To evaluate a numerical expression means to find its value by performing the operations in the correct order. An expression can include addition, subtraction, multiplication, division, and grouping symbols such as parentheses, brackets, or braces.
Always follow the Order of Operations: Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right). You can remember this order with the phrase “Please Excuse My Dear Aunt Sally.”
Parentheses show which operations should be done first in an expression. Anything inside parentheses must be solved before operations outside of them.
If an expression has parentheses, complete all operations inside them first. This helps keep the expression clear and accurate.
Brackets are used when an expression already has parentheses. They help group parts of the expression and show which operations to do next after the parentheses.
Work from the inside out: first solve parentheses, then brackets, and finally any operations outside the brackets.
Braces are used for grouping larger or more complex expressions. They often contain brackets and parentheses inside them to organize many steps clearly.
When an expression has braces, brackets, and parentheses, always start with the innermost grouping and move outward step by step.
After evaluating an expression, check each step to make sure you followed the correct order of operations and performed every operation accurately.
If you get a different answer when checking, look back at the grouping symbols and make sure you followed the order correctly. Careful steps lead to accurate results.