Division (mathematics) | Elementary arithmetic
Division is one of the four basic operations of arithmetic, the ways that numbers are combined to make new numbers. The other operations are addition, subtraction, and multiplication. At an elementary level the division of two natural numbers is, among other possible interpretations, the process of calculating the number of times one number is contained within another. This number of times need not be an integer. For example, if 20 apples are divided evenly between 4 people, everyone receives 5 apples (see picture). The division with remainder or Euclidean division of two natural numbers provides an integer quotient, which is the number of times the second number is completely contained in the first number, and a remainder, which is the part of the first number that remains, when in the course of computing the quotient, no further full chunk of the size of the second number can be allocated. For example, if 21 apples are divided between 4 people, everyone receives 5 apples again, and 1 apple remains. For division to always yield one number rather than a quotient plus a remainder, the natural numbers must be extended to rational numbers or real numbers. In these enlarged number systems, division is the inverse operation to multiplication, that is a = c / b means a × b = c, as long as b is not zero. If b = 0, then this is a division by zero, which is not defined. In the 21-apples example, everyone would receive 5 apple and a quarter of an apple, thus avoiding any leftover. Both forms of division appear in various algebraic structures, different ways of defining mathematical structure. Those in which a Euclidean division (with remainder) is defined are called Euclidean domains and include polynomial rings in one indeterminate (which define multiplication and addition over single-variabled formulas). Those in which a division (with a single result) by all nonzero elements is defined are called fields and division rings. In a ring the elements by which division is always possible are called the units (for example, 1 and −1 in the ring of integers). Another generalization of division to algebraic structures is the quotient group, in which the result of "division" is a group rather than a number. (Wikipedia).
Solving Equations Using Multiplication or Division
This video is about Solving Equations with Multiplication and Division
From playlist Equations and Inequalities
In this video, you’ll learn more about dividing numbers. Visit https://www.gcflearnfree.org/multiplicationdivision/introduction-to-division/1/ for our interactive text-based lesson. This video includes information on: • Writing division expressions • Solving division problems • Remainders
From playlist Math Basics
Dividing by a number is the same thing as multiplying by a reciprocal. This concept is particularly applicable when dividing by a fraction. Several examples are worked out and explained. From chapter 2 of the Algebra 1 course by Derek Owens
From playlist Algebra 1 Chapter 2 (Selected Videos)
From playlist Complex Multiplication
Is 2023 divisible by 3? Get the answer FAST! (no calculator)
How to use the divisibility rule for 3. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to follow and understand math instruction, with fully explained practice problems and printable worksheets, review notes and quizzes. All co
From playlist GED Prep Videos
Tesla’s 3-6-9 and Vortex Math: Is this really the key to the universe?
Today, a long overdue foray into the realm of VORTEX MATHEMATICS :) 00:00 Intro 04:16 The vortex 08:10 The maths of remainders and digital roots 13:25 Demystifying the vortex 16:30 A matter of base. The 8 fingered Tesla. 19:21 Explanation why the digital root is the remainder on division
From playlist Recent videos
Divide like a Babylonian! With our new "centimal" arithmetic (base 100) | Sociology and pure maths
Division is the most difficult of the four basic arithmetical operations. Here we shed light on the Old Babylonian approach to division in their sexagesimal or base 60 system, by translating their arithmetic to the new base 100, or centimal" . We have some critical things to say about our
From playlist Sociology and Pure Mathematics
The Practice of Mathematics - Part 12
The Practice of Mathematics Robert P. Langlands Institute for Advanced Study February 22, 2000 Robert P. Langlands, Professor Emeritus, School of Mathematics. There are several central mathematical problems, or complexes of problems, that every mathematician who is eager to acquire some
From playlist Mathematics
99% of Adults Don’t REMEMBER This math……
TabletClass Math: https://tcmathacademy.com/ Math help with division and arithmetic. For more math help to include math lessons, practice problems and math tutorials check out my full math help program at https://tcmathacademy.com/ Math Notes: Pre-Algebra Notes: https://tabletclas
From playlist GED Prep Videos
Hierarchy of Results/Direct Proof
We look at different types of mathematical results such as Theorems, Propositions, Corollaries, and Lemmas. Next, we explore the direct method of proof, giving an outline and some examples. Please Subscribe: https://www.youtube.com/michaelpennmath?sub_confirmation=1 Merch: https://teespr
From playlist Proof Writing
The Quotient Rule and Polynumber Division | Algebraic Calculus One | Wild Egg
The Quotient Rule follows easily from the Product Rule, but it has an interesting additional role in extending the Faulhaber Derivative D from polynumbers to more general quotient polynumbers. We also show how it gives us an Integral Transmutation theorem in the spirit of Leibniz. Divisi
From playlist Algebraic Calculus One
Emmy Noether: breathtaking mathematics - Georgia Benkart
Celebrating Emmy Noether Topic: Emmy Noether: breathtaking mathematics Speaker: Georgia Benkart Affiliation: University of Wisconsin-Madison Date: Friday, May 6 By the mid 1920s, Emmy Noether had made fundamental contributions to commutative algebra and to the theory of invariants.
From playlist Celebrating Emmy Noether
Proof: a³ - a is always divisible by 6 (1 of 2: Two different approaches)
More resources available at www.misterwootube.com
From playlist The Nature of Proof
Order of Operations (PEMDAS) – Let’s Learn Step by Step…
Learn the Order of Operations (PEMDAS) - "Please, Excuse, My, Dear, Aunt, Sally" which stands for Parenthesis, Exponents, Multiplication, Division, Addition and Subtraction. For more in-depth math help check out my catalog of courses. Every course includes over 275 videos of easy to fol
From playlist GED Prep Videos
The Division Algorithm and Remainder Classes
This video introduces and division algorithm and remainder classes. mathispower4u.com
From playlist Additional Topics: Generating Functions and Intro to Number Theory (Discrete Math)