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Mathematics LibreTexts

Key Terms Chapter 01: Foundations

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    Example and Directions
    Words (or words that have the same definition)The definition is case sensitive(Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages](Optional) Caption for Image(Optional) External or Internal Link(Optional) Source for Definition
    (Eg. "Genetic, Hereditary, DNA ...")(Eg. "Relating to genes or heredity")The infamous double helix; Delmar Larsen
    Glossary Entries
    absolute valueThe absolute value of a number is its distance from \(0\) on the number line.    
    additive identityThe number \(0\) is the additive identity because adding \(0\) to any number does not change its value.    
    additive inverseThe opposite of a number is its additive inverse.    
    coefficientThe coefficient of a term is the constant that multiplies the variable in a term.    
    complex fractionA fraction in which the numerator or the denominator is a fraction is called a complex fraction.    
    composite numberA composite number is a counting number that is not prime. It has factors other than \(1\) and the number itself.    
    constantA constant is a number whose value always stays the same.    
    denominatorIn a fraction, written \(\frac{a}{b}\), where \(b≠0\), the denominator \(b\) is the number of equal parts the whole has been divided into.    
    divisible by a numberIf a number \(m\) is a multiple of \(n\), then \(m\) is divisible by \(n\).    
    equationAn equation is two expressions connected by an equal sign.    
    equivalent fractionsEquivalent fractions are fractions that have the same value.    
    evaluate an expressionTo evaluate an expression means to find the value of the expression when the variables are replaced by given numbers.    
    expressionAn expression is a number, a variable, or a combination of numbers and variables using operation symbols.    
    factorsIf \(a·b=m\), then \(a\) and \(b\) are factors of \(m\).    
    fractionA fraction is written \(\frac{a}{b}\), where \(b≠0\), and \(a\) is the numerator and \(b\) is the denominator. A fraction represents parts of a whole.    
    integersThe whole numbers and their opposites are called the integers.    
    irrational numberAn irrational number is a number that cannot be written as the ratio of two integers. Its decimal form does not stop and does not repeat.    
    least common denominatorThe least common denominator (LCD) of two fractions is the least common multiple (LCM) of their denominators.    
    least common multipleThe least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.    
    like termsTerms that are either constants or have the same variables raised to the same powers are called like terms.    
    multiple of a numberA number is a multiple of \(n\) if it is the product of a counting number and \(n\).    
    multiplicative identityThe number \(1\) is the multiplicative identity because multiplying \(1\) by any number does not change its value.    
    multiplicative inverseThe reciprocal of a number is its multiplicative inverse.    
    negative numbersNumbers less than \(0\) are negative numbers.    
    numeratorIn a fraction, written \(\frac{a}{b}\), where \(b≠0\), the numerator a indicates how many parts are included.    
    oppositeThe opposite of a number is the number that is the same distance from zero on the number line but on the opposite side of zero.    
    order of operationsThe order of operations are established guidelines for simplifying an expression.    
    percentA percent is a ratio whose denominator is \(100\).    
    prime factorizationThe prime factorization of a number is the product of prime numbers that equals the number.    
    prime numberA prime number is a counting number greater than \(1\) whose only factors are \(1\) and the number itself.    
    principal square rootThe positive square root is called the principal square root.    
    rational numberA rational number is a number of the form \(\frac{p}{q}\), where \(p\) and \(q\) are integers and \(q≠0\). Its decimal form stops or repeats.    
    real numberA real number is a number that is either rational or irrational.    
    reciprocalThe reciprocal of a fraction is found by inverting the fraction, placing the numerator in the denominator and the denominator in the numerator.    
    simplify an expressionTo simplify an expression means to do all the math possible.    
    square of a numberIf \(n^2=m\), then \(m\) is the square of \(n\).    
    square root of a numberIf \(n^2=m\), then \(n\) is a square root of \(m\).    
    termA term is a constant, or the product of a constant and one or more variables.    
    variableA variable is a letter that represents a number whose value may change.    
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