Order of Operations for 5th Grade: PEMDAS Made Easy
The order of operations is the agreed-upon sequence for evaluating mathematical expressions. Without it, an expression like \(3 + 4 \times 5\) could be interpreted as \((3+4) \times 5 = 35\) or \(3 + (4 \times 5) = 23\)—and we would get different answers. In Grade 5, students use PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) to ensure everyone evaluates expressions the same way. This skill is essential for algebra, calculator use, and solving multi-step problems.
PEMDAS tells us: first do operations inside parentheses (or other grouping symbols like brackets); then evaluate exponents; then do multiplication and division from left to right; finally do addition and subtraction from left to right. Multiplication and division have equal priority, as do addition and subtraction—we perform them left to right rather than always doing all multiplications before any divisions.
DETAILED EXPLANATION
Order of operations (PEMDAS):
1. P – Parentheses (and brackets, braces): Do operations inside grouping symbols first.
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2. E – Exponents: Evaluate powers (e.g., \(2^3 = 8\)).
3. M & D – Multiplication and Division: From left to right.
4. A & S – Addition and Subtraction: From left to right.
Important: Multiplication and division are done together, left to right. Same for addition and subtraction.
Example: \(3 + 4 \times 5\). No parentheses or exponents. Do multiplication first: \(4 \times 5 = 20\). Then add: \(3 + 20 = 23\).
Example: \(20 – 12 \div 4 + 2\). Division first: \(12 \div 4 = 3\). Then left to right: \(20 – 3 = 17\); \(17 + 2 = 19\).
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WORKED EXAMPLES WITH STEP BY STEP SOLUTIONS
Example 1
Evaluate \(3 + 4 \times 5\)
Solutions:
Step 1: The expression has addition and multiplication. According to PEMDAS, multiplication is done before addition.
Step 2: Compute the multiplication first: \(4 \times 5 = 20\).
Step 3: Then add: \(3 + 20 = 23\).
Step 4: So \(3 + 4 \times 5 = 23\).
Answer: 23
Example 2
Evaluate \((6 + 2) \times 3\)
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Solutions:
Step 1: Parentheses come first. Compute \(6 + 2 = 8\).
Step 2: Replace the parentheses with 8: \(8 \times 3\).
Step 3: Multiply: \(8 \times 3 = 24\).
Step 4: So \((6 + 2) \times 3 = 24\).
Answer: 24
Example 3
Evaluate \(20 – 12 \div 4 + 2\)
Solutions:
Step 1: No parentheses or exponents. Do multiplication and division first, left to right. There is one division: \(12 \div 4 = 3\).
Step 2: Replace: \(20 – 3 + 2\).
Step 3: Do addition and subtraction left to right: \(20 – 3 = 17\); \(17 + 2 = 19\).
Step 4: So \(20 – 12 \div 4 + 2 = 19\).
Answer: 19
Example 4
Evaluate \(2 \times (5 + 3) – 4\)
Solutions:
Step 1: Parentheses first: \(5 + 3 = 8\). Expression becomes \(2 \times 8 – 4\).
Step 2: Multiplication: \(2 \times 8 = 16\). Expression becomes \(16 – 4\).
Step 3: Subtraction: \(16 – 4 = 12\).
Answer: 12
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