Questions and Answers
What are natural numbers?
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.
Signup and view all the answers
Irrational numbers can be expressed as a whole number.
Signup and view all the answers
What is absolute value?
Signup and view all the answers
What is a proper fraction?
Signup and view all the answers
What is an improper fraction?
Signup and view all the answers
Define mixed numbers.
Signup and view all the answers
What are reciprocals?
Signup and view all the answers
What is the greatest common factor (GCF)?
Signup and view all the answers
What is the least common multiple (LCM)?
Signup and view all the answers
What is the least common denominator (LCD)?
Signup and view all the answers
What does clearing fractions involve?
Signup and view all the answers
Which of the following are ways to express multiplication? (Select all that apply)
Signup and view all the answers
What does PEMDAS represent?
Signup and view all the answers
Explain the associative property.
Signup and view all the answers
What is the additive property?
Signup and view all the answers
What is the multiplicative property?
Signup and view all the answers
Define the distributive property.
Signup and view all the answers
What is a term in algebra?
Signup and view all the answers
Define a variable.
Signup and view all the answers
What is a constant?
Signup and view all the answers
What is a coefficient?
Signup and view all the answers
What is an equation?
Signup and view all the answers
What is a solution?
Signup and view all the answers
Define a solution set.
Signup and view all the answers
What is a linear equation?
Signup and view all the answers
An identity equation has only one solution.
Signup and view all the answers
What are application problems?
Signup and view all the answers
What does percent mean?
Signup and view all the answers
How is amount calculated using percent?
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!