# Unit 5 Spatial Arrangement: Addition and Subtraction

As you already know, addition and subtraction problems can be presented horizontally.

1. 12+2 = 14

⠼⠂⠸⠲⠀⠼⠂⠆⠬⠆⠀⠨⠅⠀⠼⠂⠲

When they appear vertically in print, Nemeth Code formatting for spatial representation is used.

Separation Line for spatial math | ⠒⠒⠒⠒ |

The equals sign is replaced by the separation line that extends one cell on either side of the expression, and the numeric indicator is generally not used

# Example:

$\begin{array}{r}12\\ \underset{\_}{+2}\\ 14\end{array}$⠼⠂⠸⠲⠀⠀⠀⠂⠆

⠀⠀⠀⠀⠀⠀⠬⠀⠆

⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠂⠲

The addition and subtraction problems are aligned by place value, commas, and decimals just as they are in print, and the sign of operation is placed one cell left of the widest number regardless of where it appears in print.

# Example:

$\begin{array}{r}\mathrm{1,034}\\ \underset{\_}{{+}7}\\ \mathrm{1,041}\end{array}$⠼⠆⠸⠲⠀⠀⠀⠂⠠⠴⠒⠲

⠀⠀⠀⠀⠀⠀⠬⠀⠀⠀⠀⠶

⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠐⠠⠴⠲⠂

A dollar sign is placed one cell left of the widest number and the sign of operation is placed one cell left of the dollar sign.

# Example:

$\begin{array}{r}\mathrm{\$}3.52\\ \underset{\_}{-\mathrm{\$}2.96}\\ \mathrm{\$}0.56\end{array}$⠼⠒⠸⠲⠀⠀⠀⠈⠎⠒⠨⠢⠆

⠀⠀⠀⠀⠀⠀⠤⠈⠎⠆⠨⠔⠖

⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠈⠎⠴⠨⠢⠖

Like symbols are lined up.

# Examples:

$\begin{array}{r}{5}^{{\mathrm{\prime}}}{6}^{{\mathrm{\u2033}}}\\ \underset{\_}{-{2}^{{\mathrm{\prime}}}{3}^{{\mathrm{\u2033}}}}\\ {3}^{{\mathrm{\prime}}}{3}^{{\mathrm{\u2033}}}\end{array}$⠼⠲⠸⠲⠀⠀⠀⠢⠄⠖⠄⠄

⠀⠀⠀⠀⠀⠀⠤⠆⠄⠒⠄⠄

⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠒⠄⠒⠄⠄

$\begin{array}{r}50{\mathrm{\xa2}}\\ \underset{\_}{+7{\mathrm{\xa2}}}\\ 57{\mathrm{\xa2}}\end{array}$⠼⠢⠸⠲⠀⠀⠀⠢⠴⠈⠉

⠀⠀⠀⠀⠀⠀⠬⠀⠶⠈⠉

⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠢⠶⠈⠉

# 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:

$\begin{array}{rrr}3& 5.51& \mathrm{1,999}\\ \underset{\_}{+4}& \underset{\_}{-1.43}& \underset{\_}{+202}\end{array}$⠠⠋⠔⠙⠀⠮⠀⠋⠕⠇⠇⠪⠬⠀⠁⠝⠎⠺⠻⠎⠲⠀⠸⠩

⠀⠀⠒⠀⠀⠀⠀⠢⠨⠢⠂⠀⠀⠀⠀⠂⠠⠔⠔⠔

⠀⠬⠲⠀⠀⠀⠤⠂⠨⠲⠒⠀⠀⠀⠬⠀⠀⠆⠴⠆

⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠒⠒⠒

⠸⠱

* Notice: There is one skipped cell between the separation lines of each problem.

# Brain Boost

## Regrouping Symbols

Spatial math formation often shows cancellations made in subtraction and carried numbers in addition. Nemeth uses specific braille symbols not found in print to represent and track changes. The opening cancellation symbol and closing cancellation symbol encloses the number or character to be cancelled. The new number or character is written directly above the cancelled number.

Opening Cancellation Indicator | ⠪ |

Closing Cancellation Indicator | ⠻ |

## Examples:

$\begin{array}{r}21113\\ \overline{){3}}\overline{){2}}\overline{){3}}\\ \underset{\_}{-\phantom{0}48}\\ 275\end{array}$⠀⠀⠀⠆⠀⠀⠂⠂⠀⠀⠂⠒

⠀⠀⠪⠒⠻⠪⠀⠆⠻⠪⠀⠒⠻

⠀⠒⠀⠀⠀⠀⠀⠲⠀⠀⠀⠦

⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠆⠀⠀⠀⠶⠀⠀⠀⠢

In the following example, notice how the original number is regrouped and then how the 100's place is regrouped again. The already regrouped number is cancelled and the new number written directly above it.

$\begin{array}{r}\phantom{0}910\phantom{0}\\ 1\overline{){10}}\phantom{0}\phantom{0}\\ \overline{){2}}\overline{){0}}\overline{){0}}9\\ \underset{\_}{-\phantom{0}999}\\ 1010\end{array}$⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠂⠴

⠀⠀⠀⠂⠀⠪⠂⠴⠻

⠀⠀⠪⠆⠻⠪⠀⠴⠻⠪⠀⠴⠻⠔

⠀⠤⠀⠀⠀⠀⠀⠒⠀⠀⠀⠔⠀⠔

⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠂⠀⠀⠀⠴⠀⠀⠀⠂⠀⠴

Addition is regrouped using carried numbers. The carried number is regrouped to the next place value column. The carried number is written directly above it. It is the same with carried numbers in Nemeth. A carried number indicator must be placed on the line above the original math problem. The carried numbers are written above the carried number indicator to separate them from the original problem. The carried number line should be the same length as the horizontal separation line.

Carried Number Indicator | ⠶⠶⠶⠶ |

# Examples:

$\begin{array}{r}\stackrel{12}{245}\\ \u206429\\ \underset{\_}{+57}\\ 331\end{array}$⠀⠀⠂⠆

⠶⠶⠶⠶⠶⠶

⠀⠀⠆⠲⠢

⠀⠀⠀⠆⠔

⠀⠬⠀⠢⠶

⠒⠒⠒⠒⠒⠒

⠀⠀⠒⠒⠂

$\begin{array}{r}\stackrel{\phantom{00}11}{\mathrm{2,394}}\\ \underset{\_}{+\mathrm{1,189}}\\ \mathrm{3,583}\end{array}$⠀⠀⠀⠀⠂⠂

⠶⠶⠶⠶⠶⠶⠶⠶

⠀⠀⠆⠠⠒⠔⠲

⠀⠬⠂⠠⠂⠦⠔

⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠒⠠⠢⠦⠒