Glossary - Jj Kk Ll

Justify

To provide an argument for a mathematical conjecture; it may be an intuitive argument or a set of examples that support the conjecture; the argument may include, but is not limited to, a written paragraph, measurement using appropriate tools, the use of dynamic software, or a written proof.

Key

A table for decoding or interpreting; a notation that explains something such as the value of each symbol or picture on a pictograph.

Kilogram

A metric unit to measure mass; 1 kilogram = 1000 grams. The abbreviation for kilogram is "kg."

Kilometre

A metric unit of length roughly equivalent to 6/10 of a mile; 1 kilometre=1000 metres.The abbreviation for kilometre is "km."

Law of Exponents for Multiplication

The product of two or more numbers in exponential form with the same base is equal to that base raised to the power equal to the sum of the powers of each number; i.e., add their exponents: a ^b - a^c = a^b+c Example: a⁵ - a ² = a⁷.

Law of Exponents for Division

The quotient of two numbers in exponential form with the same base is equal to that base with a power equal to the difference of the powers of each number; i.e., subtract their exponents: A^b/A^c=A^(b-c)

Least

Smallest in quantity, size, or degree.

Least Common Denominator

The smallest common multiple of two given denominators Example: The LCD of 1/3 and 1/8 is 24.

Least Common Multiple (LCM)

The smallest number (greater than zero) that is a multiple of a set of two or more numbers. Example: The least common multiple of 3 and 5 is 15. The LCM of 10x² and 4xy is 20x²y.

Leg of a Right Triangle

One of the two sides that form the right angle of a right triangle; the sides that are not the hypotenuse. (See hypotenuse)

Length

A value of distance. A line between San Francisco and Los Angeles will have a length of 422 miles. The distance between the two cities is 422 miles.In two-dimensional objects, length is closely associated with width. Units of length include miles, fathoms, meters, kilometers, light years, and many others.

Less Than (LT)

A relationship showing that the first term or expression has a value smaller than the second term or expression. The symbol that represents less than is "<." Examples: 5 < 7. or -9 < -7.

Like Denominators

A whole number, greater than zero, that is the denominator of two or more fractions.(See common denominator) Example: The fractions 2/7 and 3/7 have like (the same) denominators.

Like Terms

Terms that have the same literal part (e.g., in the expression 3x2 + 4x + 5 + 2x + 4x3 + 5x2, 3x2 and 5x2 are like terms, as are 4x and 2x).

Line

An infinite set of connected points continuing without end in both directions. They are connected with a straight path and there is only one dimension -- length.

Line Graph

A graph that uses line segments to show changes in data; the data usually represents a quantity changing over time.

Line of Best Fit

A straight line used as a best approximation of a summary of all the points in a scatter-plot* (See definition below). The position and slope of the line are determined by the amount of correlation* (See definition above) between the two paired variables involved in generating the scatter-plot. This line can be used to make predictions about the value of one of the paired variables if only the other value in the pair is known.

Line of Symmetry

A line that divides a figure into two congruent halves that are mirror images of each other. A test to determine if a figure has line symmetry is to fold the figure along the supposed line of symmetry and see if the two halves of the figure are identical.

Line Plot

A graph showing frequency of data on a number line. The graph shows each piece of data as a dot or mark.

Line Segment

A part of a line with two fixed endpoints and the points between.

Linear and Nonlinear Functional Relationships

Many functions can be represented by pairs of numbers. When the graph of those pairs results in points lying on a straight line, a function is said to be linear. When not on a line, the function is nonlinear. (Also see definition of Function)

Linear Equation

An equation of the form y = ax + b, where a and b can be any real number. An equation of the first degree that contains one or more variables. A linear equation in two variables yields a straight line when displayed in graph form (e.g., 3x – 1 = –7 or x + 2y = 12).

Linear Expression

An expression of the form ax+b where x is variable and a and b are constants; or in more variables, an expression of the form ax + by + c, ax + by + cz + d, etc.

Linear Inequalities

An inequality of the first degree that contains one or more variables. Examples: 2x + 4. Y > 3x – 2.

Linear Pair of Angles

A pair of adjacent angles formed by intersecting lines. Linear pairs of angles are supplementary.

Litre

A metric unit used to measure capacity; 1 liter = 1000 millilitres. The abbreviation for litres is "L."

Logarithm

The inverse of exponentiation; for example, a^loga^x = x.

Logic

The formal structure for reasoning.

Logical

According to the principles of logic.

Logical Reasoning

The process of using a rational, systematic series of steps based on sound mathematical procedures to arrive at a conclusion; the drawing of conclusions from given facts and mathematical principles; often used as a problem solving strategy.

Lowest Terms

The form of a fraction in which the numerator and denominator have no common factor except 1.