Grouping Symbols
Objective : To simplify expressions with and without grouping symbols.
Parentheses have been used to show you how to group the numerals in an expression. Different groupings may produce different numbers.
A grouping symbol is a device, such as a pair of parentheses, used to enclose an expression that should be simplified first. Multiplication symbols are often left out of expressions with grouping symbols.
Example 1 Simplify : a. 6(5 - 3) b. 6(5) - 3
Solution
a. 6(5 - 3) stands for 6 x (5 - 3).
The parentheses tell you to simplify 5 - 3 first. Then multiply by 6.
6(5 - 3) = 6(2) = 12 Answer
b. 6(5) stands for 6 x 5.
6(5) - 3 = 30 - 3 = 27 Answer
In example 1, note that 6(5) stands for 6 x 5. Other ways to write this product using parentheses are (6)5 and (6)(5).
Example 2
Throughout your work in algebra, you will use these symbols :
Grouping Symbols
If an expression contains more than one grouping symbols, first simplify the expression in the innermost grouping symbol. Then work toward the outermost grouping symbol until the simplest expression is found.
Example 3
When there are no grouping symbols, simplify in the following order :
1. Do all multiplications and divisions in order from left to right.
2. Do all additions and substractions in order from left to right.
Example 4
Example 5
You may wish to use a calculator to evaluate some expressions.
By : Mr. Danielz
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