Teaching Textbooks Algebra 1 Flashcards

Questions and Answers

What are operations in mathematics?

Only addition

Only subtraction

Multiplication, division, and addition

Addition, subtraction, and division (correct)

What is an equation?

Two groups of numbers with an equal sign between them

What constitutes an expression?

A group of numbers and variables

What is the solution of an equation?

The formal name for the answer to an equation Signup and view all the answers

List the five steps for finding the answer to a problem using algebra.

<ol> <li>Make x stand for whatever you're trying to find. 2. Study the facts to find the two things that must be equal; then form a word equation. 3. Turn the word equation into an algebra equation. 4. Find the equation's solution. 5. Interpret the meaning of the solution.</li> </ol> Signup and view all the answers

What does 'undoing' refer to in mathematics?

The process of subtracting a number to get rid of an addition Signup and view all the answers

What is the golden rule of algebra?

If you change the value of one side of an equation, you must change the other side by the same amount Signup and view all the answers

What are inverse operations?

When two operations undo each other Signup and view all the answers

What is rewriting in algebra?

When we change the form of an expression without altering its value Signup and view all the answers

What are equivalent expressions?

Two expressions that have the same value Signup and view all the answers

What does 'rate of change' refer to?

The speed of which something changes as time passes Signup and view all the answers

What are negative numbers?

Numbers that are less than zero Signup and view all the answers

What are positive numbers?

Numbers that are more than zero Signup and view all the answers

What is a number line?

A simple line that shows all of the numbers in order Signup and view all the answers

What are integers?

Positive and negative whole numbers and zero Signup and view all the answers

What is the opposite of a number?

A number that is the same except for having the opposite sign Signup and view all the answers

What are the order of operations rules?

<ol> <li>All multiplications and divisions are done first, starting from the left and working to right; 2. All additions and subtractions are done second, again from left to right; 3. Operations that need a different order must be enclosed in parentheses or put inside a fraction.</li> </ol> Signup and view all the answers

What is a coefficient?

The number multiplied by x Signup and view all the answers

What is a reciprocal?

A number turned upside down Signup and view all the answers

Study Notes

Algebra Terminology and Concepts

Operations: Fundamental arithmetic processes including addition, subtraction, and division.
Equation: A mathematical statement consisting of two groups of numbers (and possibly variables) separated by an equal sign.
Expression: A combination of numbers and variables representing a value, but not containing an equal sign.
Solution: The answer derived from solving an equation, formally recognized as such.

Problem Solving Process

Five-step Process:
- Assign a variable (e.g. x) to represent the unknown.
- Analyze the problem to identify two equatable elements; formulate a word equation.
- Convert the word equation into an algebraic equation.
- Calculate the solution to the algebraic equation.
- Interpret the solution to understand its real-world implications.

Algebraic Principles

Undoing: A method employed to reverse an operation, commonly by subtracting to eliminate an addition.
Golden Rule of Algebra: Ensures that any alterations made to one side of an equation must also be made to the other side by the same quantity, maintaining equivalence.
Inverse Operations: Operations that revert each other; for example, addition and subtraction or multiplication and division.

Expression Manipulation

Rewriting: The act of altering the presentation of an expression without modifying its overall value.
Equivalent Expressions: Different expressions that yield the same mathematical value upon evaluation.

Fundamental Mathematical Concepts

Rate of Change: A measure of how quickly a quantity changes over time, often related to slope in graphing functions.
Negative Numbers: Values that fall below zero, playing a critical role in various mathematical contexts.
Positive Numbers: Values that exceed zero, representing quantities above a neutral point.
Number Line: A visual representation of numbers in sequential order, illustrating the relationships between different values.
Integers: The set of whole numbers that include positive numbers, negative numbers, and zero.
Opposite of a Number: The counterpart of a given number that shares the same absolute value but differs in sign.

Operational Rules

Order of Operations:
- Perform all multiplications and divisions first, moving from left to right.
- Follow with all additions and subtractions, also left to right.
- Use parentheses or fractions to indicate any alterations to the standard order.

Algebraic Components

Coefficient: A numerical factor that multiplies a variable, indicating the scale of the variable's influence in an expression.
Reciprocal: The result of flipping a fraction or number, demonstrating its multiplicative inverse; for instance, the reciprocal of 2/3 is 3/2.

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Description

This quiz features flashcards based on key terms from the Teaching Textbooks Algebra 1 curriculum. Each card provides a definition of fundamental algebra concepts such as operations, equations, and solutions. Use these flashcards to enhance your understanding and retention of algebra essentials.