Home

Maths

Number

Order of operations: BODMAS

Select Lesson

Exam Board

Select an option

Statistics

Sets and Venn diagrams

Sampling and bias

Collecting data: types and classes of data

Mean, median, mode and range

Simple charts and graphs

Pie charts

Scatter graphs

Frequency tables: finding averages

Grouped frequency tables

Box plots - Higher

Cumulative frequency - Higher

Histograms and frequency density - Higher

Interpreting data

Comparing data sets

Probability

Basics of probability

Calculating theoretical probabilities

Probability: Expected and relative frequency

The AND / OR rules

Probability tree diagrams

Conditional probability - Higher

Experimental probability: frequency trees

Trigonometry

Pythagoras' theorem

Sin, cos, tan

Trigonometry: Finding angles and sides

Exact trigonometric values

Sine and cosine rules - Higher

3D Pythagoras - Higher

3D Trigonometry - Higher

Vectors

Vectors - Higher

Angles and geometry

Angles: types, notation and measuring

Basic angle rules

Angles in parallel lines

Circle theorems - Higher

Constructing triangles: SSS, SAS, ASA

Construction: angle and perpendicular bisectors

Construction: Loci

Bearings

Maps and scale drawings

Shapes and area

Properties of 2D shapes

Congruence: conditions for congruent triangles

Similar shapes: Scaling

The four transformations

Area and perimeter: Formulae

Area and circumference of circles: Formulae

3D shapes: faces, edges, vertices

Surface area of 3D shapes: Nets, formulae

Volume of 3D shapes: Formulae

Volume of 3D shapes: Comparing, rates of flow

Area and volume scale factors

Projections and elevations of 3D shapes

Ratio proportion and rates of change

Ratio

Direct and inverse proportion

Finding percentages and percentage change

Compound growth and decay

Converting units: metric and imperial

Converting units: area and volume

Time intervals: converting units of time

Speed, density and pressure: Formulae and units

Graphs

Coordinates and midpoints

Straight line graphs

Drawing straight line graphs

Finding the gradient of a straight line

Equation of a straight line: y = mx + c

Coordinates and ratio

Parallel and perpendicular lines

Quadratic graphs

Reciprocal and cubic graphs

Exponential graphs and circles - Higher

Trigonometric graphs - Higher

Solving equations using graphs

Graph transformations - Higher

Real-life graphs

Distance-time graphs

Velocity-time graphs - Higher

Gradients of real-life graphs - Higher

Algebra

Number

Explainer Video

Tutor: Alice

Summary

Order of operations: BODMAS

In a nutshell

BODMAS is used in multi-step calculations and when questions have a few different operations. BODMAS is an acronym for the order of operations, with the priority order of each operation.

BODMAS

BODMAS stands for Brackets, Other, Division, Multiplication, Addition, Subtraction.

Priority	BODMAS	Symbol
1	Brackets	$()$
2	Other	$\sqrt{x},\, x^n$
3	Division	$\div$
3	Multiplication	$\times$
4	Addition	$+$
4	Subtraction	$-$

Note: When there is both multiplication and division, or addition and subtraction in the question, you work from left to right.

Procedure

Calculate the value inside the brackets.
Calculate the value of any terms raised to a certain power.
Calculate the value of any terms being multiplied and/or divided.
Calculate the value of any additions and/or subtractions.

Example 1

Calculate the positive solution to $(26 - 18) \times \sqrt9$

First calculate what is inside the brackets:

$(26 - 18) = 8$ 

Secondly calculate the other operation, such as square root of $9$ :

$\sqrt 9 = 3$

Lastly multiply the results together:

$8 \times 3 = 24$ 

Therefore, the answer is $(26 - 18 ) \times \sqrt9 = \underline{24}$ 

Note: The reason the question specifies 'positive solution' is because, strictly speaking, $\sqrt{9}=\pm3$ . $-3$ is also a solution to $\sqrt{9}$ which would yield a 'negative' solution to the question also.

Example 2

Evaluate the positive solution to $\dfrac{\sqrt{(8-4)}\times15}{2^3+7}$

First calculate what is inside the brackets:

$8-4 = 4$

Calculate the other operations such as square root then the indices:

$\sqrt4 = 2\\ 2^3= 8$

Now the fraction becomes:

$\dfrac{2 \times 15}{8 +7}$

Now you may want to carry out this fraction first as it is division but in this case treat each the numerator and denominator like they have separate brackets:

$\dfrac{(2 \times 15)}{(8+7)} = \dfrac{30}{ 15}$ 

Calculate the final division:

$\dfrac{30}{15}= 2$

Therefore the positive solution to $\dfrac{\sqrt{(8-4)}\times15}{2^3+7} = \underline{2}$

Learn with Basics

Length:

Unit 1

Order of operations: BIDMAS

Unit 2

Order of operations: BIDMAS

Jump Ahead

Optional

Unit 3