Rational Numbers Courses and Certifications

Math with Mr. J

Rational and Irrational Numbers

Explore the fundamental concepts of rational and irrational numbers through clear explanations, number line identification, graphing techniques, and comparison methods.

• YouTube
• 1 hour 21 minutes
• On-Demand
• Free Video

Common Core Math Grade 8 - The Number System: Standards

Explore eighth-grade number system concepts through engaging lessons and videos, aligning with Common Core standards and enhancing classroom learning.

• Study.com
• 40 minutes
• On-Demand
• Paid Course

Common Core Math Grade 6 - The Number System: Standards

Comprehensive coverage of grade 6 number system topics, including operations, factoring, and rational numbers, aligned with Common Core standards for effective learning and assessment.

• Study.com
• 2 hours 32 minutes
• On-Demand
• Paid Course

STAAR Mathematics - Grade 7: Test Prep & Practice

Comprehensive review of Grade 7 math concepts for STAAR exam, featuring bite-sized lessons and practice quizzes to enhance understanding and test readiness.

• Study.com
• 13 hours
• On-Demand
• Paid Course

Common Core Math Grade 7 - The Number System: Standards

Explore rational numbers and integer operations through engaging video and text lessons, perfect for creating homework, discussions, and assessments aligned with 7th grade Common Core standards.

• Study.com
• 1 hour 36 minutes
• On-Demand
• Paid Course

Explorations in Core Math - Grade 7: Online Textbook Help

Engaging video lessons complement textbook, making 7th-grade math concepts easier to grasp. Covers algebraic reasoning, integers, proportions, graphs, geometry, probability, and more.

• Study.com
• 15 hours 20 minutes
• On-Demand
• Paid Course

Michael Penn

Do We Even Need the Real Numbers?

Explore the possibility of calculus using only rational numbers and discover the crucial role of the axiom of completeness in fundamental calculus theorems.

• YouTube
• 26 minutes
• On-Demand
• Free Video

Dr Trefor Bazett

How Google Designed a Smarter Calculator Than Apple

Explore how Google's calculator outperforms Apple's by using recursive real arithmetic instead of floating point, avoiding errors like 10^100+1-10^100=0 through a hybrid approach that balances accuracy and user experience.

• YouTube
• 26 minutes
• On-Demand
• Free Video

Michael Penn

Real Analysis - The Countability of the Rational Numbers

Explore a rigorous proof demonstrating the countability of rational numbers using a unique approach of representing them as a countable union of disjoint finite sets in real analysis.

• YouTube
• 21 minutes
• On-Demand
• Free Video

Insights into Mathematics

The Deep Structure of the Rational Numbers - Real Numbers and Limits Math Foundations

Explores the deep structure of rational numbers, focusing on their layered nature within [0,1]. Covers key concepts like Farey sequences and Ford circles, emphasizing rationals' importance in modern mathematics.

• YouTube
• 36 minutes
• On-Demand
• Free Video

Wrath of Math

So, There Are Basically No Fractions - The Measure of Rational Numbers is Zero

Discover why almost all real numbers are irrational by exploring measure theory and proving that rational numbers have zero measure on the number line.

• YouTube
• 22 minutes
• On-Demand
• Free Video

Insights into Mathematics

Rational Number Arithmetic with Infinity - Extended Rational Numbers and Limits

Explore arithmetic operations on integral points, extended rational numbers, and the intriguing concept of 0/0. Gain insights into projective geometry and homogeneous coordinates in this mathematical journey.

• YouTube
• 37 minutes
• On-Demand
• Free Video

Wrath of Math

Density of Rational Numbers in Real Numbers - Rudin's Proof Explained

Explore Walter Rudin's proof demonstrating that rational numbers are densely distributed within real numbers, using the Archimedean property from Baby Rudin's analysis text.

• YouTube
• 17 minutes
• On-Demand
• Free Video

Institute for Advanced Study

O-Minimality and Rational Numbers

Explore o-minimality theory and its applications to proving asymptotic estimates for rational points in definable sets across various mathematical areas.

• YouTube
• 1 hour 5 minutes
• On-Demand
• Free Video

Math with Mr. J

Rational Numbers and Number Lines - Identifying, Graphing, Comparing, and Ordering

Comprehensive guide to identifying, graphing, comparing, and ordering rational numbers on number lines. Ideal for beginners and those seeking a refresher on these fundamental mathematical concepts.

• YouTube
• 41 minutes
• On-Demand
• Free Video