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# 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.

• opening complex fraction indicator, dots six, one four five six
• closing complex fraction indicator, dots six, three four five six
• complex horizontal fraction line, dots six, three four
• diagonal complex fraction line, dots six, four five six, three four
• 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

$\genfrac{}{}{3px}{}{\frac{a}{b}}{\frac{c}{d}}$
⠠⠹⠹⠁⠌⠃⠼⠠⠌⠹⠉⠌⠙⠼⠠⠼

### Example 2

$\genfrac{}{}{3px}{}{\frac{a}{b}}{c}$
⠠⠹⠹⠁⠌⠃⠼⠠⠌⠉⠠⠼

### Example 3

$\genfrac{}{}{3px}{}{\frac{1}{2}+\frac{2}{3}}{6}$
⠠⠹⠹⠂⠌⠆⠼⠬⠹⠆⠌⠒⠼⠠⠌⠖⠠⠼

### Example 4

$\genfrac{}{}{3px}{}{\frac{x+2}{x+3}}{x+3}$
⠠⠹⠹⠭⠬⠆⠌⠭⠬⠒⠼⠠⠌⠭⠬⠒⠠⠼

### Example 5

$\genfrac{}{}{3px}{}{2\frac{1}{2}}{3\frac{1}{4}}$
⠠⠹⠆⠸⠹⠂⠌⠆⠸⠼⠠⠌⠒⠸⠹⠂⠌⠲⠸⠼⠠⠼