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Unit 16 Spatial Arrangement: Division

As you know, print division problems can be written with the divide-by sign (÷) horizontally (as in Unit 2), or they can be written spatially with a long division symbol ( ⟌ ).

In Nemeth Code, if a spatial division problem contains only a numeric dividend (number) and divisor (what it is divided by), it is written as a linear division problem with a curved or straight division symbol. No separation line is used.

Curved Division Sign	⠕
Straight Division Sign	⠸
Separation Line	⠒⠒⠒⠒

Examples:

$5\overline{)25}$

⠼⠢⠕⠆⠢

$12\stackrel{\_}{|144}$

⠼⠂⠆⠸⠂⠲⠲

Spatial Arrangements

When a division problem contains symbols other than numeric digits in its dividend or divisor, Nemeth Code formatting for spatial representation is used. Like in print, the divisor is separated from the dividend by a division sign and the separation line is placed one line above the divisor/dividend line. The separation line begins in the column just above the division symbol and extends one cell beyond the widest part of the division problem. A numeric indicator is not used.

Examples:

$2\overline{){10}^{\mathrm{\prime }}{6}^{\mathrm{″}}}$

⠀⠒⠒⠒⠒⠒⠒⠒⠒

⠆⠕⠂⠴⠄⠖⠄⠄

$5\stackrel{\_}{|\mathrm{\$}25}$

⠀⠒⠒⠒⠒⠒⠒

⠢⠸⠈⠎⠆⠢

Even if a division problem contains only a numeric dividend (number) and divisor (what it is divided by), if it also contains the quotient (answer), Nemeth Code formatting for spatial representation is used.

Example:

$\begin{array}{r}50\\ 10\overline{)500}\end{array}$

⠀⠀⠀⠀⠢⠴

⠀⠀⠒⠒⠒⠒⠒

⠂⠴⠕⠢⠴⠴

Curved Division Sign

$\begin{array}{r}15\\ 25\overline{)345}\\ \underset{\_}{23}\phantom{0}\\ 115\\ \underset{\_}{115}\\ 0\end{array}$

⠀⠀⠀⠀⠀⠂⠢

⠀⠀⠒⠒⠒⠒⠒

⠆⠒⠕⠒⠲⠢

⠀⠀⠀⠆⠒

⠀⠀⠒⠒⠒⠒⠒

⠀⠀⠀⠂⠂⠢

⠀⠀⠀⠂⠂⠢

⠀⠀⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠴

Straight Division Sign

$\begin{array}{r}12\\ 12\stackrel{\_}{|144}\\ \underset{\_}{12\phantom{0}}\\ 24\\ \underset{\_}{24}\\ 0\end{array}$

⠀⠀⠀⠀⠂⠆

⠀⠀⠒⠒⠒⠒⠒

⠂⠆⠸⠂⠲⠲

⠀⠀⠀⠂⠆

⠀⠀⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠆⠲

⠀⠀⠀⠀⠆⠲

⠀⠀⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠴

Decimals

When a spatial division problem contains a decimal, a blank space is left where the decimal point would have been carried down throughout the problem to maintain correct spacing. This also occurs when commas appear in a long division problem.

Example:

$\begin{array}{r}10\mathrm{.}2\\ 24\overline{)244\mathrm{.}8}\\ \underset{\_}{24\phantom{0}}\phantom{.0}\\ 04\phantom{.0}\\ \underset{\_}{\phantom{0}0}\phantom{.0}\\ 4\phantom{\mathrm{.}}8\\ \underset{\_}{4\phantom{\mathrm{.}}8}\\ 0\end{array}$

⠀⠀⠀⠀⠂⠴⠨⠆

⠀⠀⠒⠒⠒⠒⠒⠒⠒

⠆⠲⠕⠆⠲⠲⠨⠦

⠀⠀⠀⠆⠲

⠀⠀⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠴⠲

⠀⠀⠀⠀⠀⠴

⠀⠀⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠲_⠦

4}br") ?>⠸⠦

3333333

0}br") ?>

Repeating Decimal

A repeating decimal is expressed by modifying the repeating number with the horizontal bar symbol for directly over.

Example:

$\begin{array}{r}26.\stackrel{\_}{2}\\ 9\overline{)236\phantom{.0}}\\ \underset{\_}{18\phantom{0}}\phantom{.0}\\ 56\phantom{.0}\\ \underset{\_}{54}\phantom{.0}\\ 2\phantom{\mathrm{.}}0\\ \underset{\_}{1\phantom{\mathrm{.}}8}\\ 2\end{array}$

⠀⠀⠀⠆⠖⠨⠆⠱

⠀⠒⠒⠒⠒⠒⠒⠒⠒

⠔⠕⠆⠒⠖

⠀⠀⠂⠦

⠀⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠢⠖

⠀⠀⠀⠢⠲

⠀⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠆⠴

⠀⠀⠀⠀⠂⠦

⠀⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠆

Remainder

Just as in print, a remainder is represented by the letter "r" followed, unspaced, by a number. One space is left between the quotient and the remainder and no ELI is used. The multipurpose indicator (dot 5) is placed between the letter "r" and the numeral to prevent it from being read as subscript (Unit 11).

Example:

$\begin{array}{r}\phantom{00}19\mathrm{r}4\\ 5\stackrel{\_}{|99\phantom{00}}\end{array}$

⠀⠀⠂⠔⠀⠗⠐⠲

⠀⠒⠒⠒⠒⠒⠒⠒⠒

⠢⠸⠔⠔

Nemeth Code Indicators with Spatial Formatting

If a spatial math problem appears along with literary text, an opening Nemeth Code indicator is placed one space from the text on the same line (or the following line if there is not enough room). One line is skipped before the spatial formatting to set the Nemeth Code apart from the non-Nemeth text and one line is skipped after the spatial math formatting. A Nemeth Code terminator is then placed on the next line in cell one. One empty cell is left between separation lines horizontally when expressions appear on the same horizontal line.

Example:

Find the quotient (answer).

$\begin{array}{r}46\mathrm{r}7\\ 13\overline{)605\phantom{00}}\\ \underset{\_}{52\phantom{0}}\phantom{00}\\ 85\phantom{00}\\ \underset{\_}{78}\phantom{00}\\ 7\phantom{00}\end{array}$

⠠⠋⠔⠙⠀⠮⠀⠟⠥⠕⠞⠊⠢⠞⠀⠐⠣⠁⠝⠎⠺⠻⠐⠜⠲⠀⠸⠩

⠀⠀⠀⠀⠲⠖⠀⠗⠐⠶

⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠂⠒⠕⠖⠴⠢

⠀⠀⠀⠢⠆

⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠦⠢

⠀⠀⠀⠀⠶⠦

⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠶

⠸⠱