# Rules and Properties of Arithmetic Operations

### Associative/Distributive/Commutative Properties

### Video

This video from *Krista King* describes the associative property of addition and multiplication, and gives a worked example of the property in action.

Note: All *Krista King* content is available for free at www.youtube.com/c/Integralcalc.

Krista King’s Website: www.kristakingmath.com .

This video from *Krista King* describes the commutative property of addition and multiplication and gives some examples of using commutativity to compute a result in two different ways.

Note: All *Krista King* content is available for free at www.youtube.com/c/Integralcalc.

Krista King’s Website: www.kristakingmath.com .

This video from *Khan Academy* shows how the distributive law of multiplication over addition works, and how the same result can be achieved in two different ways. It also gives a pictorial interpretation of the law for the given example.

Note: All *Khan Academy* content is available for free at www.khanacademy.org.

### Notes

These notes from MathCentre discuss the associativity, commutativity and distributivity of multiplication, and gives both numerical and algebraic examples. There are also exercises for you to try with the answers given so you can check your work.

A pdf of this document can be downloaded here.

### The Order of Operations

### Video

This video from *patrickJMT* shows the order in which the standard arithmetic operations are to be performed, given an expression, and gives an example of a common mistake made by not considering brackets.

**Please note**: The term “PEMDAS” used in the video is also known as BEMDAS, BIMDAS, BODMAS, or BOMDAS, among other similar names. These are all just different names for the same concept.

Note: All *patrickJMT* content is available for free at www.youtube.com/user/patrickJMT.

Patrick JMT’s Website: www.patrickjmt.com.

This second video from *patrickJMT* gives more examples of computing answers using the order of operations, including a more ambiguous example.

**Please note**: The term “PEMDAS” used in the video is also known as BEMDAS, BIMDAS, BODMAS, or BOMDAS, among other similar names. These are all just different names for the same concept.

Note: All *patrickJMT* content is available for free at www.youtube.com/user/patrickJMT.

Patrick JMT’s Website: www.patrickjmt.com.

### Notes

Pages 2-3 of these notes from MathCentre show how to evaluate expressions using the rules of the order of operations. You can also find exercises near the end of page 3, with answers to these at the end of the document so you can check your work.

**Please note**: The term “BODMAS” used in these notes is also known as BEMDAS, BIMDAS, BOMDAS, or PEMDAS, among other similar names. These are all just different names for the same concept.

A pdf of this document can be downloaded here.

### Interactive Exercises

Please try this NUMBAS exercise to test what you’ve learned about the order of operations. You can interpret the term “ordinals” to mean “powers”, “indices”, or “exponents”.

**Please note**: The term “BODMAS” used in this exercise is also known as BEMDAS, BIMDAS, BOMDAS, or PEMDAS among other similar names. These are all just different names for the same concept.

Please click here to view this NUMBAS question in another window.