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Apply the order of operations with integers

Order of operations with integers means interpreting a numerical expression through grouping symbols, whole-number exponents, multiplication and division from left to right, and addition and subtraction from left to right. This understanding includes distinguishing a negative number from subtraction, applying integer sign rules correctly, and recognizing how parentheses alter an expression’s structure, providing a foundation for evaluating algebraic expressions without extending to variables, rational exponents, or advanced symbolic conventions.

Detailed Explanation: Apply the order of operations with integers

To evaluate an expression with integers, use this order:

  1. Grouping symbols such as parentheses
  2. Whole-number exponents
  3. Multiplication and division from left to right
  4. Addition and subtraction from left to right

Remember that a negative sign can be part of a number, as in −3-3, or it can show subtraction, as in 5−35-3.

Evaluate:

−3+2(4−6)2÷4−1-3+2(4-6)^2\div 4-1

Step 1: Evaluate the parentheses.

4−6=−24-6=-2

Now the expression is

−3+2(−2)2÷4−1-3+2(-2)^2\div 4-1

Step 2: Evaluate the exponent.

The exponent applies to −2-2 inside the parentheses:

(−2)2=4(-2)^2=4

So the expression becomes

−3+2(4)÷4−1-3+2(4)\div 4-1

Step 3: Multiply and divide from left to right.

First multiply:

2(4)=82(4)=8

Then divide:

8÷4=28\div 4=2

Now we have

−3+2−1-3+2-1

Step 4: Add and subtract from left to right.

−3+2=−1-3+2=-1

Then

−1−1=−2-1-1=-2

Therefore,

−2\boxed{-2}

Learn by doing: Apply the order of operations with integers

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    Order of Operations - Add, Subtract, Mutiply, Divide, and Parentheses with Exponents

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