Key Terms Chapter 01: Foundations

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Absolute Value: The absolute value of a number is its distance from \(0\) on the number line. The absolute value of a number \(n\) is written as \(|n|\).

Additive Identity: The additive identity is the number \(0\); adding \(0\) to any number does not change its value.

Additive Inverse: The opposite of a number is its additive inverse. A number and its additive inverse add to \(0\).

Coefficient: The coefficient of a term is the constant that multiplies the variable in a term.

Complex Fraction: A complex fraction is a fraction in which the numerator or the denominator contains a fraction.

Composite Number: A composite number is a counting number that is not prime. A composite number has factors other than 1 and itself.

Constant: A constant is a number whose value always stays the same.

Counting Numbers: The counting numbers are the numbers \(1, 2, 3, …\)

Decimal: A decimal is another way of writing a fraction whose denominator is a power of ten.

Denominator: The denominator is the value on the bottom part of the fraction that indicates the number of equal parts into which the whole has been divided.

Divisible by a Number: If a number \(m\) is a multiple of \(n\), then \(m\) is divisible by \(n\). (If \(6\) is a multiple of \(3\), then \(6\) is divisible by \(3\).)

Equality Symbol: The symbol “=” is called the equal sign. We read \(a=b\) as “\(a\) is equal to \(b\).”

Equation: An equation is two expressions connected by an equal sign.

Equivalent Decimals: Two decimals are equivalent if they convert to equivalent fractions.

Equivalent Fractions: Equivalent fractions are fractions that have the same value.

Evaluate an Expression: To evaluate an expression means to find the value of the expression when the variable is replaced by a given number.

Expression: An expression is a number, a variable, or a combination of numbers and variables using operation symbols.

Factors: If \(a·b=m\), then \(a\) and \(b\) are factors of \(m\). Since \(3 · 4 = 12\), then \(3\) and \(4\) are factors of \(12\).

Fraction: A fraction is written \(ab\), where \(b≠0\) \(a\) is the numerator and \(b\) is the denominator. A fraction represents parts of a whole. The denominator \(b\) is the number of equal parts the whole has been divided into, and the numerator \(a\) indicates how many parts are included.

Integers: The whole numbers and their opposites are called the integers: \(...−3, −2, −1, 0, 1, 2, 3...\)

Irrational Number: An 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 Denominator: The least common denominator (LCD) of two fractions is the Least common multiple (LCM) of their denominators.

Least Common Multiple: The least common multiple of two numbers is the smallest number that is a multiple of both numbers.

Like Terms: Terms that are either constants or have the same variables raised to the same powers are called like terms.

Multiple of a Number: A number is a multiple of \(n\) if it is the product of a counting number and \(n\).

Multiplicative Identity: The multiplicative identity is the number \(1\); multiplying \(1\) by any number does not change the value of the number.

Multiplicative Inverse: The reciprocal of a number is its multiplicative inverse. A number and its multiplicative inverse multiply to one.

Number Line: A number line is used to visualize numbers. The numbers on the number line get larger as they go from left to right, and smaller as they go from right to left.

Numerator: The numerator is the value on the top part of the fraction that indicates how many parts of the whole are included.

Opposite: The 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: \(−a\) means the opposite of the number. The notation \(−a\) is read “the opposite of \(a\).”

Origin: The origin is the point labeled \(0\) on a number line.

Percent: A percent is a ratio whose denominator is \(100\).

Prime Factorization: The prime factorization of a number is the product of prime numbers that equals the number.

Prime Number: A prime number is a counting number greater than \(1\), whose only factors are \(1\) and itself.

Radical Sign: A radical sign is the symbol \(\sqrt{m}\) that denotes the positive square root.

Rational Number: A rational number is a number of the form \(pq\), where \(p\) and \(q\) are integers and \(q≠0\). A rational number can be written as the ratio of two integers. Its decimal form stops or repeats.

Real Number: A real number is a number that is either rational or irrational.

Reciprocal: The reciprocal of \(ab\) is \(ba\). A number and its reciprocal multiply to one: \(ab·ba=1\).

Repeating Decimal: A repeating decimal is a decimal in which the last digit or group of digits repeats endlessly.

Simplified Fraction: A fraction is considered simplified if there are no common factors in its numerator and denominator.

Simplify an Expression: To simplify an expression, do all operations in the expression.

Square and Square Root: If \(n^2=m\), then \(m\) is the square of \(n\) and \(n\) is a square root of \(m\).

Term: A term is a constant or the product of a constant and one or more variables.

Variable: A variable is a letter that represents a number whose value may change.

Whole Numbers: The whole numbers are the numbers \(0, 1, 2, 3, ...\).