# Lesson 7.1: Complex Fractions

## Explanation

A complex fraction is one in which another simple fraction appears either in the numerator, in the denominator, or in both. The numerator and/or denominator can also be mixed numbers. The complex fraction indicators and complex fraction line are modifications of the simple fraction indicators and simple fraction line. Dot six is placed before the opening and closing simple fraction indicators and simple fraction line, to indicate that these are complex fraction indicators. In horizontal arrangements, a dot six is placed before the fraction line that separates the numerator of the complex fraction from the denominator of the complex fraction.

Following are guidelines for brailling a complex fraction.

The complex fraction indicators are placed at the beginning and end of the expression.

The complex fraction line, horizontal or diagonal, separates the numerator of the complex fraction from the denominator of the complex fraction. Simple fraction lines are used for simple fraction portions of the expression.

For every opening fraction indicator, simple or complex, there must be a corresponding closing fraction indicator.

### Example 1

a complex fraction with numerator of simple fraction a over b and denominator of the simple fraction c over d

⠠⠹⠹⠁⠌⠃⠼⠠⠌⠹⠉⠌⠙⠼⠠⠼

### Example 2

a complex fraction with numerator of simple fraction a over b and denominator c

⠠⠹⠹⠁⠌⠃⠼⠠⠌⠉⠠⠼

### Example 3

a complex fraction with numerator one half plus two thirds and denominator six

⠠⠹⠹⠂⠌⠆⠼⠬⠹⠆⠌⠒⠼⠠⠌⠖⠠⠼

### Example 4

a complex fraction with algebraic expressions with numerator simple fraction x plus two over x plus three and denominator x plus three

⠠⠹⠹⠭⠬⠆⠌⠭⠬⠒⠼⠠⠌⠭⠬⠒⠠⠼

### Example 5

a complex fraction with numerator of mixed number two and one half and denominator mixed number three and one fourth

⠠⠹⠆⠸⠹⠂⠌⠆⠸⠼⠠⠌⠒⠸⠹⠂⠌⠲⠸⠼⠠⠼