Overview
This lecture covers the order of operations used to evaluate mathematical expressions, introduces the PEMDAS rule, and provides practice with simplifying expressions using correct order.
The Need for Order of Operations
- Evaluating an expression means simplifying it to find its value.
- There must be one correct answer, so a standard order of operations is required.
- Incorrect order can lead to different answers for the same expression.
Order of Operations: PEMDAS Rule
- P: Perform calculations inside Parentheses (or other grouping symbols) first.
- E: Evaluate Exponents
- MD: Perform Multiplication and Division from left to right.
- AS: Perform Addition and Subtraction from left to right.
- Operations inside grouping symbols also follow PEMDAS.
Examples & Practice Problems
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Multiplication can be notated as a dot (·), parentheses, or omitted between numbers
ex: 3× 4 or 3(4)
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Exponents indicate repeated multiplication
ex: 4² = 4 × 4 = 16
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parentheses within parentheses or brackets are solved from the inside out
ex: 50 - {[5 × (7 + 1)] + 3²}
50 - {\[5 x 8\] + 3²}
50 - {40 + 3²}
50 - {40 + 9}
50 - 49
**= 1**
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A fraction bar acts as a grouping symbol; calculate numerator and denominator separately before dividing.
Translating Words to Expressions
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To convert Celsius to Fahrenheit: 2C + 30 = F
(e.g., 9°C → 2×9+30 = 48°F).
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To convert Fahrenheit to Celsius: Subtract 30 from Fahrenheit, then divide by 2 (e.g., 72°F → (72-30)/2 = 21°C).
Key Terms & Definitions
- Order of Operations — The agreed sequence for evaluating expressions to ensure one correct answer.
- PEMDAS — Acronym for Parentheses, Exponents, Multiplication/Division, Addition/Subtraction order.
- Exponent — Indicates repeated multiplication of a base number.
- Grouping Symbols — Parentheses, brackets, or fraction bars that dictate order of calculation.