Quick MathSpeak™ Tutorial

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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

verbose semantics

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

$the fraction x over y$

verbose semantics

StartFraction x Over y EndFraction

Example 3

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

verbose semantics

StartFraction x Over y EndFraction plus a equals StartFraction x plus a y Over y EndFraction

Example 4

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

verbose semantics

a plus StartFraction b Over c plus d EndFraction not-equals StartFraction a plus b Over c EndFraction plus d

Example 5

one-half minus x

verbose semantics

one-half minus x

Example 6

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

verbose semantics

StartFraction 1 Over 2 minus x EndFraction

Example 7

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

verbose semantics

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

$the fraction 20 over 5$

verbose semantics

StartFraction 20 Over 5 EndFraction

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

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

verbose semantics

StartFraction six-halves Over 3 EndFraction equals three-thirds equals 1

Example 10

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

verbose semantics

StartFraction 6 Over and two-thirds EndFraction equals CrossOut 6 With 3 EndCrossOut cross three-halves equals 9

Example 11

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

verbose semantics

5 plus StartFraction x minus one-half Over x plus one-half EndFraction

"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.

verbose semantics

In 2 Superscript y Baseline plus x Subscript n Baseline comma Superscript y Baseline is a superscript and Subscript n Baseline is a subscript period

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

Example 13

the distance formula

verbose semantics

d equals StartRoot left-parenthesis x 2 minus x 1 right-parenthesis squared minus left-parenthesis y 2 minus y 1 right-parenthesis 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

verbose semantics

StartSet x Superscript 1 Baseline comma x squared comma x cubed comma x Superscript 4 Baseline comma ellipsis comma x Superscript n Baseline EndSet

Example 15

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

verbose semantics

y Superscript left-parenthesis 2 SuperSuperscript x Superscript right-parenthesis

Example 16

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

verbose semantics

StartFraction x Superscript one-half Baseline Over 7 EndFraction