3: Write the answer using the quotient, 1, followed by a fraction whose
numerator is the remainder, 4, and whose denominator is the
Step 2: Solve by dividing numerator 9 by denominator 5.
denominator from the original fraction, 5.
Changing Mixed Numbers Into Improper Fractions
Mixed numbers can also be converted to improper fractions by following these steps:
1. Multiply the whole number by the denominator of the fraction.
2. To the product given by step 1, add the number of the numerator.
3. Write the result of step 2 as the numerator of the improper fraction. The denominator of the improper fraction should be the
denominator of the original fraction.
4. Simplify the improper fraction by diving the numerator and denominator by all common factors.
Example: Changing a Mixed Number to an Improper Fraction
Change 1 from a mixed number to an improper fraction.
Step 1: Multiply the whole number by the fraction's denominator.
1×5=5
Step 2: Add that product to the numerator of the fraction.
5+4=9
Step 3: The answer from step 2 now becomes the numerator of the improper fraction. Rewrite the answer as an improper fraction.
Step 4: Reduce the fraction.
No reduction is necessary.
Here is the same example from above in a more graphical presentation:
