Algebra 1 Chapter 1 Review of Real Numbers

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Questions and Answers

What are real numbers?

All numbers on the number line

Which of the following are natural numbers?

5 (correct)

-3

1 (correct)

What are whole numbers?

All counting numbers plus 0

What are integers?

Whole numbers and their opposites Signup and view all the answers

Define rational numbers.

Numbers that can be written as a/b where a & b are integers and b does NOT equal 0 Signup and view all the answers

What are irrational numbers?

Numbers that cannot be written as rational numbers Signup and view all the answers

What is absolute value?

The distance of a number from 0 on a number line Signup and view all the answers

What are factors?

Parts of an expression that are multiplied together Signup and view all the answers

What is a product?

The answer when you multiply a problem Signup and view all the answers

Define reciprocals.

A number multiplied by its reciprocal is 1 Signup and view all the answers

How do you multiply fractions?

The product of numerators over the product of denominators Signup and view all the answers

How do you divide fractions?

Multiplying by the reciprocal Signup and view all the answers

What happens when you add and subtract fractions?

When you have a common denominator, the numbers in the numerator are added and the denominator stays the same Signup and view all the answers

What is an algebraic expression?

A collection of numbers, variables, operating symbols and graphing symbols Signup and view all the answers

How do you evaluate expressions?

Substitute a given value for a variable then simplify Signup and view all the answers

What does it mean to solve equations?

Adding the opposite Signup and view all the answers

What are opposites or additive inverses?

The sum of a number and its opposite = 0 Signup and view all the answers

What is the commutative property of addition and multiplication?

a + b = b + a OR a * b = b * a Signup and view all the answers

State the associative properties of addition and multiplication.

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

What is the distributive property of multiplication over addition?

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

What is the additive inverse property?

a + (-a) = 0 Signup and view all the answers

Explain the multiplicative inverse property.

a * 1/a = 1 Signup and view all the answers

What is the additive identity property?

a + 0 = a Signup and view all the answers

State the multiplicative identity property.

a * 1 = a Signup and view all the answers

Define numerical coefficient.

The number multiplied by a variable Signup and view all the answers

What is a term?

An expression added to another expression Signup and view all the answers

What is combining like terms?

Adding coefficients of terms with the same variables Signup and view all the answers

What is a linear equation in one variable?

An equation with only one variable raised to the 1st power Signup and view all the answers

What are equivalent equations?

When 1 equation is the same as the other Signup and view all the answers

What is a formula?

An equation with several variables that describes a relationship among quantities. Signup and view all the answers

What does it mean to solve a formula?

Using operations to isolate a particular variable Signup and view all the answers

Study Notes

Real Numbers

Real numbers encompass all numbers present on the number line.

Natural Numbers

Defined as counting numbers starting from 1: {1, 2, 3...}.

Whole Numbers

Include all natural numbers plus 0: {0, 1, 2, 3...}.

Integers

Comprise whole numbers and their negative counterparts: {..., -2, -1, 0, 1, 2...}.

Rational Numbers

Can be expressed in the form of a fraction a/b, where a and b are integers and b ≠ 0.

Irrational Numbers

Cannot be represented as fractions; include numbers like √2 or π.

Absolute Value

Represents the distance of a number from zero on the number line, denoted as |x|.

Factors

Refers to the components or parts of an expression that perform multiplication together.

Product

The result obtained from multiplying two or more numbers.

Reciprocals or Multiplicative Inverses

A number multiplied by its reciprocal yields 1 (e.g., a × (1/a) = 1).

Multiplying Fractions

Achieved by multiplying the numerators together and the denominators together.

Dividing Fractions

Accomplished by multiplying by the reciprocal of the divisor.

Adding and Subtracting Fractions

Involves combining numerators when a common denominator exists, while the denominator remains unchanged.

Algebraic Expression

A combination of numbers, variables, and operation symbols.

Evaluating Expressions

Involves substituting a specific value for a variable and then simplifying.

Solving Equations

Achieved by adding the opposite of a number to isolate the variable.

Opposites or Additive Inverse

The sum of a number and its additive inverse equals zero.

Commutative Property of Addition and Multiplication

Addition and multiplication can be done in any order: a + b = b + a and a × b = b × a.

Associative Properties of Addition and Multiplication

The grouping of numbers does not affect the sum or product: (a + b) + c = a + (b + c) and (a × b) × c = a × (b × c).

Distributive Property of Multiplication Over Addition

Involves distributing a multiplication over an addition: a × (b + c) = ab + ac.

Additive Inverse Property

States that a number plus its additive inverse equals zero: a + (-a) = 0.

Multiplicative Inverse Property

States that a number multiplied by its multiplicative inverse equals one: a × (1/a) = 1.

Additive Identity Property

Indicates a number plus zero equals the number itself: a + 0 = a.

Multiplicative Identity Property

Indicates a number multiplied by one equals the number itself: a × 1 = a.

Numerical Coefficient

The numerical factor in a term, for example, in 10x + 5, the number 10 is the coefficient.

Term

Represents a part of an expression, for instance, in the equation 5x = 25, 5x is a term.

Combining Like Terms

Involves summing coefficients of similar variable terms, such as 5x + 10 = 2X + 40 and 3x + 10 = 40.

Linear Equation in One Variable

An equation containing a single variable raised to the first power, e.g., 2x + 15 = 25.

Equivalent Equations

Two equations are equivalent if they express the same relationship or yield the same solutions.

Formula

An equation comprising multiple variables representing relationships among quantities, such as 2a + b = c.

Solving a Formula

The process of manipulating variables to isolate a specific variable within the formula.

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Description

Test your knowledge with this flashcard quiz focusing on real numbers and their classifications. From natural to rational numbers, this review will help solidify your understanding of these essential mathematical concepts. Perfect for students preparing for algebra assessments.