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.
The Absolute Best Book to Ace Grade 5 Math
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: \(20 – 3 = 17\); \(17 + 2 = 19\).
The Ultimate Middle School Math Bundle: Grades 6–8
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 \((6 + 2) \times 3\)
Mastering Grade 5 Math
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
Related to This Article
More math articles
- Oregon OSAS Grade 7 Math Worksheets: 95 Free Printable Single-Skill PDFs with Keys
- Algebra Puzzle – Challenge 54
- Grade 5 Discussion and Research Skills: Stronger Speaking, Listening, Notes, and Sources
- How to Estimate Limit Values from the Graph?
- The Best Algebra 2 Book for Students Who Want It to Click
- 10 Most Common 3rd Grade OST Math Questions
- The Best Algebra 1 Book for South Dakota Students
- The Ultimate 7th Grade PSSA Math Course (+FREE Worksheets)
- Free Grade 4 English Worksheets for New York Students
- World Problems Involving Fractions of a Group
What people say about "Order of Operations for 5th Grade: PEMDAS Made Easy - Effortless Math"?
No one replied yet.