The same goes for solving math problems with more than one operation. An operation is a mathematical process, such as addition, subtraction, multiplication or division. Other operations include raising a number to a power and taking a root of a number. An ‘operator’ is a symbol that indicates the type of operation, such as +, –, × or ÷.

There are a number of conventions (rules) which need to be followed in order to solve these problems correctly. The order goes:

Remember!

Step 1: Do operations inside grouping symbols such as round parentheses (...), square parentheses [...], braces {...} or absolute values $\left|...\right|$|...|.

Step 2: Do exponents (powers) and square roots.

Step 3: Do multiplication and division going from left to right.

Step 4: Do addition and subtraction going from left to right.

Worked examples

Question 1

Evaluate: $\left(48\div12+5\right)\times3$(48÷12+5)×3

Think: We need to simplify the problem by using our order of operation rules. First, we perform any operations inside the parentheses; division first followed by addition. Then we perform any other multiplication or division that is remaining, working from left to right.

Do:

$\left(48\div12+5\right)\times3$(48÷12+5)×3	$=$=	$\left(4+5\right)\times3$(4+5)×3
	$=$=	$9\times3$9×3
	$=$=	$27$27

question 2

Evaluate: $48-6\times\left(8-4\right)$48−6×(8−4)

Think: Using our order of operations, we want to first perform the subtraction in the parentheses. We then want to evaluate the multiplication. Finally, we can subtract the product from $48$48.

Do:

$48-6\times\left(8-4\right)$48−6×(8−4)	$=$=	$48-6\times4$48−6×4
	$=$=	$48-24$48−24
	$=$=	$24$24

Practice questions

QUESTION 3

Evaluate $-18+21\div7$−18+21÷7

QUESTION 4

Evaluate $\left(-14\right)\div2-10\div\left(-2\right)$(−14)÷2−10÷(−2)

1.02 Review: Integer operations