# Basic Math – Order of Operation Practice & Tutorial

- Posted by Brian Stocker MA
- Date November 27, 2014
- Comments 10 comments

### 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

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

**Date Published:**Thursday, November 27th, 2014

**Date Modified:**Monday, June 26th, 2023

## 10 Comments

BIMDAS rule. Easy to remember.

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.

Thank you!

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

PEMDAS:

Please (Parentheses)

Excuse (Exponents)

My (Mult.)

Dear (Div.)

Aunt (Addition)

Sally (Subtraction)

Very Good!

Thanks for sharing this!

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.

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.

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