What is Order Of Operations? Definition, Rules, Examples, Facts
There are many operations in mathematics, such as addition, subtraction, multiplication, and division. They help us evaluate mathematical expressions.
Consider the following expression: 4+ 5 × 32 – 2
The expression consists of many operations. But which part do you calculate first?
You may start from the left and get one answer. But your friend may begin from the right and get a completely different answer!
Note: Both the methods given above are incorrect.
Hence, to avoid confusion, a standard rule was set to perform such calculations. This rule is known as the order of operations.
What Is the Order of Operations in Math?
If you have an expression where all the operations are the same (example: only addition, only subtraction, only multiplication, or only division) then the correct way to solve it would be from left to right. But for expressions with multiple operations, we need to follow the order of operations.
The order of operations is the rule that tells us the sequence in which we should solve an expression with multiple operations.
A way to remember that order is PEMDAS. Each letter in PEMDAS stands for a mathematical operation.
Order of Operations Steps:
The first step is to solve the operation within parentheses or brackets. Parentheses are used to group things together. Work out all groupings from inside to out.
Work out the exponential expressions after the parentheses.
Multiplication and Division
Next, moving from left to right, multiply and/or divide, whichever comes first.
Addition and Subtraction
Lastly, moving from left to right, add and/or subtract, whichever comes first.
Why Follow the Order of Operations?
We follow the rules of the order of operations to solve expressions so that everyone arrives at the same answer.
Here’s an example of how we can get different answers if the correct order of operations is NOT followed:
Solved Examples On Order Of Operations
Example 1: Solve: 2 + 6 × (4 + 5) ÷ 3 – 5 using PEMDAS.
Step 1 – Parentheses : 2+6 × (4 + 5) ÷ 3 – 5 = 2 + 6 × 9 ÷ 3 – 5
Step 2 – Multiplication: 2 + 6 × 9 ÷ 3 – 5 = 2 + 54 ÷ 3 – 5
Step 3 – Division: 2 + 54 ÷ 3 – 5 = 2 + 18 – 5
Step 4 – Addition: 2 + 18 – 5 = 20 – 5
Step 5 – Subtraction: 20 – 5 = 15
Example 2: Solve 4 – 5 ÷ (8 – 3) × 2 + 5 using PEMDAS.
Step 1 – Parentheses: 4 – 5 ÷ (8 – 3) × 2 + 5 = 4 – 5 ÷ 5 × 2 + 5
Step 2 – Division: 4 – 5 ÷ 5 × 2 + 5 = 4 – 1 × 2 + 5
Step 3 – Multiplication: 4 – 1 × 2 + 5 = 4 – 2 + 5
Step 4 – Subtraction: 4 – 2 + 5 = 2 + 5
Step 5 – Addition: 2 + 5 = 7
Example 3: Solve 100 ÷ (6 + 7 × 2) – 5 using PEMDAS.
Step 1 – Multiplication inside parentheses: 100 ÷ (6 + 7 × 2) – 5= 100 ÷ (6 + 14) – 5
Step 2 – Addition inside parentheses: 100 ÷ (6 + 14) – 5 = 100 ÷ 20 – 5
Step 3 – Division: 100 ÷ 20 – 5 = 5 – 5 Step 4 – Subtraction: 5 – 5 = 0
Practice Problems On Order Of Operations
Simplify 4+ (5 ×3² + 2) using PEMDAS.
Correct answer is: 51
4 + (5 × 3² + 2)
= 4 + (5 × 9 + 2
= 4 + (45 + 2)
= 4 + 47
Simplify 9 – 24 ÷ 8 × 2 + 3 using PEMDAS.
Correct answer is: 6
9 – 24 ÷ 8 × 2 + 3
= 9 – 3 × 2 + 3 (Notice that we did division before multiplication because we should go from left to right.)
= 9 – 6 + 3
= 3 + 3 (Notice that we did subtraction before addition because we should go from left to right.)
Simplify [(32 ÷ 4) + 3] × 2 using PEMDAS.
Correct answer is: 22
[(32 ÷ 4) + 3] × 2
= [8 + 3] × 2
= 11 × 2
Simplify $(3 × 5² ÷ 5)$ – $(16 — 10)$ using PEMDAS.
Correct answer is: 9
$(3 × 5² ÷ 5)$ – $(16 – 10)$
= $(3 × 25 ÷ 5)$ – $(16 – 10)$
= $(75 ÷ 5)$ – $(6)$
= 15 – 6
Frequently Asked Questions On Order Of Operations
What is the order of operations in math?
The order of operations are the rules that tell us the sequence in which we should solve an expression with multiple operations.
The order is PEMDAS: Parentheses, Exponents, Multiplication, and Division (from left to right), Addition and Subtraction (from left to right).
Is there a trick we can use to remember the order of operations?
Yes. You can use the phrase “Please Excuse My Dear Aunt Sally” to remember PEMDAS.
Can we perform subtraction before addition?
Yes, addition and subtraction are at the same level according to the PEMDAS rule. So, without brackets, we do the math from left to right if we are only dealing with addition and subtraction. For example, 9 – 6 + 3 = 3 + 3 = 6.
Can we perform division before multiplication?
Yes, multiplication and division are at the same level according to the PEMDAS rule. So, without brackets, we do the math from left to right if we are only dealing with multiplication and division. For example, 24 ÷ 8 × 2 = 3 × 2 = 6.
Are PEMDAS and BODMAS the same?
Yes. Both PEMDAS and BODMAS are acronyms for remembering the order of operations. They are different names for the same rule. What they call PEMDAS in the US is called BODMAS in the UK, Australia, India and various other countries.
NOTE – Related Readings:
Order of Operations 5th Grade Worksheets — BODMAS and PEMDAS Problems
In the world of mathematics, understanding the order of operations is crucial. 5th-grade students are introduced to the concept of Order of Operations, which helps them solve mathematical expressions accurately and efficiently. To strengthen their skills in this area, we have curated a collection of comprehensive worksheets that focus on BODMAS and PEMDAS problems.
Download 5th Grade Order of Operation Worksheets PDF
Download our comprehensive 5th-grade Order of Operation Worksheets today to provide your students with engaging practice opportunities. These worksheets cover BODMAS and PEMDAS problems, enabling students to develop a deep understanding of the Order of Operations and its practical application in solving mathematical expressions. With our worksheets, students can improve their computational skills, enhance problem-solving abilities, and gain confidence in handling complex mathematical problems.
We’ve got lots of printable 5th grade addition worksheets to practice a variety of skills. These worksheets give additional practice in the order of operations problems.
- 4 Operations and Parenthesis
- PEDMAS Including Exponents
- PEDMAS With Nested Parenthesis
4 Operations and Parenthesis
Below are our grade 5 addition worksheets on problems on the 4 operations and parenthesis.
PEDMAS Including Exponents
Below are our grade 5 addition worksheets on the problems based on PEDMAS including exponents.
PEDMAS With Nested Parenthesis
Below are our grade 5 addition worksheets on the problems on PEDMAS With Nested Parenthesis.
What is the Order of Operations?
To effectively solve mathematical expressions, students must follow a set of rules known as the Order of Operations. The Order of Operations determines the sequence in which mathematical operations should be performed. It helps avoid confusion and ensures consistent and accurate results.
BODMAS Questions for Class 5 Worksheet
Our worksheets include a wide range of BODMAS (Brackets, Orders, Division and Multiplication, Addition and Subtraction) questions specifically designed for 5th-grade students. These questions challenge students to apply the BODMAS rule to solve complex expressions and improve their computational skills.
BODMAS Problems for Class 5
With our BODMAS problems, students will gain a deeper understanding of how to solve expressions involving brackets, exponents, and various operations. The problems are tailored to the 5th-grade level, allowing students to build a strong foundation in using the BODMAS rule effectively.
BODMAS Sums for Class 5
Our BODMAS sums provide students with ample practice in applying the BODMAS rule to solve a variety of mathematical expressions. Through repetitive practice, students will enhance their problem-solving abilities and develop fluency in correctly evaluating and simplifying expressions.
In addition to BODMAS, our worksheets also include PEMDAS (Parentheses, Exponents, Multiplication and Division, Addition and Subtraction) problems. These problems challenge students to solve complex expressions by applying the PEMDAS rule. By practicing with PEMDAS problems, students will expand their problem-solving skills and gain confidence in tackling more intricate mathematical expressions.
Mastering the Order of Operations is a fundamental skill for 5th-grade students, and our collection of worksheets is designed to support their learning journey. By practicing with BODMAS and PEMDAS problems, students will strengthen their problem-solving abilities, improve computational skills, and develop a solid foundation in mathematics. Download our 5th-grade Order of Operation Worksheets today and witness the remarkable progress in your students’ ability to solve complex mathematical expressions with accuracy and confidence.
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Admission to Grade 5
Page updated on 06/01/2023
Municipal educational institution «Secondary school No. 52», Yaroslavl
Admission to the 5th profile class with in-depth study of mathematics
atiki) in the 2023-2024 academic year
(Minutes dated 05/30/2023)
Applications for admission to grade 5 with in-depth study of certain subjects (mathematics) for the 2023-2024 academic year are accepted from June 1 to June 5 inclusive in electronic form (to the school’s email address) or through the class teacher. The application form is attached.
- Order of the Department of Education of the Mayor’s Office of the City of Yaroslavl No. 01-05/90 dated January 27, 2023 “On approval of the list of general educational organizations in which individual selection is allowed upon receipt of basic general education”, order of the Department of Education of the Mayor’s Office of the city of Yaroslav la No. 01-05/163 dated February 17, 2023 “On Amendments to the List of General Educational Organizations Allowing Individual Selection in Obtaining Basic General Education”
- High School Principal Order No. 52
- Regulations on classes with in-depth study of individual subjects in educational programs of basic general education in the municipal educational institution «Secondary School No. 52»
- The procedure for organizing individual selection upon admission (enrollment in the order of transfer) of students to receive basic general education in classes with in-depth study of individual subjects in the municipal educational institution «Secondary School No. 52″ (hereinafter referred to as the Procedure)
Schedule of individual selection, information on the conditions of individual selection.
From April 17, 2023 to May 12, 2023 — accepting applications for individual selection for grade 5 with in-depth study of mathematics in electronic form (scan / photo) to the email address: [email protected]
- Application for participation in individual selection
- Consent to the processing of personal data
May 15, 2023 — additional test (test).
From May 25, 2023 to May 30, 2023 — receiving copies of the summary sheet (quarter trimester / annual assessments) in electronic form (scan / photo) to the email address: [email protected]
9003 8 No later than May 31, 2023 — announcement of the results of individual selection for grade 5 with in-depth study of mathematics on the school website and information stands at the entrance to the school.
Information about the conditions of individual selection
in grade 5 with in-depth study of mathematics
maximum 16 points
Yearly mark for the previous year of study
maximum 5 points
Composite grade point average
for the previous year of study
maximum 5 points
The maximum possible number of points in the rating
Additional test (test)
Examination contains 9 tasks. The work consists of two parts. Part 1 contains 6 tasks, part 2 — 3 tasks. The structure of the work corresponds to the idea of a differentiated approach to teaching and monitoring the knowledge and skills of students. The work provides for both checking the achievement of the level of basic training by schoolchildren, and the opportunity for students to demonstrate their knowledge at higher levels. Detailed description of the control work.
MAOU «Lyceum No. 17»: Admission to grade 5
Main date calendar
|Open day for 4th grade students and parents (legal representatives)|
|from 17.04.2023 to 26.04.2023||Acceptance of applications for participation in the Olympiad in the format PDF to the email address [email protected] (DOWNLOAD THE APPLICATION FORM)|
| 04/30/2023 (Sunday)
at 10. 00
|Mathematics Olympiad for 4th grade students|
|Placement of the results of the Olympiad on the website of the lyceum lyceum17.ru|
| May 19, 2023
from 16.00 to 17.00
|Review of Olympiad works (optional)|
|from 05/29/2023 until 06.06.2023||Submission of applications and portfolio for individual selection. Documents are accepted to the email address [email protected] only in PDF format (other formats are not accepted) common file.|
|Phone for inquiries: 58-31-64|
Regulations on the Open Mathematics Olympiad for 4th grade students 2023 (download) 5 classes
MAOU «Lyceum No. 17» for basic general education in classes with in-depth study of mathematics. Presentation. (download)
Regulation on the procedure for organizing individual selection for admission or transfer to the 5th grade of the municipal autonomous educational institution «Lyceum No. 17» of the City District of the Arkhangelsk Region «Severodvinsk» for basic general education in classes with in-depth study of mathematics (download)
Acceptance of documents for individual selection in grade 5 from May 29 to June 06, 2023
The procedure for admission to the 5th grade of the MAOU «Lyceum No. 17»
Parents (legal representatives) of students send to the e-mail of the MAOU «Lyceum No. 17» [email protected] (indicating the subject of the letter «Application Grade 5») scanned copies of the following documents (only in .pdf format, one common file):
- 9 0027 application addressed to the director of MAOU «Lyceum No. 17» in the prescribed form (download);
- report card of final grades for grade 4, certified by the head of the educational organization;
- documents confirming the individual achievements of the student (portfolio): certificates, diplomas and other documents confirming the educational and intellectual achievements of students in grades 3 and 4 at the school, municipal regional and all-Russian levels in mathematics, computer science and chess.