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Use order of operations in algebraic expressions

Order of operations establishes a consistent interpretation of algebraic expressions: evaluate grouping symbols, whole-number exponents, multiplication and division from left to right, and addition and subtraction from left to right. The learner substitutes given values for variables and evaluates expressions accurately, understanding that changing the order can change the value and that equivalent expressions must produce the same result. This scope excludes negative or rational exponents and more advanced algebraic transformations.

Detailed Explanation: Use order of operations in algebraic expressions

To evaluate an algebraic expression:

  1. Substitute the given values for the variables.
  2. Evaluate expressions inside grouping symbols, such as parentheses.
  3. Evaluate whole-number exponents.
  4. Multiply and divide from left to right.
  5. Add and subtract from left to right.

Example: Evaluate

5+2a(b+1)2÷4−35+2a(b+1)^2\div 4-3

when a=3a=3 and b=1b=1.

Step 1: Substitute the values.

5+2(3)(1+1)2÷4−35+2(3)(1+1)^2\div 4-3

Step 2: Evaluate inside the parentheses.

5+2(3)(2)2÷4−35+2(3)(2)^2\div 4-3

Step 3: Evaluate the exponent.

5+2(3)(4)÷4−35+2(3)(4)\div 4-3

Step 4: Multiply and divide from left to right.

5+6(4)÷4−35+6(4)\div 4-3 5+24÷4−35+24\div 4-3 5+6−35+6-3

Step 5: Add and subtract from left to right.

11−3=811-3=8

Therefore, the value of the expression is

8\boxed{8}

Following the order of operations is important because changing the order can change the answer.

Learn by doing: Use order of operations in algebraic expressions

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    Algebraic Function Variable Substitution - Fractional Terms (Negatives)

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