# Lesson 3.2 Spatial Arrangments

## Symbols

begin horizontal line mode

⠐⠒

spaced vertical line segment

⠸

numeric passage indicator

⠼⠼

numeric passage terminator

⠼⠄

spaced numeric indicator

⠼

## Explanation

Mathematical problems in print can be written with the numerals arranged on one print line or with numerals arranged spatially on two or more print lines. In a spatial arrangement, numerals are aligned beneath each other in columns according to place value. In spatial addition, subtraction and multiplication, the answer is written at the bottom of the problem, below the horizontal line. In standard long division, the problem is worked below the dividend with the answer or quotient written on the line above the dividend.

Follow print for the layout of a spatial arrangement. Numerals should be aligned beneath each other in columns for place value as shown in print. Columns that require vertical computation of digits (addition or subtraction) should only contain numerals. The spaced numeric indicator is formed with dots three four five six followed by a space and then the digit. This can be used to facilitate spacing of digits by place value.

The horizontal line is formed with a dot five prefix followed by dots two five in sequence. The numeric indicator is used with each numeral in the arrangement unless numeric passage is enabled. UEB permits flexibility in placement of the sign of operation. Examples in this lesson follow standard print placement for the sign of operation.

Examples 1 to 4 use numeric indicators.

### Example 1

44+51=95 (Vertically Aligned)

⠀⠀⠼⠙⠙

⠐⠖⠼⠑⠁

⠀⠀⠐⠒⠒

⠀⠀⠼⠊⠑

The spaced numeric indicator is used in Example 2 where there is no digit in the hundreds column of the subtrahend.

### Example 2

597-12=585 (Vertically Aligned)

⠀⠀⠼⠑⠊⠛

⠐⠤⠼⠀⠁⠃

⠀⠀⠐⠒⠒⠒

⠀⠀⠼⠑⠓⠑

The spaced vertical line segment, dots four five six, is used to represent the curved or straight division symbol. The numeric indicator is used unless numeric passage is enabled. The horizontal line is positioned on the line above the dividend, beginning in the same column as the spaced vertical line segment.

### Example 3

12÷3=4 (Vertically Aligned)

⠀⠀⠀⠀⠀⠀⠼⠉

⠀⠀⠀⠐⠒⠒⠒⠒

⠼⠙⠀⠸⠀⠼⠁⠃

⠀⠀⠀⠀⠀⠼⠁⠃

⠀⠀⠀⠀⠀⠐⠒⠒

When there is a remainder in a long division problem, it is written on the line with the quotient and preceded by the letter *r*. One blank cell is left after the quotient and before the letter *r*. In UEB, the remainder is written by brailling the letter *r* as it appears in print (upper or lower case) followed by the numeric indicator and the numeral.

### Example 4

17÷3=3 r2 (Vertically Aligned)

⠀⠀⠀⠀⠀⠀⠼⠑⠀⠗⠼⠃

⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒

⠼⠉⠀⠸⠀⠼⠁⠛

⠀⠀⠀⠀⠀⠼⠁⠑

⠀⠀⠀⠀⠀⠐⠒⠒

⠀⠀⠀⠀⠀⠀⠼⠃

## Numeric Passage

The numeric passage indicator sets numeric mode until the numeric passage terminator is reached. Grade 1 mode is also set. The numeric passage indicator is formed with two cells; dots three four five six in the first cell and dots three four five six in the second cell. The numeric passage terminator is formed with two cells; dots three four five six in the first cell and dot three in the second cell.

Numeric indicators are not used with the mathematical expressions in a numeric passage. If problem identifiers are present (problem numbers) the numeric indicator is used with the problem numbering. The numeric passage indicator may be placed on a line by itself above the passage and the terminator on the line below the end of the passage. Numeric passage is often used for spatial arrangements. Problems may be indented within the numeric passageo no digits appear in the same column as numeric indicators. In this lesson the digit in the leftmost position of the problem is indented two cells for consistency.

### Example 5

389-62=327 (Vertically Aligned)

⠼⠼

⠀⠀⠀⠀⠉⠓⠊

⠀⠀⠐⠤⠀⠋⠃

⠀⠀⠀⠀⠐⠒⠒

⠀⠀⠀⠀⠉⠃⠛

⠼⠄

### Example 6

132×15=660+1320=1980 (Vertically Aligned)

⠼⠼

⠀⠀⠀⠀⠁⠉⠃

⠀⠀⠐⠦⠀⠁⠑

⠀⠀⠀⠐⠒⠒⠒

⠀⠀⠀⠀⠋⠋⠚

⠀⠀⠀⠁⠉⠃

⠀⠀⠀⠐⠒⠒⠒

⠀⠀⠀⠁⠊⠓⠚

⠼⠄

### Example 7

124÷4=31 (Vertically Aligned)

⠼⠼

⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠐⠒⠒⠒⠒

⠀⠀⠙⠀⠸⠀⠁⠃⠙

⠀⠀⠀⠀⠀⠀⠁⠃

⠀⠀⠀⠀⠀⠀⠐⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠐⠒⠒

⠼⠄

### Example 8

257÷4=64 r1 (Vertically Aligned)

⠼⠼

⠀⠀⠀⠀⠀⠀⠀⠋⠙⠀⠗⠼⠁

⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠙⠀⠸⠀⠃⠑⠛

⠀⠀⠀⠀⠀⠀⠃⠙

⠀⠀⠀⠀⠀⠀⠐⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠁⠛

⠀⠀⠀⠀⠀⠀⠀⠁⠋

⠀⠀⠀⠀⠀⠀⠀⠐⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠼⠄