Types of Numbers in Mathematics

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What are natural numbers?

Whole numbers including zero

1, 2, 3, 4, 5, etc. (correct)

Any number that cannot be expressed as a whole number

0, 1, 2, 3, 4, 5, etc.

What are whole numbers?

0, 1, 2, 3, 4, 5, etc.

What are integers?

Whole numbers (both positive and negative) including zero.

Define rational numbers.

A number that can be written as a fraction with a numerator and a denominator that are integers. Signup and view all the answers

Irrational numbers can be expressed as a whole number.

False Signup and view all the answers

What is absolute value?

A number's distance from zero on a number line. Signup and view all the answers

What is a proper fraction?

The numerator is smaller than the denominator. Signup and view all the answers

What is an improper fraction?

The denominator is smaller than that of the numerator. Signup and view all the answers

Define mixed numbers.

A combination of a whole number and a fraction. Signup and view all the answers

What are reciprocals?

A/b is flipped to b/a. Signup and view all the answers

What is the greatest common factor (GCF)?

The largest factor that two or more numbers have in common. Signup and view all the answers

What is the least common multiple (LCM)?

The smallest multiple (other than zero) that two or more numbers have in common. Signup and view all the answers

What is the least common denominator (LCD)?

The least common multiple of the denominators of two or more fractions. Signup and view all the answers

What does clearing fractions involve?

Multiplying both sides (all terms) by the LCM (LCD). Signup and view all the answers

Which of the following are ways to express multiplication? (Select all that apply)

3x4 Signup and view all the answers

What does PEMDAS represent?

Order of operations. Signup and view all the answers

Explain the associative property.

Changing the grouping of numbers when using addition or multiplication does not change the outcome. Signup and view all the answers

What is the additive property?

a + 0 = a Signup and view all the answers

What is the multiplicative property?

a * 1 = a Signup and view all the answers

Define the distributive property.

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

What is a term in algebra?

Constant, product or quotient of constants or variables. Signup and view all the answers

Define a variable.

A number that might change. Signup and view all the answers

What is a constant?

The number that does not change. Signup and view all the answers

What is a coefficient?

A number multiplied by a variable in an algebraic expression. Signup and view all the answers

What is an equation?

A mathematical sentence that contains an equals sign. Signup and view all the answers

What is a solution?

The value for the variable which makes the equation true. Signup and view all the answers

Define a solution set.

The set of all values of the variable that make the equation true. Signup and view all the answers

What is a linear equation?

An equation in the form ax + b = c, with a graph that is a straight line. Signup and view all the answers

An identity equation has only one solution.

False Signup and view all the answers

What are application problems?

<ol> <li>Read the problem, 2) label the unknown, 3) verbal model, 4) write an equation, 5) solve the equation, 6) write final answer in words.</li> </ol> Signup and view all the answers

What does percent mean?

Per-hundred. Signup and view all the answers

How is amount calculated using percent?

amount = percent * base. Signup and view all the answers

Study Notes

Number Types

Natural Numbers: Positive integers starting from 1 (1, 2, 3, 4, 5, etc.).
Whole Numbers: Natural numbers including zero (0, 1, 2, 3, 4, 5, etc.).
Integers: Whole numbers that include both positive and negative values, as well as zero.
Rational Numbers: Numbers expressible as a fraction where both numerator and denominator are integers; their decimal forms either terminate or repeat.
Irrational Numbers: Numbers that cannot be expressed as fractions, including non-repeating and non-terminating decimals.

Key Mathematical Concepts

Absolute Value: Represents a number's distance from zero on a number line; denoted as |a|, always a non-negative value (e.g., |4| = 4, |-4| = 4).
Proper Fraction: A fraction where the numerator is less than the denominator (e.g., 3/5).
Improper Fraction: A fraction where the numerator is greater than or equal to the denominator (e.g., 5/3).
Mixed Numbers: A combination of a whole number and a fraction (e.g., 1 1/2).
Reciprocals: The reciprocal of a fraction (a/b) is obtained by flipping the fraction to b/a.

Factors and Multiples

Greatest Common Factor (GCF): The largest factor common to two or more numbers.
Least Common Multiple (LCM): The smallest multiple that two or more numbers share, not including zero.
Least Common Denominator (LCD): The LCM of the denominators of fractions used to find a common base for addition or subtraction.
Clearing Fractions: To eliminate fractions from an equation by multiplying all terms by the LCM or LCD.

Operations and Properties

Ways to Express Multiplication: Written in various forms: 3x4, 3*4, 3(4), (3)(4).
PEMDAS (Order of Operations): Follow the sequence of Parentheses, Exponents, Multiplication/Division (from left to right), and Addition/Subtraction (from left to right).
Associative Property: Changing the grouping in addition or multiplication does not affect the result (e.g., (7 + 4) + 8 = 7 + (4 + 8)).
Additive Property: Adding zero to a number does not change the number (a + 0 = a).
Multiplicative Property: Multiplying a number by one does not change its value (a * 1 = a).
Distributive Property: Distributing a number across a sum (a(b + c) = ab + ac).

Algebraic Terminology

Term: Represents a constant, product, or quotient of constants and variables.
Variable: A symbol that represents an unknown value (e.g., x, y, z).
Constant: A fixed value that does not change in an expression (e.g., 5 in 5x).
Coefficient: The numerical factor multiplied by a variable in an algebraic expression (e.g., 3 in 3a).
Equation: A mathematical statement asserting the equality of two expressions (e.g., x + 1 = 1).
Solution: The value for the variable that satisfies the equation (e.g., x = 0).
Solution Set: All values of the variable that make the equation true.
Linear Equation: An equation of the form ax + b = c that represents a straight line when graphed.
Identity: An equation that holds true for all values of the variable.

Problem-Solving Techniques

Application Problems: A stepwise approach to solving real-world problems, which includes reading the problem, labeling unknowns, building a verbal model, writing equations, solving them, and providing final answers in words.
Percent: Expresses a ratio per hundred, used to represent portions of a whole.
Amount Calculation: The relationship between amount, percent, and base is described as amount = percent * base.

Studying That Suits You

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

Description

This quiz explores various types of numbers including natural numbers, whole numbers, integers, rational numbers, and irrational numbers. It also covers key mathematical concepts such as absolute value, proper fractions, improper fractions, and mixed numbers. Test your understanding and deepen your knowledge of these fundamental mathematical topics!