10 Questions
What is the commutative property of addition, and provide an example?
The commutative property of addition states that the order of addends does not change the result. Example: 2 + 3 = 3 + 2.
What is the associative property of subtraction, and provide an example?
The associative property of subtraction states that the order in which numbers are subtracted does not change the result. Example: (5 - 2) - 3 = 5 - (2 + 3).
What is the distributive property of multiplication, and provide an example?
The distributive property of multiplication states that multiplication can be distributed over addition and subtraction. Example: 2 × (3 + 4) = 2 × 3 + 2 × 4.
What is the commutative property of multiplication, and provide an example?
The commutative property of multiplication states that the order of factors does not change the product. Example: 2 × 3 = 3 × 2.
What is the rule for multiplying a number by zero, and provide an example?
The rule for multiplying a number by zero is that any number multiplied by 0 is 0. Example: 2 × 0 = 0.
What is the product of powers rule, and provide an example?
The product of powers rule states that a^m × a^n = a^(m+n). Example: 2^3 × 2^4 = 2^(3+4) = 2^7.
What is the power of a product rule, and provide an example?
The power of a product rule states that (ab)^m = a^m b^m. Example: (2 × 3)^2 = 2^2 × 3^2.
What is the square root property, and provide an example?
The square root property states that √(ab) = √a × √b. Example: √(4 × 9) = √4 × √9 = 2 × 3.
What is the rule for dividing a number by zero, and provide an example?
The rule for dividing a number by zero is that it is undefined, as it is not possible to divide a number by 0. Example: 2 ÷ 0 is undefined.
What is the cube root property, and provide an example?
The cube root property states that ³√(ab) = ³√a × ³√b. Example: ³√(8 × 27) = ³√8 × ³√27 = 2 × 3.
Study Notes
Number Operations
Patterns in Addition and Subtraction
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Commutative Property: The order of addends or subtrahends does not change the result.
- Example: 2 + 3 = 3 + 2
- Example: 5 - 2 = 2 - 5 (not true, but can be rewritten as 5 - 2 = -(2 - 5))
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Associative Property: The order in which numbers are added or subtracted does not change the result.
- Example: (2 + 3) + 4 = 2 + (3 + 4)
- Example: (5 - 2) - 3 = 5 - (2 + 3)
-
Distributive Property: Multiplication can be distributed over addition and subtraction.
- Example: 2 × (3 + 4) = 2 × 3 + 2 × 4
- Example: 2 × (5 - 2) = 2 × 5 - 2 × 2
Patterns in Multiplication and Division
-
Commutative Property: The order of factors does not change the product.
- Example: 2 × 3 = 3 × 2
-
Associative Property: The order in which numbers are multiplied does not change the product.
- Example: (2 × 3) × 4 = 2 × (3 × 4)
-
Distributive Property: Multiplication can be distributed over addition and subtraction.
- Example: 2 × (3 + 4) = 2 × 3 + 2 × 4
- Example: 2 × (5 - 2) = 2 × 5 - 2 × 2
-
Multiplication by Zero: Any number multiplied by 0 is 0.
- Example: 2 × 0 = 0
- Division by Zero: Undefined, as it is not possible to divide a number by 0.
Patterns in Exponents and Roots
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Exponential Rules:
- Product of Powers: a^m × a^n = a^(m+n)
- Power of a Product: (ab)^m = a^m b^m
- Power of a Power: (a^m)^n = a^(mn)
-
Properties of Roots:
- Square Root: √(ab) = √a × √b
- Cube Root: ³√(ab) = ³√a × ³√b
These patterns and properties help simplify and solve numerical operations, making it easier to work with numbers.
Number Operations
Patterns in Addition and Subtraction
- The order of addends or subtrahends does not change the result, known as the Commutative Property.
- The order in which numbers are added or subtracted does not change the result, known as the Associative Property.
- Multiplication can be distributed over addition and subtraction, known as the Distributive Property.
Patterns in Multiplication and Division
- The order of factors does not change the product, known as the Commutative Property.
- The order in which numbers are multiplied does not change the product, known as the Associative Property.
- Multiplication can be distributed over addition and subtraction, known as the Distributive Property.
- Any number multiplied by 0 is 0, known as Multiplication by Zero.
- Division by 0 is undefined.
Patterns in Exponents and Roots
Exponents
- The product of powers is a^(m+n) when a^m is multiplied by a^n, known as the Product of Powers.
- The power of a product is a^m b^m when (ab) is raised to the power of m, known as the Power of a Product.
- The power of a power is a^(mn) when a^m is raised to the power of n, known as the Power of a Power.
Roots
- The square root of a product is √a × √b when √(ab) is calculated, known as the Square Root.
- The cube root of a product is ³√a × ³√b when ³√(ab) is calculated.
Test your understanding of the commutative, associative, and distributive properties in addition and subtraction operations.
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