Algebra 1 Review Flashcards

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Questions and Answers

What are real numbers?

The set of all irrational numbers

The set of all rational numbers

The set of all integers

The set of all rational and irrational numbers (correct)

What are rational numbers?

Terminating decimals or repeating decimals and everything else

What are integers?

Negative numbers, positive numbers, and zero

What are whole numbers?

All positive numbers and zero Signup and view all the answers

What are natural numbers?

All positive numbers Signup and view all the answers

What is the communicative property?

Changing the order of the numbers does not affect the sum or product Signup and view all the answers

What is the associative property?

Changing the grouping of numbers will not change the value Signup and view all the answers

What is the identity property?

The sum of a number and 0 is the number; the product of a number and 1 is the number Signup and view all the answers

What is the inverse property?

The sum of a number and its opposite is 0, and the product of a number and its reciprocal is 1 Signup and view all the answers

What is the zero product property?

When the product of two or more factors is zero, one of these factors must equal zero Signup and view all the answers

What is the distributive property?

A property indicating a special way in which multiplication is applied to addition of two or more numbers Signup and view all the answers

What is the reflexive property?

A quantity is congruent (equal) to itself Signup and view all the answers

What does the symmetric property state?

If a = b, then b = a Signup and view all the answers

What does the transitive property state?

If a = b and b = c, then a = c Signup and view all the answers

What does it mean if the variable has been cancelled out and the remaining numbers are NOT equal?

No solution Signup and view all the answers

What does it mean if the variable has been cancelled out and the remaining numbers ARE equal?

Infinite solutions Signup and view all the answers

What is the process for solving inequalities?

Solve them separately and then graph Signup and view all the answers

What is the property of equality?

The equals sign in an equation indicates that both sides must be the same for the equation to be true Signup and view all the answers

Study Notes

Real Numbers

Comprise all rational and irrational numbers.

Rational Numbers

Include terminating and repeating decimals, along with other numbers.

Integers

Consist of positive numbers, negative numbers, and zero.

Whole Numbers

Include all positive numbers and zero.

Natural/Counting Numbers

Comprise all positive numbers.

Commutative Property

States that order does not affect the result of addition or multiplication: ( a + b = b + a ).

Associative Property

Changing the grouping of numbers does not alter the value: ( (7 + 4) + 8 = 7 + (4 + 8) ); applicable to both addition and multiplication.

Identity Property

Sum of a number and zero equals the number itself: ( a + 0 = a ).
Product of a number and one equals the number itself: ( 1a = a ).

Inverse Property

The sum of a number and its negative counterpart is zero: ( a + (-a) = 0 ).
The product of a number and its reciprocal equals one: ( a \times \frac{1}{a} = 1 ).

Zero Product Property

If the product of factors equals zero, at least one factor must be zero: ( a \times 0 = 0 ).

Distributive Property

Indicates how multiplication interacts with addition: ( a(b + c) = ab + ac ).

Reflexive Property

A quantity is equal to itself: ( a = a ).

Symmetric Property

If one quantity equals another, then the reverse is also true: if ( a = b ) then ( b = a ).

Transitive Property

If one quantity equals a second, which equals a third, then the first equals the third: if ( a = b ) and ( b = c ), then ( a = c ).

No Solution Condition

If variables cancel out and remaining numbers differ, the answer is "no solution."

Infinite Solutions Condition

If variables cancel out and remaining numbers are equal, the answer is "infinite solutions."

Handling Inequalities

Solve each inequality separately and then graph the results.

Property of Equality

The equals sign in an equation mandates that both sides are equivalent, maintaining balance through addition, subtraction, multiplication, and division operations.

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Description

Test your understanding of key concepts in Algebra 1 with these flashcards. Covering important terminology from real numbers to various types of numbers, this review will help solidify your math foundation.