Pre-Algebra A Unit 2 - Integers and Algebraic Expressions

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the absolute value?

A whole number that can be positive, negative, or zero

The result of multiplication

A number that gives zero when added to a given number

The distance from zero on a number line from either the positive or negative side (correct)

What is the additive inverse?

A number that when added to a given number gives zero as a result

What does the Addition Property of Equality state?

If we add the same quantity to both sides of an equation, then our equation remains the same

What happens in the Associative Property of Addition?

Changing the grouping does NOT change the sum Signup and view all the answers

What is the Associative Property of Multiplication?

Changing the grouping does NOT change the product Signup and view all the answers

What does the Commutative Property of Addition dictate?

Changing the order does NOT change the sum Signup and view all the answers

What is the Commutative Property of Multiplication?

Changing the order does NOT change the product Signup and view all the answers

What is the Distributive Property?

Multiplying a number by a group of numbers added together is the same as multiplying each separately Signup and view all the answers

What does the Division Property of Equality state?

If we divide both sides of an equation by the same non-zero number, the two sides remain equal Signup and view all the answers

What is the Identity Property of Addition?

Adding zero to a number does not change that number Signup and view all the answers

What does the Identity Property of Multiplication state?

Multiplying a number by one does not change that number Signup and view all the answers

Define an integer.

A whole number that can be positive, negative, or zero Signup and view all the answers

What is an inverse operation?

An operation that undoes what was done by the previous operation Signup and view all the answers

What does it mean to isolate a variable?

Rearranging an algebraic equation so that a variable is alone Signup and view all the answers

What is the Multiplication Property of Equality?

If we multiply the same quantity on both sides of an equation, then our equation remains the same Signup and view all the answers

What does the term 'opposite' refer to in mathematics?

Numbers that are the same distance from zero, but in opposite directions Signup and view all the answers

What are the Order of Operations?

The rules that say which calculation comes first in an expression Signup and view all the answers

Define product in mathematical terms.

The result of multiplication Signup and view all the answers

What is a quotient?

The result of division Signup and view all the answers

What is a solution in algebra?

A value, or values, we can put in place of a variable that makes the equation true Signup and view all the answers

State the Subtraction Property of Equality.

If we subtract the same quantity from both sides of an equation, then our equation remains the same Signup and view all the answers

What is a variable?

A symbol which works as a placeholder for expression or quantities that may vary or change Signup and view all the answers

What does the Associative Property of Equality state?

If we add the same quantity to both sides of an equation, then our equation remains the same Signup and view all the answers

Study Notes

Absolute Value

Represents the distance from zero on a number line, regardless of direction (positive or negative).

Additive Inverse

Refers to a number that, when added to another number, results in zero.

Addition Property of Equality

States that adding the same value to both sides of an equation keeps it balanced.

Associative Property of Addition

Changing the grouping of numbers does not affect the sum: (a + b) + c = a + (b + c).

Associative Property of Multiplication

Changing the grouping of factors does not affect the product: (a x b) x c = a x (b x c).

Commutative Property of Addition

Changing the order of the numbers does not change the sum: a + b = b + a.

Commutative Property of Multiplication

Changing the order of the factors does not change the product: a x b = b x a.

Distributive Property

Multiplying a number by a sum is equivalent to multiplying each addend separately: a x (b + c) = a x b + a x c.

Division Property of Equality

Dividing both sides of an equation by the same non-zero number maintains equality.

Identity Property of Addition

Adding zero to any number does not change its value: a + 0 = a.

Identity Property of Multiplication

Multiplying any number by one does not change its value: a x 1 = a.

Integer

Defined as a whole number that can be positive, negative, or zero, without fractions or decimals.

Inverse Operation

Refers to an operation that reverses the effect of a previous operation.

Isolate

The process of rearranging an equation so that a variable stands alone.

Multiplication Property of Equality

States that multiplying both sides of an equation by the same number keeps it balanced.

Opposite

Refers to pairs of numbers that are equidistant from zero, but in opposite directions (e.g., -4 and +4).

Order of Operations

A set of rules (PEMDAS) that dictates the sequence in which calculations are performed in an expression.

Product

The outcome of multiplication operations.

Quotient

The result obtained from division operations.

Solution

Represents the value(s) that can be substituted into a variable to satisfy an equation.

Subtraction Property of Equality

States that subtracting the same number from both sides of an equation maintains equality.

Variable

A symbol used as a placeholder for quantities that may change or vary.

Associative Property of Equality

Similar to the addition property, it states that adding the same number to both sides of an equation preserves its equality.

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Description

This quiz covers key concepts from Pre-Algebra A Unit 2, focusing on integers and algebraic expressions. Test your understanding of definitions like absolute value and additive inverse, as well as properties of equality. Perfect for reinforcing essential pre-algebra skills.