Opening parentheses and solving everything inside them is the first step in the order of operations.
In every exercise, we first solve what is inside of the parentheses.
We write the result above the parentheses in a small arc or in place of the entire expression inside the parentheses.
If multiplication and division appear inside the parentheses along with addition and subtraction, multiplication and division come first, and only then do we proceed to addition and subtraction from left to right.
Parentheses Order of Operations Practice Problems
Master parentheses in PEMDAS with step-by-step practice problems. Learn to solve expressions inside brackets first using the correct order of operations.
📚Practice Solving Expressions with Parentheses
- Solve expressions inside parentheses before other operations
- Apply multiplication and division rules within brackets correctly
- Handle multiple sets of parentheses in complex expressions
- Use the PEMDAS order: parentheses, multiplication/division, addition/subtraction
- Replace parenthetical expressions with their calculated results
- Master step-by-step rewriting techniques for clarity
Understanding Parentheses in simple Order of Operations
Complete explanation with examples
Parentheses in the Order of Operations
Upon completion we proceed to -
Multiplication and division in order, from left to right.
Progressing to-
Addition and subtraction in order, from left to right.
Practice Parentheses in simple Order of Operations
Test your knowledge with 15 quizzes
\( 10 + 2 \times (3 + 1) = \)
Examples with solutions for Parentheses in simple Order of Operations
Step-by-step solutions included
Exercise #1
Solve the following problem:
Step-by-Step Solution
Apply the distributive property and proceed to multiply each term inside of the parentheses by 187:
Solve the first multiplication problem vertically, making sure to solve it in the correct order (ones multiplied by ones, ones multiplied by tens, ones multiplied by hundreds )
We should obtain the following result: 1496
Proceed to solve the second multiplication problem vertically, once again making sure to solve it in the correct order (ones multiplied by ones, ones multiplied by tens, ones multiplied by hundreds )
We should obtain the following result: 935
Now to tackle the next problem:
We should once again solve this vertically. Make sure to align the digits properly, ones under ones, tens under tens, etc.:
Subtract ones from ones, tens from tens, etc., to obtain the final result:
Answer:
Video Solution
Exercise #2
Step-by-Step Solution
First, calculate the expression within the parentheses:
Now, multiply the result by 9:
Thus, the final answer is 18.
Answer:
18
Exercise #3
Solve the following equation:
Step-by-Step Solution
First, solve the expression inside the parentheses:
Then subtract from 30:
Answer:
13
Exercise #4
Solve the following equation:
Step-by-Step Solution
First, solve the expression inside the parentheses:
Then subtract from 25:
Answer:
12
Exercise #5
Solve the following expression:
Step-by-Step Solution
Let's simplify this expression while following the order of operations which states that exponents come before multiplication and division, which come before addition and subtraction, and that parentheses come before all of them,
We will therefore start by simplifying the expression inside the parentheses and calculate the result of the addition within them, then - we will first perform the division operation:
Therefore, the correct answer is answer A.
Answer:
Video Solution
Frequently Asked Questions
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.