Teaching Notes 1.2: Simplifying Expressions That Have
Grouping Symbols
If an expression contains grouping symbols, the order of operations requires that whatever part of
the expression is contained in the grouping symbols be simplified first. A common mistake of
students is to ignore the grouping symbols when simplifying.- Explain that grouping symbols are sometimes used to enclose an expression. There are
several types of grouping symbols, including parentheses, brackets, and the fraction bar.
Parentheses are the most common. - Explain the meaning of grouping symbols. For example, 3×(4+2) means 3 groups of 6
which equals 18. Emphasize that this is quite different from 3× 4 +2, which means 3 groups
of 4 plus 2 more and is equal to 14. Have your students solve each problem. Discuss why each
provides a different answer. - Explain that all operations within parentheses should be done first, following the order of
operations. - Review the steps for the order of operations and the examples on the worksheet with your
students.
EXTRA HELP:
The multiplication sign is often omitted before a grouping symbol. Example: 3(5+4)isthesameas
3 ×(5+4).ANSWER KEY:
(1) 36 (2) 2 (3) 52 (4) 3 (5) 104 (6) 4 (7) 0 (8) 22
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(Challenge)Yes. The parentheses are not necessary. Each expression equals 3.
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