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Questions and Answers
The multiplication of two numbers, a and b, is written as a + b.
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.
The order of the numbers being multiplied does not change the result.
True
Multiplication can be distributed over subtraction.
Multiplication can be distributed over subtraction.
False
Any number multiplied by 1 becomes 0.
Any number multiplied by 1 becomes 0.
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The multiplication of matrices is a type of scalar multiplication.
The multiplication of matrices is a type of scalar multiplication.
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The multiplication symbol is denoted by the letter 'x'.
The multiplication symbol is denoted by the letter 'x'.
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Multiplication can be thought of as repeated subtraction.
Multiplication can be thought of as repeated subtraction.
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The order in which numbers are grouped for multiplication changes the result.
The order in which numbers are grouped for multiplication changes the result.
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Any number multiplied by 0 is 1.
Any number multiplied by 0 is 1.
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Multiplication can be represented using arrays.
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.
