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Questions and Answers
What does the Commutative Property of Addition state?
What does the Commutative Property of Addition state?
Changing the order of the terms in an addition equation does not affect the sum.
What does the Commutative Property of Multiplication state?
What does the Commutative Property of Multiplication state?
Changing the order of the terms in a multiplication equation does not affect the product.
What does the Associative Property of Addition state?
What does the Associative Property of Addition state?
Changing the grouping of the terms of an addition equation does not affect the sum.
What does the Associative Property of Multiplication state?
What does the Associative Property of Multiplication state?
What is the Distributive Property?
What is the Distributive Property?
Write the expression that represents the Associative Property of Addition.
Write the expression that represents the Associative Property of Addition.
Write the expression that represents the Associative Property of Multiplication.
Write the expression that represents the Associative Property of Multiplication.
Write the expression that illustrates the Commutative Property of Addition.
Write the expression that illustrates the Commutative Property of Addition.
Write the expression that illustrates the Commutative Property of Multiplication.
Write the expression that illustrates the Commutative Property of Multiplication.
Write the expression for the Distributive Property.
Write the expression for the Distributive Property.
What expression represents the total of a number a and a number b?
What expression represents the total of a number a and a number b?
What expression represents 9 increased by a number a?
What expression represents 9 increased by a number a?
What expression represents a number b plus the quotient of 8 and a number b?
What expression represents a number b plus the quotient of 8 and a number b?
What expression represents the product of 4 and the difference of 10 and a number b?
What expression represents the product of 4 and the difference of 10 and a number b?
What is a coefficient?
What is a coefficient?
What is a constant?
What is a constant?
What is a variable?
What is a variable?
What are terms in algebra?
What are terms in algebra?
Identify the coefficients in the expression 12 + 10c.
Identify the coefficients in the expression 12 + 10c.
Identify the coefficients in the expression g + 15 + 9g.
Identify the coefficients in the expression g + 15 + 9g.
Identify the constants in the expression 12 + 10c.
Identify the constants in the expression 12 + 10c.
Identify the constants in the expression g + 15 + 9g.
Identify the constants in the expression g + 15 + 9g.
Write the expression for 25 less than a number b.
Write the expression for 25 less than a number b.
Write the expression for a number x divided by 4.
Write the expression for a number x divided by 4.
Write the expression for 100 decreased by a number k.
Write the expression for 100 decreased by a number k.
Write the expression for 6 more than the product of 8 and a number x.
Write the expression for 6 more than the product of 8 and a number x.
Write the expression for 3 less than the quotient of a number y and 4.
Write the expression for 3 less than the quotient of a number y and 4.
What does the Addition Property of Zero state?
What does the Addition Property of Zero state?
What does the Multiplication Property of Zero state?
What does the Multiplication Property of Zero state?
What does the Multiplication Property of One state?
What does the Multiplication Property of One state?
Study Notes
Algebraic Properties
- Commutative Property of Addition: Order of terms does not affect the sum; e.g., a + b = b + a.
- Commutative Property of Multiplication: Order of factors does not alter the product; e.g., ab = ba.
- Associative Property of Addition: Grouping of terms does not change the sum; e.g., (a + b) + c = a + (b + c).
- Associative Property of Multiplication: Grouping of factors does not impact the product; e.g., (ab)c = a(bc).
- Distributive Property: Multiply each term inside parentheses by the term outside; e.g., a(b + c) = ab + ac.
Algebraic Expressions
- Expression for "the total of a number a and a number b" is a + b.
- Expression for "9 increased by a number a" is 9 + a.
- Expression for "a number b plus the quotient of 8 and a number b" is b + 8/b.
- Expression for "the product of 4 and the difference of 10 and a number b" is 4(10 - b).
- Expression for "25 less than a number b" is b - 25.
- Expression for "a number x divided by 4" is x/4.
- Expression for "100 decreased by a number k" is 100 - k.
- Expression for "6 more than the product of 8 and a number x" is 8x + 6.
- Expression for "3 less than the quotient of a number y and 4" is y/4 - 3.
Components of Expressions
- Coefficient: Numerical factor in a term containing a variable, e.g., in 10c, 10 is the coefficient.
- Constant: A term without a variable, e.g., in 12 + 10c, 12 is the constant.
- Variable: Symbolic representation of one or more numbers.
Identifying Components
- In the expression 12 + 10c, the coefficient is 10 and the constant is 12.
- In the expression g + 15 + 9g, the coefficients are 1 and 9, while the constant is 15.
Special Properties of Numbers
- Addition Property of Zero: The sum of any number and 0 equals the number itself; e.g., a + 0 = a.
- Multiplication Property of Zero: The product of any number and 0 yields 0; e.g., a * 0 = 0.
- Multiplication Property of One: The product of any number and 1 equals the number; e.g., a * 1 = a.
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Description
Test your understanding of key math properties in algebraic expressions with this flashcard quiz. Focus on the commutative and associative properties of addition and multiplication. Perfect for students preparing for exams or looking to reinforce their knowledge.
