This cheat sheet helps students remember the correct order to calculate expressions using BODMAS. It is useful when a question has more than one operation, such as brackets, multiplication, and addition. Without a clear order, the same expression could seem to have different answers.
BODMAS gives everyone the same agreed method.
BODMAS stands for Brackets, Orders, Division, Multiplication, Addition, and Subtraction. Brackets are completed first, then powers or roots, then division and multiplication from left to right, then addition and subtraction from left to right. Division does not always come before multiplication, and addition does not always come before subtraction.
The left-to-right rule is very important for operations on the same level.
Key Facts
- BODMAS means Brackets, Orders, Division, Multiplication, Addition, and Subtraction.
- Always calculate inside brackets first, such as .
- Orders mean powers and roots, such as and .
- After brackets and orders, do division and multiplication from left to right, such as .
- After division and multiplication, do addition and subtraction from left to right, such as .
- Multiplication and division have equal priority, so use the one that appears first from the left.
- Addition and subtraction have equal priority, so use the one that appears first from the left.
- For , multiply first, so .
Vocabulary
- BODMAS
- BODMAS is a memory aid for the order of operations: Brackets, Orders, Division, Multiplication, Addition, and Subtraction.
- Brackets
- Brackets group part of an expression so it must be calculated first, such as .
- Orders
- Orders are powers and roots, such as and .
- Operation
- An operation is a mathematical action such as , , , or .
- Expression
- An expression is a mathematical phrase made from numbers, symbols, and operations, such as .
- Left to right
- Left to right means solving operations with equal priority in the order they appear from the left side of the expression.
Common Mistakes to Avoid
- Adding before multiplying is wrong because multiplication has higher priority than addition, so is , not .
- Doing division before multiplication every time is wrong because and have equal priority and must be worked from left to right.
- Doing addition before subtraction every time is wrong because and have equal priority and must be worked from left to right.
- Ignoring brackets is wrong because brackets change the order, so but .
- Forgetting that powers come before multiplication is wrong because orders are done before and , so .
Practice Questions
- 1 Calculate .
- 2 Calculate .
- 3 Calculate .
- 4 Explain why should be worked from left to right instead of doing first.
Understanding Order of operations (UK form) (BODMAS) Memory Aid
An expression is like a set of instructions built from smaller jobs. The safest method is to find one job that can be completed, work it out, and replace it with its answer. This keeps the original structure visible.
For example, in eight plus three times four, the multiplication becomes twelve first. The expression then becomes eight plus twelve.
Writing each line helps prevent skipped steps. It also makes it easier for a teacher, classmate, or your future self to see exactly where an error began.
Brackets can contain several operations, so they need their own careful working. If one set of brackets is inside another set, start with the innermost part. Work outward one layer at a time.
A fraction bar can act like brackets too. The whole top part of a fraction is grouped together, and the whole bottom part is grouped together. This matters later when fractions appear in algebra and science.
A negative number needs care as well. A minus sign can mean subtraction, or it can be part of a number such as negative five. Clear handwriting and spacing make these meanings much easier to spot.
Order of operations appears in everyday calculations whenever a total is built from parts. A shop problem may involve working out the cost of several identical items before combining that cost with a delivery charge. In geometry, you may calculate the area of one shape before adding it to the area of another.
In science, formulas often require a value to be squared or grouped before the rest of the calculation is done. Calculators usually follow the standard order, but they only use the expression that was entered. Brackets on a calculator are useful for showing the structure you intend, especially in a long calculation.
Many mistakes come from rushing rather than from difficult arithmetic. Students may work from left to right through every symbol, or assume that multiplication must always be done before division. Another common mistake is doing only part of what is inside brackets before moving on.
Build a habit of circling brackets, marking powers, then scanning for multiplication or division before looking at addition or subtraction. Estimate the size of the answer before finishing. If several numbers are being multiplied, the result should often grow.
If a large number is divided, it should become smaller. Estimation will not prove every answer, but it can reveal an answer that does not make sense.