Mastering Basic Arithmetic: Operations, Fractions, and Percentages

The Organic Chemistry Tutor

This comprehensive video tutorial provides a thorough review of fundamental arithmetic concepts essential for middle school math success. It begins by grounding students in the basics of addition and subtraction using number lines to explain integer operations, before progressing to multi-digit column arithmetic with carrying and borrowing. The video systematically covers all four major operations—addition, subtraction, multiplication, and division—using varied strategies like standard algorithms, mental math tricks, and real-world analogies involving money to make abstract concepts concrete. Beyond basic operations, the video transitions into more complex topics including operations with decimals, long division leading to decimal answers, and operations with fractions having unlike denominators. The instructor demonstrates clear, step-by-step methods for finding common denominators and converting improper fractions to mixed numbers. The visual style mimics a blackboard, allowing students to follow the handwriting and procedural flow of each problem naturally. The final section of the video focuses on practical applications of percentages, specifically calculating tips and sales tax. It teaches powerful mental math strategies—such as finding 10%, 5%, and 1% separately to build up to complex percentages like 15% or 18%—which are invaluable life skills. This video serves as an excellent refresher for students transitioning to pre-algebra or for those needing remediation in core numeracy skills.