#
Mathematical Operators

### + , plus

Behavior: Adds two numbers or lists of numbers.

Syntax:

operand1 + operand2

operand1 plus operand2

Syntax definitions for language elements follow these formatting guidelines:

- boldface: Indicates words that must be typed exactly
- italics: Indicate expressions or other variable elements
- {} (curly braces): Indicate optional elements.
- [] (square brackets) separated by | (vertical pipes): Indicates alternative options where one or the other may be used, but not both.

Example syntax:

In this example, "open file" is required and must be typed exactly. "fileName" is a variable element; it is the path to and name of the file being opened. The following expression is optional and indicates why the file is being opened. If this expression is added, "for" is required and must be typed exactly. One of the following must be included, but only one, and they also must be typed exactly: "reading", "writing", "readwrite", "appending", or "updating".

Example:

put 12 + 97 into someSum

Example:

put a squared plus b squared into sumOfSquares

Example:

put (12,8) + (4,7) into vectorSum

### - , minus

Behavior: Subtracts one number or list of numbers from another. Subtracting one date/time from another will give the difference as a time interval, measured in seconds.

Syntax:

operand1 - operand2

operand1 minus operand2

Syntax definitions for language elements follow these formatting guidelines:

- boldface: Indicates words that must be typed exactly
- italics: Indicate expressions or other variable elements
- {} (curly braces): Indicate optional elements.
- [] (square brackets) separated by | (vertical pipes): Indicates alternative options where one or the other may be used, but not both.

Example syntax:

In this example, "open file" is required and must be typed exactly. "fileName" is a variable element; it is the path to and name of the file being opened. The following expression is optional and indicates why the file is being opened. If this expression is added, "for" is required and must be typed exactly. One of the following must be included, but only one, and they also must be typed exactly: "reading", "writing", "readwrite", "appending", or "updating".

Example:

put c^2 - sumOfSquares into difference

Example:

put (1,3,5,6) - (1,1,0,2) into diffList

### * , times, multiplied by

Behavior: Multiplies two numbers or lists, or multiplies a list by a scalar. When used with two lists of equal length, the result will be a series of products of the corresponding elements of the two lists. When one operand is a list and the other is a single (scalar) value, the result is a list of values obtained by multiplying each original list element by the scalar value.

Syntax:

operand1 * operand2

operand1 times operand2

Syntax definitions for language elements follow these formatting guidelines:

- boldface: Indicates words that must be typed exactly
- italics: Indicate expressions or other variable elements
- {} (curly braces): Indicate optional elements.
- [] (square brackets) separated by | (vertical pipes): Indicates alternative options where one or the other may be used, but not both.

Example syntax:

In this example, "open file" is required and must be typed exactly. "fileName" is a variable element; it is the path to and name of the file being opened. The following expression is optional and indicates why the file is being opened. If this expression is added, "for" is required and must be typed exactly. One of the following must be included, but only one, and they also must be typed exactly: "reading", "writing", "readwrite", "appending", or "updating".

Example:

put 2 * radius into diameter

Example:

put pi times diameter into circumference

Example:

put (1,2,3,4) * (2,2,1,3)-- result is (2,4,3,12)

Example:

put (1,2,3,4) * 4 -- result is (4,8,12,16)

Example:

put 7 multiplied by 3 -- result is 21

### / , divided by

Behavior: Divides one number or list by another, or divides a list by a scalar. The result is a quotient that may not be a whole number. Compare this to the div operator, which yields a whole number. When used with two lists of equal length, the result will be a series of quotients of the corresponding elements of the two lists. When the first operand is a list and the second is a single (scalar) value, the result is a list of values obtained by dividing each list element by the scalar value. If the second operand is zero, this operator will return the value infinity, displayed as Inf. Using an infinite value in other calculations will generally give expected results.

Syntax:

operand1 / operand2

operand1 divided by operand2

Syntax definitions for language elements follow these formatting guidelines:

- boldface: Indicates words that must be typed exactly
- italics: Indicate expressions or other variable elements
- {} (curly braces): Indicate optional elements.

Example syntax:

Example:

put pi / 2 into halfPi

Example:

put (1,2,3,4) / (2,1,1,2)-- result is (0.5,2,3,2)

Example:

put (2,4,5,8) / 2-- result is (1,2,2.5,4)

### ^ , to the power of , squared , cubed

Behavior: Raises a number to a given power.

Syntax:

operand1 to the power of operand2

operand1 squared

operand1 cubed

Syntax definitions for language elements follow these formatting guidelines:

- boldface: Indicates words that must be typed exactly
- italics: Indicate expressions or other variable elements
- {} (curly braces): Indicate optional elements.

Example syntax:

Example:

put a squared + b squared into sumOfSquares

Example:

put 6 * x^4 - 2 * y^3 into z

### % , percent

Behavior: Treats a number as a percentage, or computes add-on or discount percentages. In its simple form, % following a value divides that value by 100 (so 6% is the same as .06). However, if % is used following a + or - operator, the corresponding percent of the value to the left of that operator will be increased or decreased by the specified percent.

Syntax:

factor %

factor percent

value [ + | - | plus | minus ] factor [ % | percent ]

Syntax definitions for language elements follow these formatting guidelines:

- boldface: Indicates words that must be typed exactly
- italics: Indicate expressions or other variable elements
- {} (curly braces): Indicate optional elements.

Example syntax:

Example:

put 4% -- .04

Example:

put 50 * 4% -- 2

Example:

put 50 + 4% -- 52

Example:

put 50 - 4% -- 48

Example:

put sales plus ten percent into projectedSales

### div

Behavior: Divides one number by another, giving the result as an integer. The companion rem operator can be used to find the remainder of such an operation. Division by zero will yield the result Inf.

Syntax:

Syntax definitions for language elements follow these formatting guidelines:

- boldface: Indicates words that must be typed exactly
- italics: Indicate expressions or other variable elements
- {} (curly braces): Indicate optional elements.

Example syntax:

Example:

put cookieCount div numberOfPeople into cookiesForEach

### rem

Behavior: Calculates the integer remainder of a division. This is the complement of the div operator. The result of the rem operator will always have the same sign as its first operand.

Syntax:

Syntax definitions for language elements follow these formatting guidelines:

- boldface: Indicates words that must be typed exactly
- italics: Indicate expressions or other variable elements
- {} (curly braces): Indicate optional elements.

Example syntax:

Example:

put cookieCount rem numberOfPeople into extrasForMe

### modulo, mod

Behavior: Performs the mathematical modulo operation. Obtains the amount by which one number exceeds the next-lower even multiple of another. The modulo operator is different from the rem operator, which gives the remainder of an integer division. When both operands are positive integers, rem and modulo will yield the same results. Negative numbers and non-integer values are treated much differently by the two operators, however.

Syntax:

Syntax definitions for language elements follow these formatting guidelines:

- boldface: Indicates words that must be typed exactly
- italics: Indicate expressions or other variable elements
- {} (curly braces): Indicate optional elements.

Example syntax:

Example:

put someValue mod modulusValue into extrasForMe

### is a multiple of, is divisible by

Behavior: Checks whether one number is an exact multiple of another. That is, if the result of dividing one by the other would result in a whole number with no remainder.

Syntax:

value is {not} {a | an} {exact | even} multiple of divisor

value is {not} {exactly | evenly} divisible by divisor

Syntax definitions for language elements follow these formatting guidelines:

- boldface: Indicates words that must be typed exactly
- italics: Indicate expressions or other variable elements
- {} (curly braces): Indicate optional elements.

Example syntax:

Example:

put 2895 is a multiple of 5-- true

Example:

put 169 is divisible by 13 -- true

Example:

put 98.6 is an exact multiple of 3.14-- false

Example:

if cookieCount is evenly divisible by numberOfPeople then put "Hooray!"

### rounded to, rounded to nearest

Behavior: Rounds a value to a number of decimal places, or to the nearest multiple of another value. Also rounds to a unit name or to a variable whose value is a unit name. These operators provide an alternate syntax for calling the round() and roundToNearest() functions (see Arithmetic Calculations).

Syntax:

value rounded {to} places {{decimal} places}

value rounded to {the} nearest {multiple of} nearestMultiple

value rounded to {the} nearest unit

Syntax definitions for language elements follow these formatting guidelines:

- boldface: Indicates words that must be typed exactly
- italics: Indicate expressions or other variable elements
- {} (curly braces): Indicate optional elements.

Example syntax:

Example:

put 123.4567 rounded to 2 places-- 123.46

Example:

put 123.4567 rounded -1 decimal places-- 120

Example:

put 98.6 rounded to the nearest multiple of 3.14-- 97.34

Example:

put total rounded to nearest .25 into amountDue

Example:

put 12.345 meters rounded to the nearest foot — 41 feet

### but at least, but no less than, but at most, but no more than operators

Behavior: Limits a number to a minimum or maximum value.

Syntax:

operand but at least value

operand but no less than value

operand but at most value

operand but no more than value

Syntax definitions for language elements follow these formatting guidelines:

- boldface: Indicates words that must be typed exactly
- italics: Indicate expressions or other variable elements
- {} (curly braces): Indicate optional elements.

Example syntax:

Example:

set highScore to largest value in scores but at most 100

Example:

set lowScore to rawScore - 9 but no less than zero

Example:

set volume to myVolume but no more than 11

Example:

set roomCapacity to sizeLimit but at least 123