What are the different kinds of symbols of inclusion?

Symbols of inclusion group terms together. You’re most familiar with parentheses as a symbol of inclusion, but there are others.

Symbols of Inclusion:

Parentheses ( )

Brackets [ ]

Braces { }

Absolute Value | |

Division ???\frac{a}{b+c}???

The division sign grouped ???b+c??? and that operation must now be performed first.

Remember to follow the order of operations PEMDAS to simplify expressions:

Parentheses (all symbols of inclusion)

Exponents (powers and roots)

Multiplication/Division (from left to right or divide first)

Addition/Subtraction (from left to right or subtract first)

How to simplify expressions including parentheses, brackets, braces, and other symbols of inclusion

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Let’s do a couple more examples of how to simplify expressions with different, nested symbols of inclusion

Example

Simplify the expression.

???[15-(2+4)]\cdot5-3???

Start by simplifying the innermost parentheses.

???[15-(6)]\cdot5-3???

???[15-6]\cdot5-3???

Now finish simplifying symbols of inclusion (the brackets).

???[9]\cdot5-3???

???9\cdot5-3???

There are no exponents so move on to multiplication/division.

???45-3???

Last, simplify addition/subtraction.

???42???

Let’s try another example using symbols of inclusion.

Example

Simplify the expression.

???3[(4-1)+7]-(8+2)???

Start by simplifying the innermost parentheses.

???3[(3)+7]-(8+2)???

???3[3+7]-(8+2)???

Now finish simplifying symbols of inclusion.

???3[10]-(10)???

There are no exponents so move on to multiplication/division.

???30-10???

Last, simplify addition/subtraction.

???20???

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