The order of operations is a set of rules used to clarify which procedures should be performed first in a given mathematical expression. The standard order of operations can be remembered using the acronym **PEMDAS**:

1. **P**arentheses - Perform operations inside parentheses first.
2. **E**xponents - Solve exponents (or radicals) next.
3. **M**ultiplication and **D**ivision - From left to right, perform all multiplication and division.
4. **A**ddition and **S**ubtraction - Finally, from left to right, perform all addition and subtraction.

This order ensures that mathematical expressions are interpreted and solved consistently.

### Example:
Consider the expression \( 3 + 6 \times (5 + 4) \div 3^2 - 7 \).

1. **Parentheses**: Solve inside the parentheses: \(5 + 4 = 9\).
   Expression becomes \(3 + 6 \times 9 \div 3^2 - 7\).

2. **Exponents**: Solve the exponent: \(3^2 = 9\).
   Expression becomes \(3 + 6 \times 9 \div 9 - 7\).

3. **Multiplication and Division**: From left to right, perform multiplication and division:
   - \(6 \times 9 = 54\)
   - \(54 \div 9 = 6\)
   Expression becomes \(3 + 6 - 7\).

4. **Addition and Subtraction**: From left to right:
   - \(3 + 6 = 9\)
   - \(9 - 7 = 2\)

So, \(3 + 6 \times (5 + 4) \div 3^2 - 7 = 2\).

Would you like more details or have any questions?

### Related Questions:
1. How does the order of operations apply to complex fractions?
2. Can the order of operations change the outcome of a problem?
3. What happens if you ignore the order of operations?
4. How do calculators interpret the order of operations?
5. Are there exceptions to the standard order of operations?

### Tip:
When in doubt, use parentheses to clarify the order of operations in complex expressions. This helps prevent errors.

Explore the order of operations (PEMDAS) in mathematics with clear explanations and examples. Learn how to correctly solve mathematical expressions using parentheses, exponents, multiplication, division, addition, and subtraction. Suitable for students in Grades 5-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation