Mathematics Fundamentals
Public flashcard deck about Mathematics Fundamentals. 8 cards.
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What is the order of operations in mathematics, and what does it ensure?
The order of operations is PEMDAS/BODMAS: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). It ensures consistency and a unique result when evaluating mathematical expressions.
Define prime number and composite number. Provide an example of each.
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself (e.g., 7). A composite number is a natural number greater than 1 that has more than two distinct positive divisors (e.g., 12).
What is the difference between an integer and a rational number?
Integers are whole numbers (positive, negative, or zero), such as -3, 0, 5. Rational numbers are numbers that can be expressed as a fraction p/q, where p and q are integers and q is not zero. All integers are rational numbers, but not all rational numbers are integers (e.g., 1/2, -3/4).
Explain the concept of absolute value and provide an example.
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 two vertical bars, e.g., |-5| = 5 and |3| = 3.
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.
Define 'variable' and 'constant' in algebra.
A variable is a symbol (usually a letter) that represents a quantity that can change or vary, often denoted by x, y, or z. A constant is a value that does not change, it is fixed, like the number 5 or pi.