Mathematics
Grade 9
15 min
Properties of multiplication
Properties of multiplication
What you'll learn
- Identify the vertex (h, k) from the equation of a parabola in vertex form, y = a(x - h)² + k, with 100% accuracy on a formative assessment.
- Apply the properties of parabolas (vertex, axis of symmetry, direction of opening) to correctly write the equation of a parabola in vertex form, given its vertex and one other point, in at least 4 out of 5 problems on a summative quiz.
- Solve for the parameter 'a' in the vertex form equation y = a(x - h)² + k, when given the vertex and another point on the parabola, demonstrating the correct algebraic steps in at least 3 out of 4 examples on a worksheet.
- Explain the relationship between the parameters (a, h, k) in the vertex form equation y = a(x - h)² + k and the graphical transformations (vertical stretch/compression, horizontal translation, vertical translation) of the parent function y = x², justifying their reasoning in a short written response with at least 3 complete sentences and accurate mathematical terminology.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify and apply the Commutative, Associative, and Distributive properties to simplify polynomial and radical expressions.
Use the Distributive Property to accurately expand and factor quadratic and other polynomial expressions.
Apply the Identity and Inverse Properties of Multiplication in the context of solving linear and quadratic equations.
Recognize and use the Zero Product Property to find the roots of factored polynomial equations.
Justify the steps of an algebraic manipulation by citing the relevant property of multiplication.
Connect the properties of multiplication to the simplification of complex algebraic terms involving coefficients and variables.
Ever noticed that `5 * (x + 2)` is the same as `5x + 10`? 🤔 These fundamental rules, or prope...
2
Key Concepts & Vocabulary
TermDefinitionExample
Commutative Property of MultiplicationThis property states that the order in which two numbers or expressions are multiplied does not change the result.For numbers: `7 * 9 = 9 * 7`. For algebra: `(x + 4)(x - 2) = (x - 2)(x + 4)`.
Associative Property of MultiplicationThis property states that when multiplying three or more numbers or expressions, the way they are grouped does not change the result.For numbers: `(2 * 5) * 6 = 2 * (5 * 6)`. For algebra: `(3x)(2y) = 3(x(2y))`.
Distributive PropertyThis property links multiplication and addition/subtraction. It states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products.For numbers: `5 * (10 + 2) = 5 * 10 + 5 * 2`. For algebra: `3x(x^2 - 4) = 3x^3 - 12x`.
Id...
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Core Formulas
The Distributive Property
For any expressions a, b, and c: `a(b + c) = ab + ac`
This is the fundamental rule for expanding expressions. It is used to multiply a single term into a set of parentheses or to multiply two polynomials together (e.g., FOIL is a specific application of this property).
The Zero Product Property
If `a * b = 0`, then `a = 0` or `b = 0` (or both).
This is a powerful property used to solve equations. If you can rewrite an equation so one side is zero and the other side is a product of factors, you can solve for each factor independently.
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Sign Up Free to ContinueSample Practice Questions
Easy
The statement `(x^2 + 1) * 3x = 3x * (x^2 + 1)` is an example of which property of multiplication?
A.Commutative Property
B.Associative Property
C.Distributive Property
D.Identity Property
Easy
Which equation demonstrates the Associative Property of Multiplication?
A.5x(y + z) = 5xy + 5xz
B.(4x * 2) * 9 = 4x * (2 * 9)
C.7x * 1 = 7x
D.8x * 3 = 3 * 8x
Easy
According to the Identity Property of Multiplication, multiplying any expression by which number will result in the original expression?
A.0
B.-1
C.1
D.The expression's reciprocal
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Frequently asked questions
What grade level is "Properties of multiplication"?
Properties of multiplication is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Properties of multiplication?
You'll be able to: Identify the vertex (h, k) from the equation of a parabola in vertex form, y = a(x - h)² + k, with 100% accuracy on a formative assessment; Apply the properties of parabolas (vertex, axis of symmetry, direction of opening) to….
Is "Properties of multiplication" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with Properties of multiplication?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.