# Lesson 7.1: Ratios and Proportions

## Symbols

$:\phantom{\rule{.3em}{0ex}}\text{ratio}$

⠒

$::\phantom{\rule{.3em}{0ex}}\text{proportion}$

⠒⠒

$/\phantom{\rule{.3em}{0ex}}\text{forward slash}$

⠸⠌

## Explanation

A ratio relates two quantities through the operation of division. Ratios are often indicated by the use of the fraction line or the colon in print. In print, the colon symbol is used between the two quantities and it is read, "is to." The colon is formed with dots two five. Although the ratio sign is used to compare two numbers, it is best treated as an operation sign for purposes of spacing.

When two digits are written on the same line of print with a diagonal slash between them to represent a ratio, as in 20/20 (twenty forward slash twenty), the forward slash or solidus is used in braille. The forward slash is two cells, dots four five six, dots three four.

When two ratios are equivalent, a proportion is established. The symbol for proportion, dots two five, two five, is used to show the relationships on each side of the equality and it is read, "as."

### Example 1

$1:2$

⠼⠁⠒⠼⠃

When the ratio occurs between two letters, the grade 1 indicator must be used with the colon otherwise the colon could read as the "cc" contraction.

### Example 2

$x:y$

⠭⠰⠒⠽

### Example 3

$a+3:b-6$

⠁⠐⠖⠼⠉⠒⠃⠐⠤⠼⠋

### Example 4

$2:x=3:9$

⠼⠃⠒⠭⠀⠐⠶⠀⠼⠉⠒⠼⠊

### Example 5

$7x+2y:3y$

⠼⠛⠭⠐⠖⠼⠃⠽⠒⠼⠉⠽

### Example 6

$3:4::60:80$

⠼⠉⠒⠼⠙⠀⠒⠒⠀⠼⠋⠚⠒⠼⠓⠚

### Example 7

$x:30::4:6$

⠭⠰⠒⠼⠉⠚⠀⠒⠒⠀⠼⠙⠒⠼⠋

### Example 8

$2/3\phantom{\rule{.3em}{0ex}}\text{of the class}$

⠼⠃⠸⠌⠼⠉⠀⠷⠀⠮⠀⠉⠇⠁⠎⠎