Use the expansion shown to simplify the expression.
One-half (3 x minus two-thirds y) + 3 (StartFraction x over 2 EndFraction + one-half y)
Equals (one-half) (StartFraction 3 over 1 EndFraction x) + (one-half) (Negative two-thirds y) + (StartFraction 3 over 1 EndFraction) (one-half x) + (StartFraction 3 over 1 EndFraction) (one-half y)
Equals (three-halves x) + (negative one-third y) + (three-halves x) + (three-halves y)
= 3x +
y
Answers
Answer: 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
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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
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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
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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
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Example 5
one-half minus x
verbose semantics
one-half minus x
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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
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Example 7
the number 5 followed by the fraction three-eighths
verbose semantics
5 and three-eighths
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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
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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
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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
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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
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"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
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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
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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
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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
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Example 16
the fraction x raised to the one-half over 7
verbose semantics
StartFraction x Superscript one-half Baseline Over 7 EndFraction
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Step-by-step explanation:
Answer:
7/6 y
Step-by-step explanation: