Prime numbers | Rational numbers
The reciprocals of prime numbers have been of interest to mathematicians for various reasons. They do not have a finite sum, as Leonhard Euler proved in 1737. Like all rational numbers, the reciprocals of primes have repeating decimal representations. In his later years, George Salmon (1819–1904) concerned himself with the repeating periods of these decimal representations of reciprocals of primes. Contemporaneously, William Shanks (1812–1882) calculated numerous reciprocals of primes and their repeating periods, and published two papers "On Periods in the Reciprocals of Primes" in 1873 and 1874. In 1874 he also published a table of primes, and the periods of their reciprocals, up to 20,000 (with help from and "communicated by the Rev. George Salmon"), and pointed out the errors in previous tables by three other authors. Rules for calculating the periods of repeating decimals from rational fractions were given by James Whitbread Lee Glaisher in 1878. For a prime p, the period of its reciprocal will be equal to or will divide p − 1. The sequence of recurrence periods of the reciprocal primes (sequence in the OEIS) appears in the 1973 Handbook of Integer Sequences. (Wikipedia).
Ex: Determine the Reciprocal of Integers, Fractions, and Mixed Numbers
This video explains how to determine the reciprocal of various rational numbers.
From playlist Multiplying and Dividing Fractions
Prealgebra 3.04e - Reciprocals
A brief introduction to reciprocals: The reciprocal of a number, the reciprocal of a fraction, and the fact that any number multiplied by its reciprocal is 1.
From playlist Prealgebra Chapter 3 (Complete chapter)
Ex: Rational Equation App - Find a Number Given the Sum of Reciprocals
This video explains how to solve a number problem given the sum of reciprocals. http://mathispower4u.com
From playlist Solving Applications using Rational Equations
The reciprocal answers the question, "How many groups of ___ are in 1?" What patterns do reciprocals follow?
From playlist Arithmetic operations | 6th Grade | Khan Academy
From playlist Pre-Algebra/Introductory Algebra
Find the Reciprocal of a Square root of a Fraction
#shorts This video explains how to determine the reciprocal of the square root of a fraction. https://mathispower4u.com
From playlist Math Shorts
Powered by https://www.numerise.com/ Reciprocal graphs 1
From playlist Important graphs
Multiplicative Inverse and Reciprocals
http://www.youtube.com/view_play_list?p=8E39E839B4C6B1DE
From playlist Common Core Standards - 6th Grade
Richard Taylor "Reciprocity Laws" [2012]
Slides for this talk: https://drive.google.com/file/d/1cIDu5G8CTaEctU5qAKTYlEOIHztL1uzB/view?usp=sharing Richard Taylor "Reciprocity Laws" Abstract: Reciprocity laws provide a rule to count the number of solutions to a fixed polynomial equation, or system of polynomial equations, modu
From playlist Number Theory
The Reciprocal Prime Series (this proof should be taught in calculus!)
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From playlist Cool Math Series
Euler-Mascheroni V: The Meissel-Mertens Constant
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From playlist Analysis
Reciprocal rule (KristaKingMath)
► My Derivatives course: https://www.kristakingmath.com/derivatives-course Learn how to use reciprocal rule to calculate the derivative of a function. In order to understand the formula, we'll derive it from the quotient rule formula, then use the reciprocal rule formula to find the deriv
From playlist Calculus I
Euler-Mascheroni III: Another NUCLEAR proof of the infinitude of primes
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From playlist Analysis
Why did they prove this amazing theorem in 200 different ways? Quadratic Reciprocity MASTERCLASS
The longest Mathologer video ever, just shy of an hour (eventually it's going to happen :) One video I've been meaning to make for a long, long time. A Mathologerization of the Law of Quadratic Reciprocity. This is another one of my MASTERCLASS videos. The slide show consists of 550 slides
From playlist Recent videos
Theory of numbers: Quadratic reciprocity
This lecture is part of an online undergraduate course on the theory of numbers. We state and law of quadratic reciprocity for Legendre symbols, and prove it using Gauss sums. As applications we show how to use it to calculate Legendre symbols and to test Fermat numbers to see if they are
From playlist Theory of numbers
The Reciprocals of Primes - Numberphile
Matt Parker explores the work of William Shanks - and boots up the ShanksBot. More links & stuff in full description below ↓↓↓ Matt Parker's 2022 Pi Day Video: https://youtu.be/dtiLxLrzjOQ Discussing William Shanks on Objectivity: https://youtu.be/7yTXMeiVBCc Prime Number playlist: https
From playlist Matt Parker (standupmaths) on Numberphile
Division of Fractions Using Formal Rules
This video explains how to determine the quotient of fractions by writing an equivalent product.
From playlist Multiplying and Dividing Fractions
Quadratic Reciprocity Examples -- Number Theory 24
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From playlist Number Theory v2