If we have negative integers in our expression, we still follow the exact same rules; we just need to be careful when evaluating the terms involving negatives.

Examples

Example 1

Evaluate 5+9\times(-6).

Worked Solution

Create a strategy

We first need to evaluate the multiplication, and then the addition.

Apply the idea

\displaystyle 5+9\times(-6)	\displaystyle =	\displaystyle 5+(-54)	Evaluate the multiplication
	\displaystyle =	\displaystyle -49	Evaluate

Example 2

Evaluate (7-8)\times(-5).

Worked Solution

Create a strategy

We first need to evaluate the operation in the brackets, and then the multiplication.

Apply the idea

\displaystyle (7-8)\times(-5)	\displaystyle =	\displaystyle (-1)\times(-5)	Evaluate 7-8
	\displaystyle =	\displaystyle 5	Evaluate

Example 3

Evaluate 21\div(-7)\times2.

Worked Solution

Create a strategy

Evaluate the multiplication and division from left to right.

Apply the idea

\displaystyle 21\div(-7)\times2	\displaystyle =	\displaystyle -3\times2	Evaluate 21\div(-7)
	\displaystyle =	\displaystyle -6	Evaluate

Idea summary

The order of operations is as follows:

Evaluate whatever is contained in brackets.
Evaluate any powers.
Evaluate any multiplication or division, reading from left to right.
Evaluate any addition or subtraction, reading from left to right.

Outcomes

ACMNA183

Carry out the four operations with rational numbers and integers, using efficient mental and written strategies and appropriate digital technologies

1.02 Mixed operations with integers

Ideas

Mixed operations with integers

Examples

Example 1

Example 2

Example 3

Outcomes

ACMNA183

What is Mathspace

About Mathspace