# Unit 3 Grouping Symbols in Nemeth Code

Grouping symbols are a way to organize math problems that contain groups. They show where one grouping of characters begins and ends. In Nemeth Code, the numeric indicator is not used after an opening grouping symbol. Just as with the dollar sign, no indicator is needed because the numeral does not occur right after an empty space. No space is left between the grouping symbol and the expression that it encloses.

Grouping Sign | Opening | Closing |

Opening/closing parenthesis ( ) | ⠷ | ⠾ |

Opening/closing brackets [ ] | ⠈⠷ | ⠈⠾ |

Opening/closing braces { } | ⠨⠷ | ⠨⠾ |

# Parenthesis, Brackets and Braces

Parentheses, brackets, and braces are examples of grouping symbols. They serve the following purposes:

*Numbering*

(1)

⠷⠂⠾

1)

⠼⠂⠾

* Notice that a numeric indicator is required if there is no opening parenthesis.

*Separating for clarity*

5-(-4)

⠼⠢⠤⠷⠤⠲⠾

(+) or (-)

⠷⠬⠾⠀⠕⠗⠀⠷⠤⠾

*Indicate multiplication*

2(3)

⠼⠆⠷⠒⠾

*Group numbers together*

(3+4)(5-2)

⠷⠒⠬⠲⠾⠷⠢⠤⠆⠾

5(2+5) = 35

⠼⠢⠷⠆⠬⠢⠾⠀⠨⠅⠀⠼⠒⠢

*Ordered pairs*

(3, 4)

⠷⠒⠠⠀⠲⠾

[0, 1]

⠈⠷⠴⠠⠀⠂⠈⠾

*Grouping sets*

{1, 3, 5, 7, 9}

⠨⠷⠂⠠⠀⠒⠠⠀⠢⠠⠀⠶⠠⠀⠔⠨⠾

[Sun., Mon., Tues., …]

⠈⠷⠠⠎⠥⠝⠲⠠⠀⠠⠍⠕⠝⠲⠠⠀⠠⠞⠥⠑⠎⠲⠠⠀⠄⠄⠄⠈⠾

Although a sign of comparison usually requires a space before and after the symbol, a space is NOT required between a sign of comparison and a grouping sign, indicator, or punctuation symbol.

# Example:

(< or >)

⠷⠐⠅⠀⠕⠗⠀⠨⠂⠾

Is three times(x) four equal(=) to 12?

⠠⠊⠎⠀⠞⠓⠗⠑⠑⠀⠞⠊⠍⠑⠎⠷⠈⠡⠾⠀⠋⠕⠥⠗⠀⠑⠟⠥⠁⠇⠷⠨⠅⠾⠀⠞⠕⠀⠼⠂⠆⠸⠦

# Brain Boost

# Nesting

Parentheses, brackets and braces all have the same effect. When there is more than one grouping in a problem, different grouping symbols are used for each group. Multiple grouping symbols can be nested together in one expression. The order of nesting is parentheses first, then brackets, and then braces. {[( )]}.

# Example:

Parentheses first.

2 + (6-4)

⠼⠆⠬⠷⠖⠤⠲⠾

If there are two levels of groupings in a math problem, use brackets next.

12 ÷ [2 + (6-4)]

⠼⠂⠆⠨⠌⠈⠷⠀⠆⠬⠷⠖⠤⠲⠾⠈⠾

If there are three levels of grouping, use braces next.

25 + {12 ÷ [2 + (6-4)]}

⠼⠆⠢⠬⠨⠷⠂⠆⠨⠌⠈⠷⠆⠬⠷⠖⠤⠲⠾⠈⠾⠨⠾

All math problems are solved from the innermost grouping symbols to the outermost grouping symbols.

## Example:

First solve the parentheses, next solve the brackets, and last, solve the braces.

10 + {15 ÷ [3 + (6-4)]}

10 + {15 ÷ [3 + 2]}

10 + {15 ÷5}

10 + 3

13

⠼⠂⠴⠬⠨⠷⠂⠢⠨⠌⠈⠷⠒⠬⠷⠖⠤⠲⠾⠈⠾⠨⠾

⠼⠂⠴⠬⠨⠷⠂⠢⠨⠌⠈⠷⠒⠬⠆⠈⠾⠨⠾

⠼⠂⠴⠬⠨⠷⠂⠢⠨⠌⠢⠨⠾

⠼⠂⠴⠬⠒

⠼⠂⠒