SciTech-Mathmatics-Multiplication Product = Multiplier × Multiplicand, Properties{Closure, Commutative, Associative, Distributive, Identity, Zero}

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Proof of the Divison Algorithm

https://mathcenter.oxford.emory.edu/site/math125/proofDivAlgorithm/
The Division Algorithm
If a and b are integers, with a>0,
there exist unique integers q and r such that
$ b=qa+r$ \(0≤r<a\)

The integers q and r are called the quotient and remainder,
respectively, of the division of b by a.

Multiplication

In mathematics, multiplication is a method of finding the product of two or more numbers.
It is one of the basic arithmetic operations, that we use in everyday life.
The major application we can see in multiplication tables.

In arithmetic, the multiplication of two numbers represents the repeated addition of one number with respect to another.
These numbers can be whole numbers, natural numbers, integers, fractions, etc.
If m is multiplied by n, then it means either m is added to itself ‘n’ number of times or vice versa.

Multiplication (denoted by ‘×’) in Maths, is a mathematical operation, apart from addition, subtraction and division.
Students learn the four basic arithmetic operations in their primary classes themselves.
Here we will learn to solve multiplication problems in an easy and quick way.

Table of contents:

• Definition of Multiplication
• Multiplication Symbol
• Multiplication Formula
• Multiplication Properties
  • Closure Property $ (A \times B) \in K, \text{if }A \in K\text{ and } B \in K $
  • Commutative property: $ A \times B = B \times A $
  • Associative property: $ (A \times B) \times C = A \times ( B \times C ) $
  • Distributive property $ A \times ( B + C) = A \times B + A \times C $
  • Identity property $ A \times 1 = A, A \times A^{-1} = A^{-1} \times A = 1 $
  • Zero property: $ A \times 0 = 0 \times A = 0 $
• Multiplication Rules
• Multiplication Signs
• Multiplication Table
• Multiplication of Fractions
• Multiplication of Decimals
• Multiplication Tricks
• Solved Problems
• FAQs

What is Multiplication?

Multiplication is the \(\text{process of calculating}\) the \(\text{product of two or more numbers}\).
The multiplication of numbers say, ‘a’ and ‘b’, is stated as ‘a’ multiplied by ‘b’.

In Maths, the basic explanation of multiplication is adding a number, with respect to another number, repeatedly.

For example, if we are multiplying 2 by 3, that means 3 is added to itself two times, i.e. 3 + 3 = 6. This is a simple technique for kids to multiply numbers.

Multiplication Symbol

The symbol of multiplication is denoted by a cross sign (×), also sometimes by a dot (.).
Examples:
\(8 \times 20 = 8 \times 2 \times 10 = 160\)
\((9) \cdot (10) = 90\)

Multiplication Formula

The multiplication formula is given by:
\(\large \text{Multiplier} \times \text{Multiplicand} = \text{Product}\)

• Multiplicand is the \(\large \text{total number}\ of\ \text{objects in each group}\)
• Multiplier is the \(\large \text{number}\ of\ \text{equal groups}\)
• Product is the \(\large \text{result of multiplication}\ of\ \text{multiplier and multiplicand}\)
• Example:$ If\ \text{Multiplier} = 5\ , \text{Multiplicand} = 8\text{ then the product is }\text{Product} = 40$