How to simplify symbols of inclusion (grouping symbols) like parentheses, brackets, etc.
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.
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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.
symbols of inclusion are symbols like Parentheses,
Brackets,
Braces,
Absolute Value, and
Division.
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???
