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. Parentheses - Perform operations inside parentheses first.
2. Exponents - Solve exponents (or radicals) next.
3. Multiplication and Division - From left to right, perform all multiplication and division.
4. Addition and Subtraction - 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.