Back To Course

High School Algebra I: Help and Review25 chapters | 291 lessons

Watch short & fun videos
**Start Your Free Trial Today**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Betty Bundly*

Betty has a master's degree in mathematics and 10 years experience teaching college mathematics.

In this lesson, we will learn about working with improper fractions. Although a topic of elementary mathematics, fractions are important and occur in everyday calculations. Knowing how to calculate with fractions is an important lifelong skill.

All fractions contain two parts: a numerator and denominator. In the fraction 2/3, the number 2 is the numerator and the number 3 is the denominator. The **denominator** tells how many equal-sized parts make one whole and the **numerator** tells how many of those parts are being counted. So, 2/3 means that a whole contains 3 equal-sized parts, and only 2 of the 3 are being counted.

Sometimes, the number of parts being counted is actually more than the number of parts in the whole. The fraction 4/3 is an example of this, and these types of fractions are called **improper fractions**. Since you only need 3 parts to make 1 whole and 4 parts are being counted, the fraction 4/3 actually represents a number greater than 1 whole, and this is true for all improper fractions.

You can make many fractions that are **equivalent**, or equal in value, to one that you're given. One way is to multiply the numerator and denominator by the same number. For example, the fraction 1/2 is equivalent to 3/6 because if I multiply both 1 and 2 by 3, I get 3 in the numerator and 6 in the denominator.

(1 * 3)/(2 * 3) = 3/6

These fractions represent the same value. I can also make an equivalent fraction by dividing the numerator and denominator by the same number. For example, consider the fraction 6/4. I can divide both the numerator and denominator by the number 2.

(6 / 2)/(4 / 2) = 3/2

This means that the fraction 3/2 is equivalent or equal to the fraction 6/4.

To demonstrate that these two fractions represent equal amounts, two diagrams are shown. In one, we see 6/4 represented as two rectangles, where each is divided into 4 equal parts and 6 parts total shaded. The second diagram shows two equal-sized rectangles but divided differently; each rectangle is divided into 2 equal-sized parts and 3 parts total shaded. Although they are divided differently, the two rectangles can be seen to represent the same amount.

The terms 'simplifying' or 'reducing' means the same thing when referring to fractions, so these terms can be used interchangeably.

When you reduce a fraction, it becomes simpler because the number of parts in the whole is made small as possible, without changing the value of the fraction. We found that 6/4 = 3/2. While both represent the same amount, 3/2 has 2 parts to make one whole and 2 is smaller than the 4 parts to make one whole in the fraction 6/4.

It is possible to make a fraction simpler without completely simplifying it. Consider, for example, the fraction 18/12. To make a simpler fraction, I could divide the top and bottom by 3.

(18 / 3)/(12 / 3) = 6/4

This fraction is simpler because I now have 4 parts to make one whole instead of 12. However, we know from working with this same fraction above that it can be simplified further to 3/2.

A fraction is **simplified**, or **reduced to lowest terms**, when there is no number other than 1 that divides into both the numerator and denominator. We would say that 6/4 and 18/12 reduce to the fraction 3/2. In fact, all equivalent fractions will always reduce to the same fraction in lowest terms.

To reduce a fraction to lowest terms, try to find the largest number that divides into both numerator and denominator. This number is also known as the greatest common divisor, or GCD, for both the numerator and denominator. The multiplication tables may be helpful. Notice, for example, that both 18 and 12 are in the 6 time tables, and it is the largest multiplication table that contains both 18 and 12. So, to reduce this fraction, we divide both 18 and 12 by 6.

(18 / 6)/(12 / 6) = 3/2

It's better to use the GCD because if you don't use the GCD first, more than one division step will be necessary. After dividing once, check again for another number that can be divided into numerator and denominator. Remember, the numerator and denominator must be divided by the same number or the new fraction will not be equivalent to the original one.

A fraction can also be reduced by factoring the numerator and denominator into prime factors, then cancelling all common factors. To show this method on 18/12, the steps would be:

- Factor 18 into prime factors: 18 = 3 * 3 * 2
- Factor 12 into prime factors: 12 = 3 * 2 * 2
- Rewrite the numerator and denominator as a product of prime factors. 18/12 = (3 * 3 * 2)/(3 * 2 * 2)
- Cancel all factors common to the numerator and denominator. The remaining factors will be the reduced fraction. In this case, one factor of 3 and 2 are common and can be cancelled. (3 * 2 * 3)/(3 * 2 * 2) = 3/2

An **improper fraction** is one where the numerator is larger than the denominator. All improper fractions are greater than one whole. To reduce an improper fraction, you must use division to find an equivalent fraction with the smallest number of parts in the whole. One method is to divide the numerator and denominator by the same number. They must be divided by the same number or the new fraction will not equivalent to the original one. A fraction can also be reduced by factoring both numerator and denominator into prime factors, then cancelling all common factors.

To unlock this lesson you must be a Study.com Member.

Create your account

Already a member? Log In

BackDid you know… We have over 79 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
22 in chapter 3 of the course:

Back To Course

High School Algebra I: Help and Review25 chapters | 291 lessons

- What is a Decimal Place Value? 6:19
- Comparing and Ordering Decimals 8:56
- Addition, Subtraction, Multiplication, and Division with Decimal Notation 4:50
- Adding and Subtracting Decimals: Examples & Word Problems 6:53
- Multiplying and Dividing Decimals: Examples & Word Problems 5:29
- How to Estimate with Decimals to Solve Math Problems 8:51
- How to Build and Reduce Fractions 3:55
- How to Find Least Common Denominators 4:30
- Comparing and Ordering Fractions 7:33
- Changing Between Improper Fraction and Mixed Number Form 4:55
- How to Add and Subtract Like Fractions and Mixed Numbers 4:14
- How to Add and Subtract Unlike Fractions and Mixed Numbers 6:46
- Multiplying Fractions and Mixed Numbers 7:23
- Dividing Fractions and Mixed Numbers 7:12
- Practice with Fraction and Mixed Number Arithmetic 7:50
- Estimation Problems using Fractions 7:37
- Solving Problems using Fractions and Mixed Numbers 7:08
- How to Solve Complex Fractions 5:20
- Using the Number Line to Compare Decimals, Fractions, and Whole Numbers 6:46
- How to Simplify Word Problems with Fractions Using Whole Numbers 3:38
- How to Solve Algebra Problems with Fractions
- How to Reduce or Simplify Improper Fractions 6:37
- What is an Improper Fraction? - Definition & Example 3:43
- Partial Fraction Decomposition: Rules & Examples
- Partial Fractions: Rules, Formula & Examples
- Unlike Fractions: Definition & Examples 5:54
- Go to High School Algebra - Decimals and Fractions: Help and Review

- PTE Academic Test: Practice & Study Guide
- TOEIC Listening & Reading: Test Prep & Practice
- Florida Supplemental Exam for Appraisers: Study Guide
- PFS Exam Study Guide - CPA Personal Financial Specialist
- Learning Calculus: Basics & Homework Help
- Castle History for Elementary School
- Planet Earth for Elementary School
- What Animals Eat for Elementary School
- Adaptations for Elementary School
- Aquatic Animal Adaptations for Elementary School
- Excelsior College BS in Business Degree Plan Using Study.com
- IELTS General Training Reading: Format & Task Types
- IELTS General Training Writing: Format & Task Types
- Gates-MacGinitie Reading Test Scores
- IELTS General Training Test: Structure & Scoring
- Supply and Demand Activities for Kids
- Speed Reading for Kids

- What Is the Uniform Commercial Code? - Definition & Example
- Cultural Globalization: Definition, Factors & Effects
- Effects of Fiscal & Monetary Policy on Personal Finance
- Effective Email Marketing Tips
- Information Technology: Roles & Responsibilities
- Following Directions Social Stories
- If-Then Activities for Kids
- Conglomerate Merger: Definition & Examples
- Quiz & Worksheet - Brabantio in Othello
- Quiz & Worksheet - FDR's First Inaugural Address
- Quiz & Worksheet - Using the Z Test Formula
- Quiz & Worksheet - What Is Gemeinschaft?
- Muscle Contraction Flashcards
- Water Polo Flashcards

- AP Biology: Exam Prep
- US History: Curriculum Resource & Lesson Plans
- Environmental Science 101: Environment and Humanity
- NY Regents Exam - Living Environment: Test Prep & Practice
- How to Apply to College: Guidance Counseling
- The Role of the Police Department: Help and Review
- Mathematical Sequences and Series: Homework Help
- Quiz & Worksheet - Characteristics of Autobiographical Essays
- Quiz & Worksheet - Consumer Protection Governmental Agencies
- Quiz & Worksheet - Characteristics of Centripetal Force
- Quiz & Worksheet - The Yom Kippur War
- Quiz & Worksheet - Position Statements

- The Great Plains: Facts & History
- Andrew Jackson on Indian Removal: History & Explanation
- 504 Plans in Maryland
- Finding Travel Grants for Teachers
- Common Core Narrative Writing Prompts
- What Is Science? - Lesson Plan
- How to Find Classroom Grants for Teachers
- Behavior Rubric Examples
- Paraprofessional Certification in Texas
- MCAT Tips
- NYSTCE Score Report Information
- Illinois Common Core Math Standards

Browse by subject