Mathematics Fundamentals
Public flashcard deck about Mathematics Fundamentals. 8 cards.
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What is the difference between a rational and an irrational number?
A rational number can be expressed as a fraction p/q, where p and q are integers and q is not zero. Its decimal representation either terminates or repeats. An irrational number cannot be expressed as such a fraction, and its decimal representation neither terminates nor repeats. Examples: Rational - 1/2, 0.75, 2.333...; Irrational - pi, sqrt(2).
Explain the order of operations (PEMDAS/BODMAS).
PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). BODMAS stands for Brackets, Orders (powers and square roots, etc.), Division and Multiplication (from left to right), Addition and Subtraction (from left to right). This order ensures consistent results when evaluating mathematical expressions.
What is a prime number, and what is a composite number?
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples: 2, 3, 5, 7, 11. A composite number is a natural number greater than 1 that is not prime, meaning it has at least one divisor other than 1 and itself. Examples: 4 (divisors: 1, 2, 4), 6 (divisors: 1, 2, 3, 6).
Define the absolute value of a number.
The absolute value of a number is its distance from zero on the number line, regardless of direction. It is always non-negative. It is denoted by vertical bars, e.g., |x|. If x >= 0, then |x| = x. If x < 0, then |x| = -x.
What is the distributive property of multiplication over addition?
The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. Mathematically, a(b + c) = ab + ac.
What is a variable in mathematics?
A variable is a symbol, usually a letter, that represents a quantity that can change or vary, or that may take on any of a specified set of values. It is used to express general relationships and solve equations.