Order of Operations with Parentheses Practice Problems

Master PEMDAS/BODMAS rules with step-by-step parentheses practice problems. Solve advanced order of operations exercises with confidence using proper mathematical sequence.

📚Practice Solving Order of Operations with Parentheses
  • Solve multi-step expressions by identifying and evaluating parentheses first
  • Apply PEMDAS/BODMAS rules correctly in complex mathematical expressions with grouping symbols
  • Master the sequence: parentheses, exponents, multiplication/division, addition/subtraction from left to right
  • Work through expressions containing multiple operations including division, multiplication, and parentheses
  • Build confidence solving real-world math problems requiring proper order of operations
  • Develop systematic problem-solving approach for advanced arithmetic expressions

Understanding Parentheses in advanced Order of Operations

Complete explanation with examples

In previous articles, we have seen what is the order of operations for addition, subtraction, multiplication, and division and also the order we must follow when there are exponents.

When the exercise we need to solve includes parentheses, we always (always!) start with the operation contained within them.

  1. Parentheses
  2. Exponents and roots
  3. Multiplications and divisions
  4. Additions and subtractions

Reminder: when an exercise presents operations that have the same precedence, that is, multiplications and divisions or additions and subtractions, we will solve the exercise from left to right.

Visual representation of BODMAS/PEMDAS rule emphasizing Brackets (Parentheses) as the first step in arithmetic problem-solving, crucial for accurate mathematical operations

Detailed explanation

Practice Parentheses in advanced Order of Operations

Test your knowledge with 27 quizzes

\( (2+1\times2)^2= \)

Examples with solutions for Parentheses in advanced Order of Operations

Step-by-step solutions included
Exercise #1

8×(5×1)= 8\times(5\times1)=

Step-by-Step Solution

According to the order of operations, we first solve the expression in parentheses:

5×1=5 5\times1=5

Now we multiply:

8×5=40 8\times5=40

Answer:

40

Video Solution
Exercise #2

25(5+0)= 25(5+0)=

Step-by-Step Solution

According to the order of operations, we will first solve the expression in parentheses:

5+0=5 5+0=5

Now we will get the expression:

25×5= 25\times5=

Let's solve the expression vertically:

25×5 25\\\times5

We will be careful to solve the expression in the correct order, ones with ones and then ones with tens

And we will get:

125 125

Answer:

125 125

Video Solution
Exercise #3

Solve the following problem:

187×(85)= 187\times(8-5)=

Step-by-Step Solution

Apply the distributive property and proceed to multiply each term inside of the parentheses by 187:

187×8187×5= 187\times8-187\times5=

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 )

187×8 187\\\times8

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 )

187×5 187\\\times5

We should obtain the following result: 935

Now to tackle the next problem:

1496935= 1496-935=

We should once again solve this vertically. Make sure to align the digits properly, ones under ones, tens under tens, etc.:

1496935 1496\\-935

Subtract ones from ones, tens from tens, etc., to obtain the final result: 561 561

Answer:

561 561

Video Solution
Exercise #4

9×(2×1)= 9 \times (2 \times 1) =

Step-by-Step Solution

First, calculate the expression within the parentheses:

2×1=2 2 \times 1 = 2

Now, multiply the result by 9:

9×2=18 9 \times 2 = 18

Thus, the final answer is 18.

Answer:

18

Exercise #5

Solve the following equation:

30(10+7)= 30 - (10 + 7) =

Step-by-Step Solution

First, solve the expression inside the parentheses:
10+7=1710 + 7 = 17

Then subtract from 30:
3017=1330 - 17 = 13

Answer:

13

Frequently Asked Questions

What is the correct order of operations with parentheses?

+
The correct order is PEMDAS/BODMAS: 1) Parentheses/Brackets first, 2) Exponents/Orders, 3) Multiplication and Division (left to right), 4) Addition and Subtraction (left to right). Always solve what's inside parentheses before any other operations.

Why do parentheses come first in order of operations?

+
Parentheses indicate grouping and show which operations should be performed together first. They override the normal order of operations, ensuring mathematical expressions are solved correctly and consistently across all problems.

How do you solve 4+(6÷2) step by step?

+
Step 1: Solve inside parentheses first: 6÷2 = 3. Step 2: Replace the parentheses with the result: 4+3. Step 3: Perform addition: 4+3 = 7. The final answer is 7.

What happens when there are multiple parentheses in one problem?

+
Solve each set of parentheses separately first, then continue with the remaining operations following PEMDAS/BODMAS order. For example, in (21+3)×2×4-(22÷2), solve both (21+3)=24 and (22÷2)=11 first, then proceed with multiplication and subtraction.

Do you multiply or divide first when they're in the same problem?

+
When multiplication and division appear together, work from left to right in the order they appear. They have equal precedence, so the left-to-right rule applies after solving any parentheses and exponents first.

How do you remember the order of operations with parentheses?

+
Use memory aids like PEMDAS (Please Excuse My Dear Aunt Sally) or BODMAS (Brackets, Orders, Division/Multiplication, Addition/Subtraction). The key is remembering parentheses/brackets always come first, then follow the sequence systematically.

What are common mistakes students make with parentheses in order of operations?

+
Common errors include: 1) Not solving parentheses first, 2) Working left to right without following PEMDAS, 3) Forgetting that multiplication and division have equal priority, 4) Not properly handling multiple sets of parentheses. Always identify and solve all parentheses before proceeding.

Can you have parentheses inside parentheses in math problems?

+
Yes, nested parentheses are common in advanced problems. Solve the innermost parentheses first, then work outward. For complex expressions, you might also see brackets [ ] and braces { } to show different levels of grouping.

More Parentheses in advanced Order of Operations Questions

Continue Your Math Journey

Practice by Question Type