Quick MathSpeak™ Tutorial

Tutorial Settings

Without Semantic Interpretation, MathSpeak speaks the symbols as they appear and cannot deduce their meaning. For example, the cross-sign can be either cross-multiplication or cross-product, so MathSpeak will just say "cross." Since it is sometimes ambigious whether a comma is a delimiter or a comma within a number, numbers are spelled out except for the highest level of Semantic Interpretation.

Example 1

the equation 3 plus 4 cross-multiplied by 2 minus negative 2 equals 3 plus 8 plus 2 equals 13

brief	3 plus 4 cross 2 minus minus 2 equals 3 plus 8 plus 2 equals 1 3
brief semantics	3 plus 4 times 2 minus negative 2 equals 3 plus 8 plus 2 equals 13
brief semantics high	3 plus 4 times 2 minus negative 2 equals 3 plus 8 plus 2 equals 13

For most fractions, the beginning is indicated with "start fraction", the horizontal line is indicated with "over", and the end of the fraction is indicated by "end fraction". For the semantic interpretation, most numeric fractions are spoken as they are in natural speech. Also if a number is followed by a numeric fraction, the word "and" is spoken in between.

Example 2

$the fraction x over y$

brief	StartFrac x Over y EndFrac
brief semantics	StartFrac x Over y EndFrac
brief semantics high	TheFrac x Over y EndFrac

Example 3

$the fraction x over y followed by plus a equals the fraction with x plus a y in the numerator and y in the denominator$

brief	StartFrac x Over y EndFrac plus a equals StartFrac x plus a y Over y EndFrac
brief semantics	StartFrac x Over y EndFrac plus a equals StartFrac x plus a y Over y EndFrac
brief semantics high	TheFrac x Over y EndFrac plus a equals TheFrac x plus a y Over y EndFrac

Example 4

$the variable a plus the fraction with b in the numerator and c plus d in the denominator not-equals-sign the fraction with a plus b in the numerator and c in the denominator plus d$

brief	a plus StartFrac b Over c plus d EndFrac not-equals StartFrac a plus b Over c EndFrac plus d
brief semantics	a plus StartFrac b Over c plus d EndFrac not-equals StartFrac a plus b Over c EndFrac plus d
brief semantics high	a plus TheFrac b Over c plus d EndFrac not-equals TheFrac a plus b Over c EndFrac plus d

Example 5

brief	StartFrac 1 Over 2 EndFrac minus x
brief semantics	one-half minus x
brief semantics high	one-half minus x

Example 6

$the fraction with 1 in the numerator and 2 minus x in the denominator$

brief	StartFrac 1 Over 2 minus x EndFrac
brief semantics	StartFrac 1 Over 2 minus x EndFrac
brief semantics high	TheFrac 1 Over 2 minus x EndFrac

Example 7

$the number 5 followed by the fraction three-eighths$

brief	5 StartFrac 3 Over 8 EndFrac
brief semantics	5 and three-eighths
brief semantics high	5 and three-eighths

Notice that the following numeric fraction is not spoken as "twenty-fifths," since this could be confused with the ordinal value of 25.

Example 8

$the fraction 20 over 5$

brief	StartFrac 2 0 Over 5 EndFrac
brief semantics	StartFrac 20 Over 5 EndFrac
brief semantics high	TheFrac 20 Over 5 EndFrac

Fractions that contain other fractions are spoken differently than simple fractions, the beginning of the indicators are repeated to indicate the number of levels of nested fractions.

Example 9

$the fraction six-halves over 3 equals the fraction 3 over 3 equals 1$

brief	StartStartFrac StartFrac 6 Over 2 EndFrac OveOver 3 EndEndFrac equals StartFrac 3 Over 3 EndFrac equals 1
brief semantics	StartFrac six-halves Over 3 EndFrac equals three-thirds equals 1
brief semantics high	StartFrac six-halves Over 3 EndFrac equals three-thirds equals 1

Example 10

$the fraction six over two-thirds equals 6 crossed-out with 3 above times the fraction 3 over 2 with the 2 crossed out equals 9$

brief	StartStartFrac 6 OveOver StartFrac 2 Over 3 EndFrac EndEndFrac equals StartCancel 6 CancelBy 3 EndCancel cross StartFrac 3 Over StartCancel 2 EndCancel EndFrac equals 9
brief semantics	StartFrac 6 Over and two-thirds EndFrac equals CrossOut 6 With 3 EndCrossOut cross three-halves equals 9
brief semantics high	StartFrac 6 Over and two-thirds EndFrac equals CrossOut 6 With 3 EndCrossOut cross three-halves equals 9

Example 11

$the number 5 plus the fraction with x minus one-half in the numerator and x plus one-half in the denominator$

brief	5 plus StartStartFrac x minus StartFrac 1 Over 2 EndFrac OveOver x plus StartFrac 1 Over 2 EndFrac EndEndFrac
brief semantics	5 plus StartFrac x minus one-half Over x plus one-half EndFrac
brief semantics high	5 plus StartFrac x minus one-half Over x plus one-half EndFrac

"Raised to the power of" is indicated by the term "superscript" - implying that the term following has the level of "raised power." "Super-superscript" implies that there are two levels of superscripts in sequence. A superscript level will continue until a different level is stated. If the expression continues at the original base level, the term baseline is stated.

Example 12

An example that is mainly narrative. See MathSpeak rendering below.

brief	In 2 Sup y Base plus x Sub n Base comma Sup y Base is a superscript and Sub n Base is a subscript period
brief semantics	In 2 Sup y Base plus x Sub n Base comma Sup y Base is a superscript and Sub n Base is a subscript period
brief semantics high	In 2 Sup y Base plus x Sub n Base comma Sup y Base is a superscript and Sub n Base is a subscript period

Square roots are stated with "start root" at the beginning and "end root" at the end.

Example 13

brief	d equals StartRoot l-par x 2 minus x 1 r-par Sup 2 Base minus l-par y 2 minus y 1 r-par Sup 2 Base EndRoot
brief semantics	d equals StartRoot l-par x 2 minus x 1 r-par squared minus l-par y 2 minus y 1 r-par squared EndRoot
brief semantics high	d equals StartRoot l-par x 2 minus x 1 r-par squared minus l-par y 2 minus y 1 r-par squared EndRoot

Example 14

the set with the variables x raised to the first power, x squared, x cubed, x raised to the fourth power, ellipsis, x raised to the n power

brief	l-brace x Sup 1 Base comma x Sup 2 Base comma x Sup 3 Base comma x Sup 4 Base comma ellipsis comma x Sup n Base r-brace
brief semantics	StartSet x Sup 1 Base comma x squared comma x cubed comma x Sup 4 Base comma ellipsis comma x Sup n Base EndSet
brief semantics high	StartSet x Sup 1 Base comma x squared comma x cubed comma x Sup 4 Base comma ellipsis comma x Sup n Base EndSet

Example 15

the variable y raised to the power of the quantity openning-parenthesis 2 raised to the power of x closing-parenthesis

brief	y Sup l-par 2 SupSup x Sup r-par
brief semantics	y Sup l-par 2 SupSup x Sup r-par
brief semantics high	y Sup l-par 2 SupSup x Sup r-par

Example 16

$the fraction x raised to the one-half over 7$

brief	StartFrac x Sup StartFrac 1 Over 2 EndFrac Base Over 7 EndFrac
brief semantics	StartFrac x Sup one-half Base Over 7 EndFrac
brief semantics high	StartFrac x Sup one-half Base Over 7 EndFrac

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