Geometric Visualization of Fraction Addition and Subtraction

This GeoGebra applet demonstrates fraction addition and subtraction through circular geometric representations. It uses Least Common Multiple (LCM) and Greatest Common Divisor (GCD) calculations to find common denominators, visualizing the process through circle segmentation, translation, and shading. The interactive visualization includes geometric representations of numerators and denominators, animated circle cutting and merging after finding common denominators, helping learners grasp the geometric meaning behind fraction operations. Students can manipulate the numerators and denominators of two fractions and watch in real time as the circles are divided into equal parts, shaded regions are combined or subtracted, and the results are simplified. This hands-on approach bridges the gap between abstract arithmetic procedures and concrete visual understanding, making it especially valuable for students who struggle with the concept of common denominators or the mechanics of renaming fractions before performing addition or subtraction. By seeing how fractional parts physically align and overlap on identical circles, learners develop an intuitive sense of why the standard algorithm works rather than merely memorizing steps. The applet was originally created by Morton Betts and translated into Chinese by Samsam.