3  3. Order of Operations in R

NOTE: The contents of this document was adapted from https://www.datamentor.io/r-programming/precedence-associativity/

3.1 Standard numeric operators, i.e. + - * / ^

R recognizes the “order of operations” of the standard mathematical operators, (+ - * / ^). Many students are familiar with the acronym “PEMDAS” order of operations for the standard arithmetic operators (+ - * / ^). This stands for:

First: Parentheses
Second: Exponents
Third: Multiplication and Division (in the order that they appear)
Fourth: Addition and Subtraction (in the order that they appear)

2 + 6 * 5    # 6 * 5 is done first

[1] 32

(2 + 6) * 5  # (2 + 6) is done first

[1] 40

Additional operators in R

In addition to the standard mathematical operators, R recognizes numerous other “operators”. For example:

82 %/% 10 # answer is 8 as the %/% operator performs integer division  

[1] 8

82 %% 10  # answer is 2 as the %% operator results in the "remainder" of a division. 

[1] 2

As you learn R you will become familiar with many additional operators.

R defines an “order of operations” that goes beyond PEMDAS. R’s complete order of operations includes all of R’s operators. This “order of operations” is summarized in the table below. Operators that appear higher in the table have a “higher precedence” (i.e. they are done before operators that appear lower in the table).

For example, you can see that the ^ operator appears before the other arithmetic operators. Similarly, * and / appear above + and -.
However, note that %/% and %% appear above * and /. This would explain why code below produces the output that it does (read the code and the #comments)

# In the following code, 25 %% 2 is done first 
# (remember %% is remainder - so 25 %% 2 is 1 and 100/1 is 100)
100 / 25 %% 2   

[1] 100

# The parentheses in the code below changes this so that the (100/25) is now
# done first. This leads to a different answer.
# (remember %% is remainder - so 100/25 is 4 and 4 %% 2 is 0)
(100 / 25) %% 2   

[1] 0

Operator Associativity

It is possible to have multiple operators of same precedence in an expression. In this case the order of execution is determined through associativity. The associativity of operators is given in the table below. We can see that most of them have left to right associativity.

Example 2: Operator Associativity in R

The / operator is “left to right associative”. This means that 6 / 3 / 2 is evaluated as (6 / 3) / 2 due to left to right associativity of the / operator.

However, the ^ operator is “right to left associative”. This means that 2 ^ 1 ^ 3 is evaluated as 2 ^ (1 ^ 3) due to right to left associativity of the ^ operator.

6 / 3 / 2   # same as (6 / 3) / 2, because / is left to right associative

[1] 1

2 ^ 1 ^ 3   # same as 2 ^ (1 ^ 3), because ^ is right to left associative

[1] 2

However, these defaults can be changed by using (parentheses).

6 / (3 / 2)

[1] 4

(2 ^ 1) ^ 3

[1] 8

Precedence and Associativity of different operators in R from highest to lowest

The list of operators below contains the basic operators but is not 100% complete. For the full list, see the official documentation by typing ?Syntax in RStudio or see this webpage: https://www.rdocumentation.org/packages/base/versions/3.6.2/topics/Syntax

Operator Precedence in R
Operator	Description
^	Exponent
-x, +x	Unary minus, Unary plus
%%,  %/%, (and any other %% operator)	Modulus (AKA Remainder), Integer Division
*, /	Multiplication, Division
+, –	Addition, Subtraction
<, >, <=, >=, ==, !=	Comparisons
!	Logical NOT
&, &&	Logical AND
|, ||	Logical OR
->, ->>	Rightward assignment
<-, <<-	Leftward assignment
=	Leftward assignment