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# Lesson 6.4: Complex Fractions

## Review

A simple fraction is one whose numerator and denominator are both numerals consisting of only digits, decimal points, commas or separator spaces, and whose fraction line is drawn between two vertically or nearly vertically arranged numerals. When the numerator or denominator are not entirely numeric as defined above, general fraction indicators must be used. The opening general fraction indicator is formed with dots one two three five six and the closing general fraction indicator is formed with dots two three four five six. The general fraction line is two cells; dots four six in the first cell and dots three four in the second cell.

## Explanation

In mathematics, a complex fraction is defined as one that contains a fraction in the numerator, in the denominator, or in both. The entire fraction is enclosed in general fraction indicators and the general fraction line is used between the numerator and denominator of the overall complex fraction since the numerator and/or denominator are not entirely numeric as defined above. The fraction in the numerator and/or denominator is written accordingly. The general fraction indicators must be in grade 1 mode.

### Example 1

$\frac{\frac{1}{2}}{3}$
⠰⠷⠼⠁⠌⠃⠨⠌⠼⠉⠾

### Example 2

$\frac{\frac{x}{y}}{z}$
⠰⠰⠷⠷⠭⠨⠌⠽⠾⠨⠌⠵⠾

### Example 3

$\frac{\frac{a}{b}}{\frac{a}{c}}$
⠰⠰⠷⠷⠁⠨⠌⠃⠾⠨⠌⠷⠁⠨⠌⠉⠾⠾

### Example 4

$\frac{\frac{1}{2}+\frac{2}{3}}{3}$
⠰⠷⠼⠁⠌⠃⠐⠖⠼⠃⠌⠉⠨⠌⠼⠉⠾

### Example 5

$\frac{\frac{a+2}{a+3}}{a+3}$
⠰⠰⠷⠷⠁⠐⠖⠼⠃⠨⠌⠁⠐⠖⠼⠉⠾⠨⠌⠁⠐⠖⠼⠉⠾

### Example 6

$\frac{1\frac{1}{2}}{3\frac{1}{4}}$
⠰⠷⠼⠁⠼⠁⠌⠃⠨⠌⠼⠉⠼⠁⠌⠙⠾

In Example 7, the letter b immediately follows the digit 7 in the denominator. The letter must be placed in grade 1 mode to avoid confusion with the digit 2.

### Example 7

$\frac{\frac{a}{b}}{7b}$
⠰⠰⠷⠷⠁⠨⠌⠃⠾⠨⠌⠼⠛⠰⠃⠾