009. Order of Operations in Arithmetic

Learning Intentions

• To know the convention for determining order of operations in an expression involving more than one operation
• Evaluate arithmetic expressions involving more than one operation

Pre-requisite Summary

• Understanding basic arithmetic operations: addition, subtraction, multiplication, division
• Knowledge that multiplication and division have higher priority than addition and subtraction
• Understanding parentheses and their role in changing order of evaluation
• Familiarity with simple calculations and ability to perform operations accurately

Worked Examples

Worked Example 1

Evaluate Use the order of operations:

a)

b)

Worked Example 2

Include parentheses to change order:

a)

b)

Worked Example 3

Combine multiple operations:

a)

b)

Worked Example 4

Use a mixture of parentheses and multiple operations:

a)

b)

Problems

Problem 1

a)

b)

Problem 2

a)

b)

Problem 3

a)

b)

Problem 4

a)

b)

Exercises

Understanding and Fluency

Exercise 1.

Evaluate:

a)

b)

c)

Exercise 2.

Evaluate with parentheses:

a)

b)

c)

Exercise 3.

Evaluate mixed operations:

a)

b)

c)

Exercise 4.

Evaluate using parentheses:

a)

b)

c)

Reasoning

Exercise 5.

Explain why is not .

Exercise 6.

A student writes . Explain the mistake.

Exercise 7.

Why do parentheses change the order of operations?

Exercise 8.

Compare and . Explain the difference in answers.

Problem-solving

Exercise 9.

A shop sells pens for dollars each and a notebook for dollars. How much does a customer pay if they buy pens and notebook?

Exercise 10.

A factory produces items per hour. On Monday, they make hours in the morning and hours in the afternoon. How many items are produced?

Exercise 11.

Evaluate using correct order.

Exercise 12.

Evaluate .

Exercise 13.

A bus travels km in the morning and km in the afternoon. It stops times for km each. How far does it travel in total?

Potential Misunderstandings

• Students may perform operations strictly left to right without following order of operations
• Students may ignore multiplication/division precedence over addition/subtraction
• Students may misplace parentheses or ignore them
• Students may incorrectly evaluate expressions with multiple layers of parentheses
• Students may treat subtraction or division as commutative
• Students may not Check work by reverse operations

:)