Frequently Asked Questions
Everything you need to know about Parentheses in simple Order of Operations
What comes first in order of operations with parentheses?
+ Parentheses always come first in the order of operations (PEMDAS/BODMAS). You must solve everything inside parentheses before moving to multiplication, division, addition, or subtraction. Even within parentheses, follow the order: multiplication and division first, then addition and subtraction from left to right.
How do you solve expressions with multiple parentheses?
+ Solve each set of parentheses one at a time, working from left to right. Calculate the result for each parenthetical expression, replace it in the original equation, then remove those parentheses. Continue until all parentheses are eliminated before proceeding with other operations.
What order do you follow inside parentheses?
+ Inside parentheses, follow the same order of operations: 1) Any nested parentheses first, 2) Multiplication and division from left to right, 3) Addition and subtraction from left to right. For example, in (7+3×6), solve 3×6=18 first, then 7+18=25.
Do you always rewrite the entire equation after solving parentheses?
+ You can either rewrite the entire equation or use small arcs above parentheses to show results. For simple expressions, rewriting helps avoid confusion. For complex expressions with multiple parentheses, drawing small arcs above each set and writing results there can be more efficient.
What happens after you solve all parentheses in an expression?
+ After solving all parentheses, proceed with the remaining order of operations: 1) Multiplication and division from left to right, 2) Addition and subtraction from left to right. Remove the parentheses completely and work with the simplified expression.
Why do parentheses come first in PEMDAS?
+ Parentheses indicate which operations should be performed first, overriding the normal order of operations. They group parts of an expression that must be calculated as a unit before being used in the rest of the equation. This ensures mathematical expressions are evaluated consistently and correctly.
How do you handle parentheses with multiplication outside them?
+ First solve what's inside the parentheses, then multiply the result by the number outside. For example, in 5×(3+2), solve (3+2)=5 first, then calculate 5×5=25. The multiplication happens after the parentheses are resolved.
Can you have parentheses inside parentheses?
+ Yes, nested parentheses are common in complex expressions. Always solve the innermost parentheses first, working outward. For example, in ((2+3)×4)+1, solve (2+3)=5 first, then (5×4)=20, and finally 20+1=21.