Eli5, people are saying that pemdas is absolute and that 1000 / 5(4-2) = m could be either 100 or 400 because the variable m isn’t defined. Could you all elaborate on what that means?
In: 0
When you multiply something you can omit the multiplication sign. This is called implied multiplication.
For example `2×y` can be written as `2y`. Mathematicians do anything to write less symbols.
This implied multiplication is one half of the problem. The other half is the way we write divisions on one line.
If you write “proper” math you’d write divisions like this: https://i.imgur.com/AwjnAmM.gif
That expression is perfectly clear with no room for ambiquity. But when you try to write it on one line you get this: `1/2y`
And `1/2y` is ambiquous. If you do the implied multiplication first it means `1/(2×y)` but otherwise it means `(1/2)×y`.
Since mathematicians hate writing extra symbols they silently have agreed that `1/2y` means `1/(2×y)`. If you instead meant `(1/2)×y` you would just write `y/2`. Now both expressions can be written with so few symbols and mathematicians around the world are happy.
This is an unwritten rule that implied multiplication is done first. But not everyone follows that rule so you shouldn’t rely on it too much.
For example Texas instruments says this https://education.ti.com/en/customer-support/knowledge-base/ti-83-84-plus-family/product-usage/11773:
> Implied multiplication has a higher priority than explicit multiplication to allow users to enter expressions, in the same manner as they would be written. For example, the TI-80, TI-81, TI-82, and TI-85 evaluate 1/2X as 1/(2*X), while other products may evaluate the same expression as 1/2*X from left to right. Without this feature, it would be necessary to group 2X in parentheses, something that is typically not done when writing the expression on paper.
> This order of precedence was changed for the TI-83 family, TI-84 Plus family, TI-89 family, TI-92 Plus, Voyage™ 200 and the TI-Nspire™ Family. Implied and explicit multiplication is given the same priority.
Additionally the ISO-80000-2 standard says this:
> [Either[multiplication sign] can be omitted if no misunderstanding is possible](https://i.imgur.com/OwIi5Pq.png)
In the end the expression `1000/5(4-2)` is intentionally made so that misunerstanding will occur. It is not properly written. You can slap the person who presented it and demand that they rewrite it so that no misunderstanding is possible.
—-
I’d like to also point out that any and all problems with “division is done before multiplication” or “multiplication is done before division” rise from the way we write math on one line.
The single line division and multiplication combination hides what number multiplies what and that leads to confusion.
For example `2/3*5`. Without reading further quickly say what number is the `5` multiplying.
If you said that `5` multiplies `3` you are wrong.
If you write it “properly” you immediately see that `5` in fact multiplies `2`.
If you write the “proper” way as shown above you can do multiplications and divisions in any order you want and always get the exact same result. When done properly division and multiplication **always** have same “priority”.
Latest Answers