Order of Operations
Order of operations is the set of rules that define the sequence in which calculations should be performed in a mathematical expression. Following the order of operations ensures that everyone arrives at the same correct answer when evaluating mathematical expressions.
The Order of Operations Rules
- Parentheses: Perform operations inside parentheses first. If there are nested parentheses, start with the innermost set.
- Exponents: Perform any calculations involving exponents (or powers) next.
- Multiplication and Division: Perform multiplication and division operations from left to right.
- Addition and Subtraction: Perform addition and subtraction operations from left to right.
Remembering the Order
An easy way to remember the order of operations is to use the acronym PEMDAS:
- P: Parentheses
- E: Exponents
- M: Multiplication
- D: Division
- A: Addition
- S: Subtraction
Examples
Let's work through an example to illustrate the order of operations:
Simplify the expression: 3 + 5 × (2 - 4)²
- Start with the parentheses: 2 - 4 = -2
- Next, calculate the exponent: (-2)² = 4
- Finally, perform the multiplication: 5 × 4 = 20
- Add the result to 3: 3 + 20 = 23
Study Guide
Here are some tips to remember when dealing with order of operations:
- Always start with operations inside parentheses or brackets.
- Next, evaluate any exponents or powers.
- Then, perform multiplication and division from left to right.
- Finally, perform addition and subtraction from left to right.
- Use the acronym PEMDAS to help remember the order of operations.
Remembering and applying the order of operations is crucial in solving math problems accurately. With practice, it becomes easier to perform calculations following these rules.
[Order Of Operations] Related Worksheets and Study Guides:
.◂Math Worksheets and Study Guides Fifth Grade. Order of Operations
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Order of Operations 
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Order of Operations Worksheet/Answer key
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Order Of Operations
Activity LessonWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyWorksheet/Answer keyThe resources above cover the following skills:
Algebra (NCTM)
Use mathematical models to represent and understand quantitative relationships.
Model problem situations with objects and use representations such as graphs, tables, and equations to draw conclusions.
Connections to the Grade 5 Focal Points (NCTM)
Algebra: Students use patterns, models, and relationships as contexts for writing and solving simple equations and inequalities. They create graphs of simple equations. They explore prime and composite numbers and discover concepts related to the addition and subtraction of fractions as they use factors and multiples, including applications of common factors and common multiples. They develop an understanding of the order of operations and use it for all operations.