Complex Fractions

As you have already learned, a simple fraction is a fraction whose numerator and denominator contain only numeric digits, commas, or decimal points, and where the numerator is elevated above the denominator. The numbers are separated by the simple fraction line. The simple fraction line does NOT terminate numeric mode so a numeric indicator is not required for the second number.

Examples:

⠼⠁⠌⠙

1¼

⠼⠁⠼⠁⠌⠙

General Fraction Symbols

If either the numerator or denominator in a fraction contains anything other than a digit, comma, or decimal, the fraction must be enclosed between general fraction grouping symbols and a general fraction line is used to separate the numerator from the denominator. Since these symbols also have a contracted meaning, a grade 1 indicator must be used if the expression is not already in uncontracted mode.

General Fraction Open indicator	⠷
General Fraction Close indicator	⠾
General Fraction line	⠨⠌
Continuation indicator	⠐

Example:

$\frac{a}{b}$

opening indicator	numerator	fraction line	denominator	closing indicator
⠷	⠁	⠨⠌	⠃	⠾

⠰⠷⠁⠨⠌⠃⠰⠾

Note: Both the opening and closing general fraction indicators required a grade 1 indicator.

Examples:

$5 = \ \frac{2}{x}$

⠼⠑⠀⠐⠶⠀⠰⠷⠼⠃⠨⠌⠭⠾

Note: In the above example the grade 1 indicator was needed for the first general fraction indicator because the default mode was contracted and the general fraction opening indicator has a contracted meaning (of). The numeric indicator set uncontracted mode for the remainder of the expression, so a grade 1 indicator was not required for the second general fraction indicator.

Both of the following transcriptions are correct. It is usually preferable to use the grade 1 word indicator if an expression requires two or more grade 1 indicators but the choice can be made based on which provides more clarity.

$\frac{a + b}{c}$

⠰⠷⠁⠐⠖⠃⠨⠌⠉⠰⠾

⠰⠰⠷⠁⠐⠖⠃⠨⠌⠉⠾

All rules for mode and level change indicator can be applied to the numerator and/or denomination of a complex fraction.

Examples:

$\frac{5\frac{1}{2}}{y}\ = \ \ 22$

⠰⠷⠼⠑⠼⠁⠌⠃⠨⠌⠽⠾⠀⠐⠶⠀⠼⠃⠃

Note: The grade 1 indicator is needed for the first fraction indicator and then the numeric indicator sets uncontracted mode until the space.

Complex fraction in numerator

$\frac{6 - \frac{1}{x}}{x + y}$

⠰⠷⠼⠋⠐⠤⠷⠼⠁⠨⠌⠭⠾⠨⠌⠭⠐⠖⠽⠾

Superscript in numerator

$\frac{5x^{2} - 1\ }{x - 4}$

⠰⠷⠼⠑⠭⠔⠼⠃⠐⠤⠼⠁⠨⠌⠭⠐⠤⠼⠙⠾

Superscript in numerator and denominator

$\frac{24x^{3}y^{2}}{32xy^{4}}$

⠰⠷⠼⠃⠙⠭⠔⠼⠉⠽⠔⠼⠃⠨⠌⠼⠉⠃⠭⠽⠔⠼⠙⠾

Other symbol in fraction

$\frac{12}{20\%} = \frac{x}{100\%}$

⠰⠷⠼⠁⠃⠨⠌⠼⠃⠚⠨⠴⠾⠀⠐⠶⠀⠰⠷⠭⠨⠌⠼⠁⠚⠚⠨⠴⠾

Abbreviations in fraction

$\frac{2,500mL}{500L} = 1,250mL$

⠰⠷⠼⠃⠂⠑⠚⠚⠍⠠⠇⠨⠌⠼⠑⠚⠚⠠⠇⠾⠀⠐⠶⠀⠼⠁⠂⠃⠑⠚⠍⠠⠇

Words in fractions

$\frac{distance}{rate} = time$

⠰⠷⠙⠊⠌⠨⠑⠨⠌⠗⠁⠞⠑⠰⠾⠀⠐⠶⠀⠐⠞

Note: The words "distance" and "time" are contracted because the expression is in the default mode.

Run-overs

When an expression runs over to the second line, a division should occur at a natural break if possible and the equal sign should stay with the answer. Run-overs continue in the third cell of the second line and every line afterward.

Example:

$\frac{1}{x} - \frac{1}{y} = \ \frac{y}{xy} - \frac{x}{xy} = \ \frac{y - x}{xy}$

⠰⠰⠰⠷⠼⠁⠨⠌⠭⠾⠐⠤⠷⠼⠁⠨⠌⠽⠾⠀⠐⠶⠀⠷⠽⠨⠌⠭⠽⠾⠐⠤⠷⠭⠨⠌⠭⠽⠾

⠀⠀⠐⠶⠀⠷⠽⠐⠤⠭⠨⠌⠭⠽⠾⠰⠄

Continuation Indicator

If there are no natural breaks in an expression that runs over to a second line, a dot 5 continuation indicator can be used. There is no print equivalent. The dot 5 indicator is placed at the end of the line and the expression is continued on the following line.

Example:

$\frac{4x^{- 1} + 2y^{- 1}}{5x^{- 2} - 2y^{- 2}}$

⠰⠰⠰⠷⠼⠙⠭⠔⠣⠐⠤⠼⠁⠜⠐⠖⠼⠃⠽⠔⠣⠐⠤⠼⠁⠜⠨⠌⠼⠑⠭⠔⠣⠐⠤⠼⠃⠜⠐⠤⠐

⠀⠀⠼⠃⠽⠔⠣⠐⠤⠼⠃⠜⠾⠰⠄

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