Order of Operations Worksheet With Step-by-Step Answers
An order of operations worksheet helps students solve calculations in a consistent sequence rather than simply working from left to right. It is useful for practising brackets, exponents, multiplication, division, addition and subtraction, with each line showing how an expression changes from one step to the next.
For Australian learners, these exercises suit classroom revision, homework, tutoring and independent practice. A Year 6 student in Perth may begin with simple brackets, while a Year 8 class in Melbourne might work with negative numbers, powers and mixed operations. A reusable worksheet can support both levels when the questions are arranged from accessible examples to more demanding problems.
Why The Calculation Order Matters
Mathematical expressions can produce different answers when operations are completed in different sequences. For example, in (6 + 4 \times 3), multiplying first gives (6 + 12 = 18). Adding first would give (10 \times 3 = 30), which is incorrect under the standard convention.
The usual sequence is brackets, orders, division and multiplication, then addition and subtraction. “Orders” means powers and roots, such as (3^2) or (\sqrt{16}). Division and multiplication have equal priority, so they are handled from left to right. Addition and subtraction also share priority and are solved from left to right.
Some classrooms use the acronym BIDMAS or BODMAS, while others use PEMDAS. The labels vary, but the mathematical meaning is the same. Students should focus on the priority of operations rather than memorising an acronym without understanding what each part represents.
A Simple Method For Students
The first step is to scan the entire expression and identify any brackets. Complete the innermost bracketed calculation before moving to powers, multiplication or other operations. Writing one new line for each major step makes the reasoning easier to check.
Consider:
[ 18 - (4 + 2) \times 2 ]
First solve the brackets:
[ 18 - 6 \times 2 ]
Then multiply:
[ 18 - 12 ]
Finally subtract:
[ 6 ]
A student should avoid writing several unrelated changes on one line. Clear working is especially important when a teacher is checking whether an incorrect answer came from a bracket, multiplication or subtraction mistake.
For expressions without brackets, mark the multiplication and division signs before beginning. In (24 \div 6 \times 3), work from left to right: (24 \div 6 = 4), followed by (4 \times 3 = 12). It is incorrect to multiply (6 \times 3) first simply because multiplication appears in the acronym.
Worked Examples With Answers
A good worksheet includes examples that model the process before students attempt independent questions. Start with a calculation such as:
[ 7 + 5 \times 2 ]
Multiplication comes first:
[ 7 + 10 = 17 ]
The answer is 17. The addition is completed only after the multiplication has been reduced.
A second example can include an exponent:
[ 3^2 + 4 \times 2 ]
Evaluate the power:
[ 9 + 4 \times 2 ]
Complete the multiplication:
[ 9 + 8 ]
Add the remaining numbers:
[ 17 ]
For a more advanced question, use nested brackets:
[ 30 - [2 \times (3 + 4)] ]
Work inside the round brackets:
[ 30 - [2 \times 7] ]
Multiply inside the square brackets:
[ 30 - 14 ]
Subtract:
[ 16 ]
These step-by-step answers show why students should preserve the structure of the expression until each priority operation has been completed.
Building An Effective Practice Sheet
A balanced printable worksheet should combine direct calculations, missing-number problems and short word problems. Direct questions develop fluency, while missing-number tasks test whether students understand the relationship between operations. For example, in (5 + \Box \times 3 = 20), the blank must be 5 because (5 + 5 \times 3 = 20).
Use a gradual difficulty range. Early questions might contain two operations, such as (9 + 6 \div 3). Later problems can include brackets and powers, such as (2(5 + 3)^2). Avoid presenting every difficult feature at once, since a learner may make errors because of reading load rather than mathematical reasoning.
Australian teachers and tutors can adapt the context to familiar situations. A worksheet might use Australian dollars in a shopping calculation, distances between suburbs in kilometres, or a basketball statistics example based on a local school competition. A class in Sydney, Adelaide or Darwin may find familiar settings more engaging than generic international examples.
For printable learning resources and reusable classroom material, the Myfundrazor about page gives useful context about the site behind these worksheets. Teachers can also keep an editable version so they can change names, values and difficulty for different groups.
Common Errors And Clear Corrections
The most frequent error is solving from left to right without considering priority. In (8 + 12 \div 4), a student who adds first may write (20 \div 4 = 5). The correct process is (12 \div 4 = 3), followed by (8 + 3 = 11).
Another common mistake is treating multiplication as automatically more important than division. They have the same priority. In (36 \div 3 \times 2), divide first because it appears first from the left: (36 \div 3 = 12), then (12 \times 2 = 24).
Students may also forget that subtraction and addition are equal in priority. For (15 - 6 + 2), calculate from left to right: (15 - 6 = 9), then (9 + 2 = 11). The answer is not 7, which would result from adding 6 and 2 before subtracting.
Negative signs require special attention. In (-3^2), the exponent applies to 3 before the negative sign, giving (-9). In ((-3)^2), the brackets make the entire negative number the base, giving (9). Include both forms only after students are comfortable with positive-number expressions.
Checking Work And Choosing The Right Version
Students should estimate an answer before calculating when possible. For (49 + 19 \times 2), an estimate of about 90 helps identify an unlikely answer such as 136. Estimation does not replace exact working, but it provides a useful reasonableness check.
The answer key should show enough detail to reveal the method without overwhelming the page. A teacher copy can include every intermediate line, while a student copy may provide a working box beneath each question. Keep the final answer visually separate so learners can check it after completing the exercise.
| Worksheet version | Suitable learner | Main skills | Example format |
|---|---|---|---|
| Foundation | Upper primary or early Year 7 | Addition, subtraction, multiplication and division | (8 + 3 \times 4) |
| Developing | Year 7–8 | Brackets and left-to-right rules | (24 \div 3 + (6 - 2)) |
| Consolidation | Year 8–9 | Powers, nested brackets and negatives | (2[4 + (3^2 - 5)]) |
| Extension | Confident secondary students | Mixed operations and algebraic thinking | (5 + 2(7 - 3)^2) |
A resource-sharing community can also help teachers compare approaches to worked examples, formatting and classroom accessibility. The education resource network is one place to explore broader ideas for presenting reusable learning materials online.
Print the worksheet on A4 paper, leave generous space for working and place the answers on a separate page. For remote learning or tutoring, save the same resource as an editable document so values can be changed without redesigning the page.
Download or create a set of order of operations exercises that matches the learner’s current level, then complete the first example together. Encourage students to write every operation in sequence, check their answer with the worked key and correct the step where the process changed direction.