# Does PEMDAS Apply to All Math Equations?

• MHB
• SigmaS
In summary, PEMDAS is a convention used in math to prevent ambiguity, but in higher level math, it may not always be followed due to the complexity of the equations. However, it is still generally applied and serves its purpose. When rewording equations, PEMDAS is still relied upon, and it is important to use parentheses to avoid any ambiguity. Overall, PEMDAS is an international convention that helps us understand mathematical expressions without having to use excessive parentheses.
SigmaS
I was told PEMDAS isn't always followed, particularly in higher level math.
Is this true? Because I recall the purpose of PEMDAS is to prevent ambiguity, and without it, at any level, would result in ambiguity, even though it's just a convention and not something we can really prove.

Also, when you reword equations are you still relying on the concept of PEMDAS? Like, for example, to say $\frac{5}{3}n=15 \equiv 5n=45$ is to validate PEMDAS, yes?

SigmaS said:
I was told PEMDAS isn't always followed, particularly in higher level math.
Is this true? Because I recall the purpose of PEMDAS is to prevent ambiguity, and without it, at any level, would result in ambiguity, even though it's just a convention and not something we can really prove.

Also, when you reword equations are you still relying on the concept of PEMDAS? Like, for example, to say $\frac{5}{3}n=15 \equiv 5n=45$ is to validate PEMDAS, yes?

Hi SigmaS, welcome to MHB! ;)

In higher level math we don't always deal with regular multiplication and addition.
Even then, PEMDAS is usually applied, since it does indeed eliminate ambiguity without being wordy about it.
And yes, this is international convention, so we can always assume it.

In $\frac{5}{3}n=15$ there is no ambiguity. The division is specified in such a way that it has to come first - as if it was in parentheses. So PEMDAS is irrelevant here. It only becomes relevant when we type it into a calculator, because then PEMDAS requires us to use parentheses. That is, we have to type [M]( 5 / 3 ) * n[/M] to get what was written.

Anyway, there is no need to 'validate' PEMDAS. It's just a rule that says when parentheses can be omitted without changing the expression.
The parentheses cannot be omitted in for instance $5/(3\times n)$, because $5/3\times n$ means something different.
It's different with $(5/3)\times n$, since that is the same as $5 / 3 \times n$.
In case of doubt, we should add parentheses first — according to PEMDAS — and then reword the equation.

## 1. Does PEMDAS apply to all math equations?

Yes, PEMDAS stands for the order of operations in math, which should be followed in all equations to ensure accurate results.

## 2. What does PEMDAS stand for?

PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right). This is the order in which operations should be performed in an equation.

## 3. Can PEMDAS be used in equations with only addition and subtraction?

Yes, PEMDAS still applies to equations with only addition and subtraction, as these operations should be performed in order from left to right.

## 4. Is PEMDAS the only way to solve math equations?

No, there are other methods and strategies for solving equations, such as the distributive property, factoring, and substitution. However, PEMDAS is a fundamental rule that should be followed in all equations.

## 5. Do I always have to use PEMDAS in the same order?

Yes, PEMDAS should always be followed in the same order. This ensures consistency and avoids confusion in solving equations.

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