Questions and Answers
The multiplication of two numbers, a and b, is written as a + b.
False
The order of the numbers being multiplied does not change the result.
True
Multiplication can be distributed over subtraction.
False
Any number multiplied by 1 becomes 0.
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The multiplication of matrices is a type of scalar multiplication.
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The multiplication symbol is denoted by the letter 'x'.
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Multiplication can be thought of as repeated subtraction.
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The order in which numbers are grouped for multiplication changes the result.
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Any number multiplied by 0 is 1.
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Multiplication can be represented using arrays.
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Study Notes
Multiplication
Definition: Multiplication is a basic arithmetic operation that represents repeated addition. It is denoted by the multiplication symbol × or *.
Notation: The multiplication of two numbers, a and b, is written as:
a × b or a * b
Properties:
-
Commutative Property: The order of the numbers being multiplied does not change the result.
- a × b = b × a
-
Associative Property: The order in which numbers are multiplied does not change the result when multiplying more than two numbers.
- (a × b) × c = a × (b × c)
-
Distributive Property: Multiplication can be distributed over addition.
- a × (b + c) = a × b + a × c
Types of Multiplication:
- Scalar Multiplication: The multiplication of a number by a single number.
- Matrix Multiplication: The multiplication of matrices (arrays of numbers).
Rules:
-
Multiplication by Zero: Any number multiplied by 0 is 0.
- a × 0 = 0
-
Multiplication by One: Any number multiplied by 1 remains the same.
- a × 1 = a
Examples:
- 2 × 3 = 6
- 4 × 5 = 20
- 6 × (2 + 3) = 6 × 2 + 6 × 3 = 12 + 18 = 30
Multiplication
- Multiplication represents repeated addition and is denoted by the multiplication symbol × or *.
Notation
- The multiplication of two numbers, a and b, is written as a × b or a * b.
Properties
- The order of numbers being multiplied does not change the result, known as the Commutative Property: a × b = b × a.
- The order in which numbers are multiplied does not change the result when multiplying more than two numbers, known as the Associative Property: (a × b) × c = a × (b × c).
- Multiplication can be distributed over addition, known as the Distributive Property: a × (b + c) = a × b + a × c.
Types of Multiplication
- Scalar Multiplication involves the multiplication of a number by a single number.
- Matrix Multiplication involves the multiplication of matrices (arrays of numbers).
Rules
- Any number multiplied by 0 is 0: a × 0 = 0.
- Any number multiplied by 1 remains the same: a × 1 = a.
Examples
- 2 × 3 = 6.
- 4 × 5 = 20.
- 6 × (2 + 3) = 6 × 2 + 6 × 3 = 12 + 18 = 30.
Multiplication
Definition
- Represents repeated addition
- Denoted by the multiplication symbol × (or · in some countries)
Properties
- Commutative Property: order of numbers being multiplied doesn't change the result
- Associative Property: order in which numbers are grouped for multiplication doesn't change the result
- Distributive Property: multiplication can be distributed over addition
Multiplication Rules
- Multiplication by 0: any number multiplied by 0 is 0
- Multiplication by 1: any number multiplied by 1 is the number itself
Multiplication Strategies
- Repeated Addition: multiplication can be thought of as repeated addition
- Arrays: multiplication can be represented using arrays
- Counting On: multiplication can be thought of as counting on by a certain number a certain number of times
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Description
Learn about the definition, notation, and properties of multiplication, a fundamental arithmetic operation. Understand the commutative and associative properties of multiplication.
