Math Properties and Algebraic Expressions Chapter 3

Questions and Answers

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?

Changing the order of the terms in a multiplication equation does not affect the product.

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?

Changing the grouping of the terms of a multiplication problem does not affect the product. Signup and view all the answers

What is the Distributive Property?

Multiply each number in the parentheses by the number outside the parentheses. Signup and view all the answers

Write the expression that represents the Associative Property of Addition.

a + b + c = a + (b + c) Signup and view all the answers

Write the expression that represents the Associative Property of Multiplication.

abc = a(bc) Signup and view all the answers

Write the expression that illustrates the Commutative Property of Addition.

a + b + c = b + a + c Signup and view all the answers

Write the expression that illustrates the Commutative Property of Multiplication.

abc = cab Signup and view all the answers

Write the expression for the Distributive Property.

a(b + c) = ab + ac Signup and view all the answers

What expression represents the total of a number a and a number b?

a + b Signup and view all the answers

What expression represents 9 increased by a number a?

9 + a Signup and view all the answers

What expression represents a number b plus the quotient of 8 and a number b?

b + 8/b Signup and view all the answers

What expression represents the product of 4 and the difference of 10 and a number b?

4(10 - b) Signup and view all the answers

What is a coefficient?

The numerical factor of a term that contains a variable. Signup and view all the answers

What is a constant?

A term without a variable. Signup and view all the answers

What is a variable?

A symbol that represents one or more numbers. Signup and view all the answers

What are terms in algebra?

Parts of an algebraic expression. Signup and view all the answers

Identify the coefficients in the expression 12 + 10c.

10 Signup and view all the answers

Identify the coefficients in the expression g + 15 + 9g.

1 and 9 Signup and view all the answers

Identify the constants in the expression 12 + 10c.

12 Signup and view all the answers

Identify the constants in the expression g + 15 + 9g.

15 Signup and view all the answers

Write the expression for 25 less than a number b.

b - 25 Signup and view all the answers

Write the expression for a number x divided by 4.

x/4 Signup and view all the answers

Write the expression for 100 decreased by a number k.

100 - k Signup and view all the answers

Write the expression for 6 more than the product of 8 and a number x.

8x + 6 Signup and view all the answers

Write the expression for 3 less than the quotient of a number y and 4.

y/4 - 3 Signup and view all the answers

What does the Addition Property of Zero state?

The sum of any number and 0 is that number. Signup and view all the answers

What does the Multiplication Property of Zero state?

The product of any number and 0 is 0. Signup and view all the answers

What does the Multiplication Property of One state?

The product of any number and 1 is that number. Signup and view all the answers

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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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.