The order of operations is a set of rules that defines the order in which different mathematical operations should be performed. These operations include addition, subtraction, multiplication, division, and parentheses. The purpose of the order of operations is to ensure that everyone gets the same answer when evaluating mathematical expressions.

- 1. Parentheses: Simplify expressions inside parentheses first.
- 2. Exponents: Evaluate expressions with exponents (powers) next.
- 3. Multiplication and Division: Perform multiplication and division from left to right.
- 4. Addition and Subtraction: Perform addition and subtraction from left to right.

One common acronym to remember the order of operations is PEMDAS:

- P: Parentheses
- E: Exponents
- M: Multiplication
- D: Division
- A: Addition
- S: Subtraction

Let's go through an example to demonstrate the order of operations:

Example 1: Evaluate the expression 4 + 5 * 3.

According to the order of operations, we should perform the multiplication before the addition. So, 5 * 3 equals 15. Then, add 4 to 15 to get the final answer of 19.

Example 2: Evaluate the expression (6 + 2) * 4^{2}.

First, simplify the expression inside the parentheses: 6 + 2 equals 8. Then, evaluate the exponent: 4^{2} equals 16. Finally, multiply 8 by 16 to get the final answer of 128.

Here are some tips to master the order of operations:

- 1. Memorize the PEMDAS acronym to remember the order of operations.
- 2. Practice solving various expressions using the order of operations rules.
- 3. Use parentheses to clarify the order of operations when needed.
- 4. Check your work by following the order of operations step by step.

Remembering and applying the order of operations is crucial for solving math problems accurately. Understanding these rules will help you simplify complex expressions and equations with confidence.

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Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Develop an initial conceptual understanding of different uses of variables.

Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.