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Apply the order of operations with integers

Order of operations with integers means interpreting a numerical expression according to the structure established by grouping symbols, exponents with nonnegative integer powers, multiplication and division from left to right, and addition and subtraction from left to right. This includes recognizing that a negative sign and an exponent may have different scope, rather than treating all operations as equivalent, and supports accurate evaluation of algebraic expressions; variables, arbitrary rational or real exponents, and advanced symbolic manipulation are outside this scope.

Detailed Explanation: Apply the order of operations with integers

Follow the order of operations:

  1. Simplify inside grouping symbols, such as parentheses.
  2. Evaluate exponents.
  3. Multiply and divide from left to right.
  4. Add and subtract from left to right.

Work through this example:

−22+3(5−8)÷3-2^2+3(5-8)\div 3

Step 1: Simplify the parentheses.

5−8=−35-8=-3

Now the expression is

−22+3(−3)÷3-2^2+3(-3)\div 3

Step 2: Evaluate the exponent.

The exponent applies to 22, not to the negative sign:

−22=−(22)=−4-2^2=-(2^2)=-4

So the expression becomes

−4+3(−3)÷3-4+3(-3)\div 3

Step 3: Multiply and divide from left to right.

First multiply:

3(−3)=−93(-3)=-9

Then divide:

−9÷3=−3-9\div 3=-3

Now the expression is

−4+(−3)-4+(-3)

Step 4: Add.

−4+(−3)=−7-4+(-3)=-7

Therefore,

−7\boxed{-7}

Be careful: −22=−4-2^2=-4, but (−2)2=4(-2)^2=4 because the parentheses make the negative number part of the base.

Learn by doing: Apply the order of operations with integers

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    Order of Operations - Add, Subtract, with Exponents

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