ArtsAutosBooksBusinessEducationEntertainmentFamilyFashionFoodGamesGenderHealthHolidaysHomeHubPagesPersonal FinancePetsPoliticsReligionSportsTechnologyTravel

Basic Fractions (Curious Concepts Precalculus 1.4)

Updated on August 28, 2013
fractions: multiplying, dividing, adding, and subtracting
fractions: multiplying, dividing, adding, and subtracting

Self-explain Learning Technique

Self-explain Learning Technique helps people to better comprehend, and remember any thing they want to learn. It my sound strange, but it is many times more effective then re-reading. To use this technique, give short answers to the prompted questions. The more previous knowledge-and-life experience that you incorporate into your answer, the more effective this learning technique is. On average it improves learning by over 2.5 standard deviations; the difference between a C student and an A student.

How have you struggled with fractions?

Fractions are the way we express parts or groups of parts: 2/3 means that we have 2 of 3 parts. This can also be conintued on past a complete whole: 4/3 means we have 4 of 3 part; we have enough 1/3's to make 1 complete whole and have another one 1/3.

Strangely, it is more to know how to muliply and divide fractions before we try to add and subtract them.

Multiplying Fractions

We multiply fractions by multiplying the numerators together and place it over the product of the denominators. This can easily be remembered as multiplying straight across.

(a/b)(C/D) = (aC)/(bD)


(3/7)(6/5) = [3(6)] / [7(5)] = 18/35

Self-explain Learning Technique

How would accidentally flipping the number being divided effect your answer?

Dividing Fractions

Dividing fractions is very similar to multiplying fractions. The key difference is that we flip the fraction that we are dividing by before we multiply straight across.

(a/b) / (C/D) = (a/b)(D/C) = (aD) / (bC)

Adding Fractions

We always try to express a fraction in the easiest way to understand it. We can do this by making the bottom number the smallest possible Integer. If we have 2/4 we express it as ½. We know that 2/4 is the same as ½ because both 2 and 4 can be divided by 2. This will reduce 2/4 into ½, making it easier to understand.

What if we wanted to add 7/3 to ½? We first start by finding a common denominator. The simplest and easiest way to get a common denominator is to multiply both fractions by 1 ;). 1 can be expressed as 3/3 and 2/2. We multiply 7/3 by 2/2, getting 14/6. Then we multiply ½ by 3/3 getting 3/6. now we can add: 14/6 + 3/6 = 17/6. We only add the top number (numerator), the bottom number (denominator) remains the same.

We can not reduce 17/6 because 17 is not divisible by 3 or 2. We can leave it as an improper fraction almost anywhere other then basic math courses.

If we are in a basic math course, we want to better understand the value of fractions greater then 1. This is why we do not use improper fractions as our final answer. If we are given the fraction 17/6 we can turn it into a mixed number. First we find out how many times 6 goes into 17. 6 goes into 17, 2 times. We write 2 as a whole number. Next too the 2 we write the remaining fraction: 5/6. our final answer will be 2 and 5/6.

Self-explain Learning Technique

How would you add to a negative fraction?

Subtracting Fractions

Subtraction is the same as adding a negative: a-b = a+(-b). We subtract fractions just like how we add them. The only minor difference is that we are adding a negative value: 5/2 + (-1/2). Since the denominators are the same we just subtract the top numbers or add a loss: 5-1 = 4. We place this over the denominator and get 4/2. The Numerator, 4 can be evenly divided by the Denominator, 2. Our final answer will be 2, because 4 halves is the same as 2.


    0 of 8192 characters used
    Post Comment

    No comments yet.


    This website uses cookies

    As a user in the EEA, your approval is needed on a few things. To provide a better website experience, 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:

    Show Details
    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 a cloud services platform that we used to host our service. (Privacy Policy)
    CloudflareThis is a cloud CDN service that we use to efficiently deliver files required for our service to operate 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 or domains, for performance and efficiency reasons. (Privacy Policy)
    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 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)
    Google YouTubeSome articles have YouTube videos embedded in them. (Privacy Policy)
    VimeoSome articles have Vimeo videos embedded in them. (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)
    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)
    MavenThis supports the Maven widget and search functionality. (Privacy Policy)
    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 advertisement has successfully resulted in the desired action, such as signing up for the HubPages Service or publishing an article on the HubPages Service.
    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)
    ClickscoThis is a data management platform studying reader behavior (Privacy Policy)