Skip to Main Content Skip to Main Navigation Skip to Footer
UNG Logo
  • Info For...
    • Accepted Students
    • Current Students
    • Parents & Family
    • Faculty & Staff
    • Alumni
    • Business & Community
    • International Students
  • Quicklinks
    • Directories
    • myUNG
    • Academic Catalogs
    • Athletics
    • Banner
    • Bookstore
    • Calendars
    • Campuses & Maps
    • Continuing Education
    • D2L
    • Employment / HR
    • IT Service Desk
    • Libraries
    • UNG Foundation
  • Admissions
  • Corps of Cadets
  • Academics
  • Cost & Aid
  • Student Life
  • News & Events
  • Athletics
  • About Us

Find the most up-to-date information on the Presidential Search site.

Learning Support
  • What is Learning Support?
    How do I know my Placement?
    What are the requirements?
  • Placement Types
    English Learning Support
    Math Learning Support
  • Resources
    Placement Test Practice
    Study Resources
    Learning Support Courses
  • FAQ
  • Policies & Guidelines
  • Contact
    1. UNG
    2. Academics
    3. Learning Support
    4. Video Transcripts

    Mistake 5 - Simplifying Complex Fractions Incorrectly

    The common mistake number five is that students often flip the denominator or multiply by the reciprocal too early. Let me go ahead and show you the mistake that you look at a complex fraction and say, "Well I know that this is 1 over x and I know that I keep that. Then I change the sign to multiplication from a division and then I just flip this last fraction here. So that's going to be x over 2 plus 1. So now I’ve got, of course  - I can cancel out the x's. And then I can cancel out, let’s see, nothing else. So, it looks like 2 plus 1 is 3 so that equals one-third." Be careful of this. This is definitely the error. What happens is that students will often take the reciprocal of this without actually realizing that the time to take the reciprocal is when you have one fraction on top and one fraction in the denominator. Notice, there are two things here. You do have a one fraction here but then there’s also a whole number there, which if you wanted to, you can make into a fraction to say "2 over 1." And so really, there’s two fractions. So, you're going to have to put it as one whole fraction, meaning one denominator not two different denominators (where this would be an x and that would be a 1). So, this is what is the correct way to do. So the correct way is to go ahead and get this into one fraction. So let's simplify it to that. We've got 1 over x divided by (our least common denominator is going to be x), so we have 2x plus 1. And so now, since we have this top part here into one fraction and then this denominator into another fraction, we can go ahead and apply the reciprocal rule. We've got to keep the first one, change the sign to multiplication and then flip the last one (or multiply by the reciprocal). Notice I can cancel out these x's. And what I am left with is simply 1 over 2x plus 1.

    UNG Logo
    • Contact Us
    • Request Information
    • Quick Facts
    • Campus Maps & Directions
    • Student Consumer Information
    • Campus Safety
    • Emergency Information
    • Employment/HR
    • UNG Policies & Procedures
    • UNG Alumni Association
    • UNG Foundation
    • Ethics & Compliance Hotline
    • Human Trafficking Notice
    • Equal Empl. Opportunity

    © 2023 The University System of Georgia and the University of North Georgia.

    UNG follows the section 508 Standards and WCAG 2.0 for web accessibility. If you require this content in another format, please send an email to the ADA Coordinator.

    Use of military-themed imagery does not constitute endorsement by the U.S. Department of Defense.

    • Accreditation
    • Accessibility
    • Privacy Policy
    Establishing Connection...
    AskNigel