Simplifying and Evaluating Expressions With Integers That Use all Four Operations
Now we’ll simplify expressions that use all four operations–addition, subtraction, multiplication, and division–with integers. Remember to follow the order of operations.
Order of operations is a set of rules in mathematics that dictates the sequence in which operations should be performed to correctly solve an expression. It is commonly remembered by the acronym PEMDAS which stands for Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
For instance, in the expression [latex]8 + (4 * 2)^2 ÷ 4 - 2[/latex] using the order of operations we must:
Parentheses/Brackets: Perform the operation inside the parentheses first.
This gives us: [latex]8 + (8)^2 ÷ 4 - 2[/latex]
Exponents/Orders: Next, solve for the exponent.
This gives us: [latex]8 + 64 ÷ 4 - 2[/latex]
Multiplication and Division: Perform multiplication and division operations from left to right.
This gives us: [latex]8 + 16 - 2[/latex]
Addition and Subtraction: Finally, carry out addition and subtraction from left to right.
This gives us: [latex]24 - 2 = 22[/latex]
So, the result of the expression [latex]8 + (4 * 2)^2 ÷ 4 - 2[/latex] following the order of operations is [latex]22[/latex].