Hello there. This math post is on adding fractions. Fractions is one of those topics that people dislike and find difficult. This post will act as a guide with fractions (and rational expressions). The first couple of sections are ideal for grades four to about grade six (age 11/12). The last section on adding rational expressions together is more for high school students (Grade 11). <center><img src="https://learnfractions.files.wordpress.com/2010/12/fractions-chart.png" /></center> <center><a href="Phttps://learnfractions.files.wordpress.com/2010/12/fractions-chart.png">Image Source</a></center> ### Sections --- * The Purpose Of Adding Fractions * Adding Fractions With Same Denominators * Lowest Common Multiples * Adding Fractions With Unlike Denominators * Adding Rational Expressions Together (High-School Level) ### The Purpose Of Adding Fractions --- From an early age, addition involved finding the total of whole numbers and putting numbers together. When we have parts of wholes such as fractions, knowing how to add and subtract fractions is a useful math skill. Applications of adding fractions include buying pieces of fabric, measuring ingredients for cooking and baking, money and distances. <center><img src="https://embed-ssl.wistia.com/deliveries/1ca1580c28e958d809b58f68372d00434ebac9ad.jpg?image_crop_resized=480x300" /></center> <center><a href="https://embed-ssl.wistia.com/deliveries/1ca1580c28e958d809b58f68372d00434ebac9ad.jpg?image_crop_resized=480x300">Image Source</a></center> ### Adding Fractions With Same Denominators --- The simplest case with adding fractions is when the denominators are the same. Recall that the denominator of a fraction is the bottom number. (We also prefer the bottom to not be zero to avoid division by zero.) With the case, you keep the denominator the same and simply just add the numerators (top numbers) together. <center><img src="http://4.bp.blogspot.com/_PtvSlguKUWI/TQgXcN4wFyI/AAAAAAAAAD8/NnmCVXOdLE0/s1600/Fractions-18.png" /></center> <center><a href="http://4.bp.blogspot.com/_PtvSlguKUWI/TQgXcN4wFyI/AAAAAAAAAD8/NnmCVXOdLE0/s1600/Fractions-18.png">A Visual: Image Source</a></center> ### Lowest Common Multiples --- Before we get into adding fraction with different denominators, it is important to know least common multiples between two or more numbers. A multiple is the result from multiplying a number by a whole number. Examples include 8 from 2 x 4, 20 from 10 x 2 and 100 from 10 x 10. *Common Multiples* The number 2 has multiples which consist of 2, 4, 6, 8, 10 and so on. Essentially, we are counting by twos and each number is from multiplying 2 by a whole number such as 1, 2, 3. The number 10 has multiples which are 10, 20, 30, 40 and so on. Common multiples of 2 and 10 consist of multiples that are in 2 and are in 10. The common multiples for 2 and 10 are 10, 20, 30, 40 and so on. *Least Common Multiples* What we seek are least common multiples when it comes to adding fractions with different denominators. The least common multiple of 2 and 10 is 10. To achieve 10 from 2 is through 2 x 5 and to get 10 from 10 is simply 10 x 1. This idea will help in the next section. <center><img src="http://www.mathx.net/image/least_common_multiple.gif" /></center> <center><a href="http://www.mathx.net/image/least_common_multiple.gif">Image Source</a></center> ### Adding Fractions With Unlike Denominators --- ![example01.PNG](https://steemitimages.com/DQmcmk3hWiaDggR7MW64jKWq7aimn2AK5b9JfYnXFBJMvE7/example01.PNG) ![example02.PNG](https://steemitimages.com/DQmc6UtNHHjK3iwkMxfc81VGcb9SgGoLV28UsFiaBtujq2L/example02.PNG) ### Adding Rational Expressions Together (High-School Level) --- As one learns more math they slowly see less numbers and more variables like x. Instead of having numbers on the denominator, we have unknowns like x, y, and z. ![example_12.PNG](https://steemitimages.com/DQmZVbtv8fGWxaBA4E1upU2nnXwd6Digcdxt8mZfDvzuzRe/example_12.PNG) ![example_34.PNG](https://steemitimages.com/DQmcGJ64NWp2j3sLfAtiMg85FdqtPGHRzm6roo1QgqEbT4A/example_34.PNG) <center><img src="http://mathatube.com/images/like_fractions-00.jpg" /></center> <center><a href="http://mathatube.com/images/like_fractions-00.jpg">Image Source</a></center> --- Reference: https://www.mathsisfun.com/definitions/multiple.html The screenshots in the examples were from my RStudio Markdown work.