In the last lesson we learned the rules for Order of Operations. We use the sentence: Please Excuse My Dear Aunt Sally to help us remember these rules: Until now we have worked with whole numbers only. Let's look at a few examples involving integers. Example 1: Evaluate this arithmetic expression: (-3)2 + -8 ÷ -2 Solution: In Example 1, the parentheses are used to indicate multiplication. They make it clear that negative 3 is being multiplied by itself, or squared. The parentheses distinguish this problem from -1 times 3 squared. (-3)2 = (-3)(-3) = +9 Negative three squared equals positive 9 -32 = -1(3)(3) = -1(+9) = -9 Negative
one times three squared equals negative 9 Thus, when working with integers, it is a good idea to use parentheses to indicate multiplication. Let's look at some more examples. Example 2: Evaluate this arithmetic expression: (-8)(-5) ÷ 23 Solution:
In the next example, we will use both brackets [ ] and parentheses ( ). We will evaluate the expression from the innermost set of parentheses to the outermost set of brackets. Note that we are using the symbol · for multiplication instead of an "x" in the solution. Example 3: Evaluate this arithmetic expression: 16 - [3(6 - 3) - 12] Solution:
In the next example, the fraction bar is used to indicate division. We must first evaluate each expression above and below the fraction bar. Then we can divide the numerator by the denominator. Example 4: Evaluate this arithmetic expression: Solution: Summary: The rules for the order of operations are:
Tips: When evaluating arithmetic expressions with integers, we suggest that you:
ExercisesDirections: Complete each exercise by applying the rules for order of operations. Click once in an ANSWER BOX and type in your answer; then click ENTER. After you click ENTER, a message will appear in the RESULTS BOX to indicate whether your answer is correct or incorrect. To start over, click CLEAR.
Sign Up For Our FREE Newsletter!Sign Up For Our FREE Newsletter!How do you solve order of operations with integers?Summary: The rules for the order of operations are:. Simplify all operations inside Parentheses (and Brackets).. Simplify all Exponents, working from left to right.. Perform all Multiplications and Divisions, working from left to right. ... . Perform all Additions and Subtractions, working from left to right.. What are integer rules?Multiplication and Division of Integers. RULE 1: The product of a positive integer and a negative integer is negative. RULE 2: The product of two positive integers is positive. RULE 3: The product of two negative integers is positive.
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