Domain Glossary

a ad+bc (of Simple Fractions) In irreduced form, + = b d bd Backspace Button/Key The key labeled "Backspace" or "←" on a traditional physical or soft keyboard. Some traditional physical keyboards also have a “Delete” key (that deletes the character to the right of the cursor). Bar Style of Typesetting Typesetting a fraction with the numerator over a horizontal bar a over the denominator, for example b Binary Expression A left-side , followed by an operator, followed by a right- side operand. (See also: Equals Button/Key) Binary An operation that takes a left-side operand and a right-side operand. Note: All binary operations use infix notation. That is, the operator is between the two . Button A widget on a graphical user interface that can be "pressed" with the mouse (i.e., by clicking on it). (See also: Soft Key) Clear Button/Key A button or key that can be used to reset the state of the calculator and clear the display. Closed (Under an Operation) A set is closed under an operation if the evaluation of that operation on members of the set always produces members of the set. Common Factor/Divisor A factor that two given numbers have in common. For example, 5 is a common factor of 10 and 35. Component Loosely, a part of a mixed fraction. Specifically, an element of the set {wholes, numerator, denominator}. (See also: Wholes, Numerator, Denominator) Current Expression The expression that is currently being added to or modified. Current Mixed Fraction The mixed fraction that is currently being added to or modified.

Page 1 Denominator The number below the division bar in a fraction. It is sometimes described as the number of parts in a single entity. (See also: Wholes, Numerator) Digit Loosely, a one-character number. Specifically, an element of the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. Display The GUI element/widget that is used to present the current expression (and related information) to the user. a c ad Division (of Simple Fractions) In irreduced form, ÷ = b d bc Division Bar The horizontal line that is vertically between the numerator and the denominator of a fraction in the bar style of typesetting. Enter Key The key labeled "Enter" or "Return" on a traditional physical keyboard. Many keyboards have two Enter keys, one on the main section and on one the number pad. Equals Button/Key A button or key that can be used to evaluate a binary expression. Euclidean Algorithm An algorithm for finding the greatest common divisor of two numbers a and b. Factor An integer that can be divided evenly (i.e., without remainder) into a given integer number. For example, 5 is a factor of 10 because 10/5 is exactly 2. Focus In a GUI, the widget that has the focus is the widget that will respond to refers to the component that is selected to receive input. Fractional Part The numerator, division bar, and denominator of a mixed fraction. Greatest Common Divisor (GCD) The greatest common divisor of two positive integers a and b is the largest common factor of a and b. (See also: Euclidean Algorithm) History An ordered list of expressions (not including the current expression). Improper Fraction A simple fraction in which the numerator is greater than or equal to the denominator.

Page 2 Improper Form A mixed fraction can be converted to an improper fraction using n wd+n the observation: w = d d Input Field A GUI element that is used by a user to provide input to the system. Inverse, Multiplicative In irreduced form, the multiplicative inverse of the simple fraction a b is defined as for positive values of a and b. b a Irreduced Form A simple fraction that is not in reduced form is said to be in irreduced form. Key A key on a physical keyboard (either the main section or the number pad). Keyboard/Keypad A collection of keys or a collection of buttons that are simulating keys. (See also: Physical Keyboard/Keypad and Soft Keyboard/Keypad) Mixed Fraction A mixed fraction is made up of three integers - the number of wholes, a numerator, and a denominator. (A mixed fraction is sometimes also called a mixed number.) In some settings, a mixed fraction is said to consist of the number of wholes and a proper fraction. In Fragile, the numerator need not be less than the denominator. Hence, a mixed number consists of the number of wholes and any simple fraction. n Mixed Form An improper fraction can be rewritten as a mixed fraction in d irreduced form with a wholes of n/d and a fractional part of n%d where / represents integer division and % represents the d remainder after integer division (i.e., the mod operator). A proper fraction is in mixed form with a wholes of 0. a c ac Multiplication (of Simple Fractions) In irreduced form, × = . b d bd

Page 3 Mixed Irreduced Form The result of performing an operation on mixed fractions is said to be in mixed irreduced form if it has a wholes (if appropriate) and the fractional part has not been reduced. So, the numerator is never greater than or equal to the denominator but the numerator and denominator may not be the least components. (See the definitions of the various operations.) Number Button/Key A button or key that is used to input a single digit. Number Pad A collection of number keys or a collection of number buttons that are simulating number keys along with a collection of related operation keys/buttons. (See also: Physical Keyboard/Keypad and Soft Keyboard/Keypad) Numerator The number above the division bar in a fraction. It is sometimes described as the number of parts in the entity of interest. (See also: Denominator, Wholes) Operation Button/Key A button or key that is used to input a binary or unary operation/operator. Pending Operation The (binary) operation that has not yet been evaluated (because the Enter Button/Key has not yet been pressed). Physical Keyboard A mechanical or electronic input device consisting of a set of labeled keys. Many physical keyboards have a main section (containing the alphabetic and numeric keys as well as some special--purpose keys), movement section containing arrow keys, a number pad, and a row of function keys (along the top). Position Button/Key The button or key that is used to move between the components of a mixed fraction. Proper Fraction A simple fraction in which the numerator is less than the denominator. Reduced Form A simple fraction is in reduced form if it is written in its lowest components. The reduced form can be found by dividing both the numerator and denominator by the greatest common divisor. A mixed fraction is in reduced form if its fractional part is both proper and in reduced form. (See also Irreduced Form.)

Page 4 Result The result of evaluating a binary or unary expression. Sign Button/Key The button or key that is used to change the sign of the current mixed fraction. Simple Fraction A simple fraction is made up of two integers - a numerator, and a denominator. The denominator represents the number of parts in a complete entity. The numerator represents the number of parts in the entity of interest. Simplified Form Another name for a Reduced Form. Slash / Slash Style of Typesetting Typesetting a fraction as a/b Soft Key Another name for a Button. Soft Keyboard A collection of Buttons. Solidus A steep slash. a Solidus Style of Typessting Typesetting a fraction as (i.e., with the numerator raised b above the baseline and the denominator lowered below the baseline). Subtraction (of Simple Fractions) In irreduced form, ignoring the fact that the numerator and a c ad−bc denominator should not each be signed, − = . b d bd Unary Operation An operation that takes a single operand. Note: All unary operations use postfix notation. That is, the operator follows the operand. Wholes The number of wholes in a mixed fraction. (See also: Denominator, Numerator). Widget A part of a graphical user interface. Widgets are sometimes also called controls. (See also: Button, Display, and Input Field.)

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