ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

How to Reduce Fractions

Updated on January 15, 2015
Reducing fractions makes the fractions easier to read and look less intimidating.
Reducing fractions makes the fractions easier to read and look less intimidating. | Source

Why do we simplify or reduce fractions? We reduce fractions because it makes math and life simpler! If I said I have 8/16 of a pizza you probably would have to stop and think about how much that really is. 8/16 is the same as 1/2. If I said 1/2, you'd probably know right off the bat how much that is. Reducing fractions is easy. If you want to know more about reducing fractions, read on!

What does 'divisible' mean?

(of a number) capable of being divided by another number without a remainder.

For example: 24 is divisible by 4 because 4 times 6 is 24

Reducing Fractions to Lowest Terms

What is reducing fractions to their lowest terms? Essentially, we are making the fraction as small as possible. To reduce a fraction to its lowest terms is very easy. All you need to know is division. To reduce the fraction to lowest terms, you need to find out if a certain number is divisible with the numerator (the top number) AND the denominator (the bottom number). A number is divisible by another if, when you divide them, you don't have a remainder.

Tips and Tricks for Divisibility

You don't always have to do division in order to find out if a number is divisible with another.

  • A number will be divisible by 2 if its last digit is an even number.
  • A number will be divisible by 3 if the sum of its digits is divisible by 3.
  • A number will be divisible by 4 if the number formed in the last two digits is divisible by 4.
  • A number will be divisible by 5 if the last digit is a 5 or a 0.
  • A number will be divisible by 6 if it's also divisible by 2 and 3.
  • A number will be divisible by 9 if the sum of its digits is divisible by 9.
  • A number will be divisible by 10 if the last digit ends in a 0.

To start reducing a fraction, find the factors of each number.
To start reducing a fraction, find the factors of each number. | Source

The first step...

To reduce a fraction to lowest terms, you must first take the original fraction and find all the factors of the numbers. For an example, we'll use the fraction 48/120.

Let's start with 48 and find all the factors. We know that 1 and 48 are factors because 1*48 is 48. 2*24 is 48...so on a so forth. Follow the divisibility tips and divide. Remember, a number doesn't go into 48 evenly, it's not divisible thus, not a factor. By the time you are done, you will discover that the factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, and 48.

Now let's do 120. Follow the same steps with 48 except plug in numbers for 120. 1*120 is 120 so 1 and 120 are both factors of 120. 2*60 is 120 so 2 and 60 are also factors of 120. By the time you are done with this number, you will discover that 1, 2, 3, 4, 5, 6, 8, 10, 12, 15, 20, 24, 30, 40, 60, and 120 are all factors of 120.

After you find the factors of each number, find the common factors between the two and find the greatest common factor.
After you find the factors of each number, find the common factors between the two and find the greatest common factor. | Source

After you find the factors...

After you find the factors, look for all the matching factors between the numerator and denominator. By doing this, you are finding all the common factors.

The common factors between 48 and 120 are 1, 2, 3, 4, 6, 8, 12, and 24.

Now you want to find the greatest common factor (or the GCF for short.) The greatest common factor of 48 and 120 is 24 because it is the highest common factor between the two.

Lastly, divide both numbers by their greatest common factor to get the simplified or reduced fraction.
Lastly, divide both numbers by their greatest common factor to get the simplified or reduced fraction. | Source

Now comes the fun part...

After you find the greatest common factor, you can finally simplify the fraction. To do this, you must divide the numerator and the denominator by its GCF. In this case, the GCF is 24.

Let's start with the numerator. 48 divided by 24 is 3. The new numerator is now 3.

Do the same to the denominator. 120 divided by 24 is 5. The new denominator is now 5.

Double check that you cannot reduce the fraction anymore. The only numbers that go into 3 and 5 are 1 and itself. Therefore, it cannot be reduced anymore.

Your reduced fraction is now 3/5. Congratulations! You just reduced a fraction!

Practice what you learned!

view quiz statistics

Comments

    0 of 8192 characters used
    Post Comment

    • LagunaAlkaline profile image
      Author

      Amanda 5 years ago from Camas, WA

      You are welcome!! I am glad you enjoyed it.

    • btrbell profile image

      Randi Benlulu 5 years ago from Mesa, AZ

      Fun hub. It's interesting to see it written down after all these years of "just knowing" it! Thank you for sharing!

    • LagunaAlkaline profile image
      Author

      Amanda 5 years ago from Camas, WA

      Thank you for the kind words. I am sorry that you feel your 9 year old wouldn't understand. I am planning making a video to add to this a little later and will be certain to explain in a way a 9 year old would understand.

    • Lady Wordsmith profile image

      Linda Rawlinson 5 years ago from Lancaster, UK

      This is great, very useful, for an adult. But I doubt that my 9-year-old son would be able to follow your instructions, and this is the kind of work he is struggling with at school but needs to learn.

      Good hub though.

      Linda.

    working

    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, hubpages.com uses cookies (and other similar technologies) and may collect, process, and share personal data. Please choose which areas of our service you consent to our doing so.

    For more information on managing or withdrawing consents and how we handle data, visit our Privacy Policy at: "https://hubpages.com/privacy-policy#gdpr"

    Show Details
    Necessary
    HubPages Device IDThis is used to identify particular browsers or devices when the access the service, and is used for security reasons.
    LoginThis is necessary to sign in to the HubPages Service.
    Google RecaptchaThis is used to prevent bots and spam. (Privacy Policy)
    AkismetThis is used to detect comment spam. (Privacy Policy)
    HubPages Google AnalyticsThis is used to provide data on traffic to our website, all personally identifyable data is anonymized. (Privacy Policy)
    HubPages Traffic PixelThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized.
    Amazon Web ServicesThis is used to collect data on traffic to articles and other pages on our site. Unless you are signed in to a HubPages account, all personally identifiable information is anonymized. (Privacy Policy)
    CloudflareThis is used to quickly and efficiently deliver files such as javascript, cascading style sheets, images, and videos. (Privacy Policy)
    Google Hosted LibrariesJavascript software libraries such as jQuery are loaded at endpoints on the googleapis.com or gstatic.com domains, for performance and efficiency reasons. (Privacy Policy)
    Facebook LoginYou can use this to streamline signing up for, or signing in to your Hubpages account. No data is shared with Facebook unless you engage with this feature. (Privacy Policy)
    PaypalThis is used for a registered author who enrolls in the HubPages Earnings program and requests to be paid via PayPal. No data is shared with Paypal unless you engage with this feature. (Privacy Policy)
    Google AdSense Host APIThis service allows you to sign up for or associate a Google AdSense account with HubPages, so that you can earn money from ads on your articles. No data is shared unless you engage with this feature. (Privacy Policy)
    Features
    Google Custom SearchThis is feature allows you to search the site. (Privacy Policy)
    Google MapsSome articles have Google Maps embedded in them. (Privacy Policy)
    Google ChartsThis is used to display charts and graphs on articles and the author center. (Privacy Policy)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (Privacy Policy)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    Marketing
    Google AdSenseThis is an ad network. (Privacy Policy)
    Google DoubleClickGoogle provides ad serving technology and runs an ad network. (Privacy Policy)
    Index ExchangeThis is an ad network. (Privacy Policy)
    SovrnThis is an ad network. (Privacy Policy)
    Facebook AdsThis is an ad network. (Privacy Policy)
    Amazon Unified Ad MarketplaceThis is an ad network. (Privacy Policy)
    AppNexusThis is an ad network. (Privacy Policy)
    OpenxThis is an ad network. (Privacy Policy)
    Rubicon ProjectThis is an ad network. (Privacy Policy)
    TripleLiftThis is an ad network. (Privacy Policy)
    Say MediaWe partner with Say Media to deliver ad campaigns on our sites. (Privacy Policy)
    Remarketing PixelsWe may use remarketing pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to advertise the HubPages Service to people that have visited our sites.
    Conversion Tracking PixelsWe may use conversion tracking pixels from advertising networks such as Google AdWords, Bing Ads, and Facebook in order to identify when an advertisements has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    Statistics
    Author Google AnalyticsThis is used to provide traffic data and reports to the authors of articles on the HubPages Service. (Privacy Policy)
    ComscoreComScore is a media measurement and analytics company providing marketing data and analytics to enterprises, media and advertising agencies, and publishers. Non-consent will result in ComScore only processing obfuscated personal data. (Privacy Policy)
    Amazon Tracking PixelSome articles display amazon products as part of the Amazon Affiliate program, this pixel provides traffic statistics for those products (Privacy Policy)