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Basic Math – Order of Operation Practice & Tutorial

Order of Operation – Rules, Examples and Practice Questions

The order of operation rules are:

Rule 1:  Start with calculations inside brackets or parentheses.
Rule 2: Then, solve multiplications and division, from left to right.
Rule 3: Finally, additions and subtraction, from left to right.

 Example 1

Solve 16 + 5 x 8

Based on the rules above, start with multiplication.

This gives: 16 + 40 = 56

Note that if the rule was not followed, and addition was done first, the answer would be different and incorrect, as in,

16 + 5 x 8

21 x 8 = 168 (wrong answer)

Example 2

3 +(35 – 21) x 2

Solve the problem inside the brackets first. Then multiplication, and finally addition.

3 + (35 – 21) x 2
3 + (14) x 2
3 + 28
= 31

 

Order Of Operation Practice Questions

 

1. 7 + 2 x (6 + 3) ÷ 3 – 7 

a.  6
b.  5
c.   7
d.  4

2. 11 + 19 x 2

a. 60
b. 50
c. 49
d. 54

3. (14 + 2) x 2 + 3

a.     21
b.     35
c.     80
d.     43

4. 120 ÷ (6 + 12 x 2)

a.     150
b.     40
c.     6
d.     4

5. 12 + 2 x 44

a.     100
b.     616
c.     110
d.     600

6.  10 x 2 – (7 + 9)

a.     21
b.     16
c.     4
d.     13

Answer Key

1. A
2. C
3. B
4. D
5. A
6. C

Common Mistakes with Order of Operation on a Test

Misinterpreting PEMDAS. The PEMDAS rule is (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction). This can be misinterpreted as a strict order of operations where multiplication must always be done before division, which is incorrect. The rule actually says to perform operations within parentheses first and then applying the other operations in order from left to right.

Errors with multiplication and division.  Multiplication and division have equal precedence and should be performed from left to right. Assuming multiplication should always be done before division, is incorrect.

Not simplifying fractions.  Always simplify them before performing other operations.

 More – Order of Operation Practice and Tutorials

Math Goodies
Math Playground – Video

Written by, Brian Stocker MA., Complete Test Preparation Inc.

Date Published: Thursday, November 27th, 2014
Date Modified: Monday, June 26th, 2023

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Brian Stocker MA

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    10 Comments

  1. Gavin
    June 4, 2017
    Reply

    BIMDAS rule. Easy to remember.

  2. Brian
    June 4, 2017
    Reply

    I think it is PIMDAS – Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. … The original order of operations in some countries was BODMAS, which stands for Brackets, Orders or Powers, Division, Multiplication, Addition, Subtraction.

  3. Anonymous
    June 20, 2017
    Reply

    Thank you!

  4. MI
    January 27, 2018
    Reply

    BEDMAS=brackets, exponents, division, multiplication, addition then subtracting

  5. MK
    June 4, 2018
    Reply

    PEMDAS:
    Please (Parentheses)
    Excuse (Exponents)
    My (Mult.)
    Dear (Div.)
    Aunt (Addition)
    Sally (Subtraction)

  6. Brian
    June 5, 2018
    Reply

    Very Good!

  7. Anonymous
    August 20, 2018
    Reply

    Thanks for sharing this!

  8. Ryan Wildes
    August 29, 2018
    Reply

    I am useless with mathematics but need to practice before I start a nursing degree. Thanks for explaining how to do these kind of sums, helped me a lot.

  9. Anonymous
    October 14, 2018
    Reply

    GEMS
    Groupings
    Exponents/Square Roots
    Multiplication/Division
    Subtraction/Addition

    Each one you do you also have to do the opposite item at the same time.

  10. Anonymous
    December 7, 2021
    Reply

    BODMAS…….. bracket off division multiplication addition and subtraction

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