# Lesson 9.2: Ratios and Proportions

## Ratios

Ratios are often indicated by the use of the fraction line or the ratio sign. A ratio relates two quantities through the operation of division; it is read, "is to." The braille symbol for ratio is dot five dot two. In print, the symbol that is used has the same appearance as a print colon, that is, two dots, one above the other. In braille, however, the literary colon should not be used, as its configuration is the same as the Nemeth numeral three. The sign for ratios is a mathematical sign of comparison and is not a colon. It should not be used as a mark of punctuation, nor should a mark of punctuation be used for ratio. The print representation of this symbol may show no spaces between it and the numerals or expressions associated with it. In braille, however, a space must be placed before and after the symbol because it is a sign of comparison.

## Proportions

When two ratios are equivalent, a proportion is established. If a ratio is used to show the relationships on each side of the equality, then the symbol for proportion that is used is dots five six dots two three, rather than the equals sign. The symbol is read as, "as."

### Example 1

two is to seven

⠼⠆⠀⠐⠂⠀⠼⠶

### Example 2

one is to five

⠼⠂⠀⠐⠂⠀⠼⠢

### Example 3

seven x plus two y is to three y

⠼⠶⠭⠬⠆⠽⠀⠐⠂⠀⠼⠒⠽

### Example 4

three is to four as seventy five is to one hundred

⠼⠒⠀⠐⠂⠀⠼⠲⠀⠰⠆⠀⠼⠶⠢⠀⠐⠂⠀⠼⠂⠴⠴

### Example 5

x is to twenty five as four is to five

⠭⠀⠐⠂⠀⠼⠆⠢⠀⠰⠆⠀⠼⠲⠀⠐⠂⠀⠼⠢