# Unit 16 Spatial Arrangement: Multiplication

When multiplication problems or expressions appear vertically in print, Nemeth Code formatting for spatial representation is used.

Separation Line for Spatial Math | ⠒⠒⠒⠒ |

Like spatial arrangements for addition and subtraction, the equals sign is replaced by a separation line that extends one cell on either side of the expression, and the numeric indicator is generally not used. Unlike spatial arrangements for addition and subtraction, the multiplication symbol is placed directly in front of the multiplier rather than left of the widest number because multiplication problems are not lined up by place value.

# Example:

$\begin{array}{r}206\\ \underset{\_}{{\times}7}\\ 1442\end{array}$⠼⠂⠸⠲⠀⠀⠀⠆⠴⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠶

⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠂⠲⠲⠆

The multiplication problem should be lined up according to the print copy with commas, decimals, dollar signs and other symbols following print spacing.

# Example:

$\begin{array}{r}{\mathrm{\$}}5{\mathrm{.}}00\\ \underset{\_}{\times 4{\mathrm{.}}5}\\ {\mathrm{\$}}22.50\end{array}$⠼⠆⠸⠲⠀⠀⠀⠀⠈⠎⠢⠨⠴⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠲⠨⠢

⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠈⠎⠆⠆⠨⠢⠴

# Multiplier of More Than One Digit

When there is more than one digit in the multiplier, each digit of the multiplier performs the multiplication process and the partial product is written below the separation line. Then, just as in print, the partial products are added together to create the final product. The partial products are lined up by place value and a second separation line is placed between the partial product and the final product.

# Example:

$\begin{array}{r}213\\ \underset{\_}{\times 23}\\ 639\\ \underset{\_}{\u2064426\phantom{0}}\\ 4899\end{array}$⠼⠒⠸⠲⠀⠀⠀⠆⠂⠒

⠀⠀⠀⠀⠀⠀⠈⠡⠆⠒

⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠖⠒⠔

⠀⠀⠀⠀⠀⠀⠲⠆⠖

⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠲⠦⠔⠔

# Carried Numbers

When a multiplication problem is regrouped using carried numbers, a carried number line must be placed on the line above the original math problem. The carried numbers are written above the carried number line to separate them from the original problem. The carried number line should be the same length as the horizontal separation line.

Carried Number Indicator | ⠶⠶⠶⠶ |

_{Example: }

$\begin{array}{r}\stackrel{2}{6}\stackrel{3}{5}9\\ \underset{\_}{\times \phantom{00}4}\\ 2636\end{array}$
⠀⠀⠆⠒

⠶⠶⠶⠶⠶⠶

⠀⠀⠖⠢⠔

⠀⠀⠈⠡⠲

⠒⠒⠒⠒⠒⠒

⠀⠆⠖⠒⠖

# 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:

$\begin{array}{rrrrr}3& 5& 12& 7& 10\\ \underset{\_}{\times 4}& \underset{\_}{\times 1}& \underset{\_}{\times 2}& \underset{\_}{\times 7}& \underset{\_}{\times 9}\\ \phantom{0}\\ 6& 8& 15& 2& 11\\ \underset{\_}{\times 4}& \underset{\_}{\times 8}& \underset{\_}{\times 2}& \underset{\_}{\times 9}& \underset{\_}{\times 5}\end{array}$⠠⠋⠔⠙⠀⠮⠀⠏⠗⠕⠙⠥⠉⠞⠲⠀⠸⠩

⠀⠀⠀⠒⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠂⠆⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠂⠴

⠀⠈⠡⠲⠀⠀⠀⠈⠡⠂⠀⠀⠀⠈⠡⠆⠀⠀⠀⠈⠡⠶⠀⠀⠀⠈⠡⠔

⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒

⠀⠀⠀⠖⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠂⠢⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠂⠂

⠀⠈⠡⠲⠀⠀⠀⠈⠡⠦⠀⠀⠀⠈⠡⠰⠀⠀⠀⠈⠡⠔⠀⠀⠀⠈⠡⠢

⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒⠀⠒⠒⠒⠒⠒

⠸⠱