Question

The order of operations is a rule that tells the correct sequence of steps for evaluating a math expression. We can remember the order using

Answer 1

PEMDAS or BIDMAS

Explanation:

You want to know how to remember the order of operations.

Acronyms

Commonly used acronyms for the Order of Operations are ...

PEMDAS

BIDMAS

The letters of these stand for ...

P, B — parentheses or brackets

E, I — exponents or indices

M, D — multiplication and division

A, S — addition and subtraction

Precedence

Expressions enclosed in grouping symbols (parentheses or brackets) have the highest precedence. They are evaluated first, according to the order of operations.

Exponents (indices) are evaluated next. A sequence of exponent operations, such as a^b^c is evaluated right to left, as a^(b^c), unless parentheses modify the order.

Because exponents and indices have a higher precedence than other arithmetic operations, something like 2^3x is evaluated as (2^3)x, not 2^(3x), and √2p is (√2)p, not √(2p). It is fairly common to see a square root erroneously written as 3^1/2 = (3^1)/2 = 3/2 when 3^(1/2) = √3 is intended.

Multiplication and division have the same precedence. Even though M precedes D (or D precedes M, depending on which acronym you use), they are evaluated in order of appearance left to right. As with exponents, a common error is forgetting to put parentheses around numerators and denominators. For example, 3/2π is different from 3/(2π).

Similarly, addition and subtraction have the same precedence and are evaluated in order of appearance, left to right.

Composition

The composition (ring) operator (∘) is used to signify a sequence of functional or transformation operations. For example (f∘g)(x) is the composition of functions f and g. The functions or transformations in a composition are evaluated right to left:

(f∘g)(x) = f(g(x))

Special notations

Operations performed on functions can be written in confusing ways. For example, ...

`y = f^(-1)(x)\qquad\text{means }x=f(y),\text{ not }y=(1)/(f(x))`

The notation using a positive exponent stands in contrast:

`\sin^4(x)\qquad\text{usually means }(\sin(x))^4,\text{ not }\sin(\sin(\sin(\sin(x))))`

On the other hand, an exponent applied to a function name can mean recursive application of the function, as in sin²( ) = sin(sin(...)). It can also mean an n-th derivative. Context is important in such situations.