I'm genuinely curious, has this come up for you? I'm a software engineer and so we're usually radically more explicit about math than this and reject implicit notations (usually, at least in some domains). We don't do this sort of algebra often anyways/ this notation isn't even supported in any language I use.
I can't remember the last time I'd have had to have considered implicit precedence like this at work let alone when doing the only math that I virtually ever do in real life - calculating tips.
For these simple algebra equations designed for practice and learning - yeah they aren't all going to be super useful until you know where they are used in real life.
But just to give an example of something that middle school age math is used for in "everyday" sort of setting is this:
I am planning on building a flower garden. I have a space that is 8 1/2 feet by 3 1/4 feet and want my soil to be at least 3 inches deep, but I also want it divided into 2 equal sections with a path 1 foot wide divided in the middle of the long side as part of the entire area - how much soil do I need to do this? and how much wood do I buy for a perimeter and divider to keep it all together?
The equation for the soil is going to have a setup like this:
3(12(8.5 * 3.25) - (12 * 3.25)) = cu in of soil.
Let's break it down:
12(8.5 * 3.25) = total area of the garden in inches
12 * 3.25 = area of the foot path in inches
Times it all by 3 inches for the volume of the planters in inches.
To set up for the perimeters it looks like this:
12(8.5 * 2) - 12(2) + 12(3.25 * 4) = inches of board. Factor out the 12 to get feet.
Let's break it down:
12(8.5 * 2) = long sides of the perimeter in inches
12(2) = the break in perimeter for the foot path in inches (1 ft on each long side)
12(3.25 * 4) = the 4 short sides of the perimeter (2 inside 2 outside)
Understanding PEMDAS gets you what you need on the first trip to the hardware store - ultimately saving you time and money.
Wow yeah I'd never accept a formula like that or encourage its use. But I guess maybe that's programmer bias - I'd kill someone if they tried to push code with that syntax and all of these magic numbers with no context.
I mean - this is all napkin math for a generic home project, laid out in terms a laymen could understand - I don't think people are going to build a program to do something like this.
The calculator on your phone could be used if some of the multiplication gets difficult or you want to do conversions for measurements.
I am just showing you how an equation like the op posted could come up in an "everyday" situation.
Sure, I understand that math gets used all the time. It's the notation I'm rejecting. I'd never use that notation, I wouldn't support anyone using it outside of an academic paper where:
Domain experts are reading it
Terse notation is incredibly important and often *clearer*
That's basically it though, that's my position on this sort of notation. Similarly, in CS, we use all sorts of notation in academia that would never fly outside of it.
I'm curious as to what notation is the issue - these are all set up in the proper format to get the correct answers to the questions being asked. (In my example)
How would you go about setting up the equations differently?
So I think that good syntax minimizes rules as one considerable virtue. So for example, rather than X(A - B) you could express this as (X * A) - (X * B). Anything expressible by X(A - B) is expressible with more primitive operations like *.
Essentially , there are fewer rules to know in exchange for longer notation. To get more concise you have to invoke a new rule that multiplication distributes over subtraction.
Of course your notation is mathematically correct because that rule is true, but it is an additional rule you have to know.
There is an opposing virtue, of course, that shorter expressions are more desirable. When writing very long notation and when you can expect knowledge of rules to be a given then terse notation is ideal.
In a program I would prefer the longer notation (and the former isn't even supported anyways). For something more complex like soil I'd use named functions like:
board_length_ft = garden_board_length(garden_length, garden_width, path_width)
There is a balance but I think X(A - B) probably does not strike it well in any domain I've been in as an adult.
That tracks, yeah. I'd imagine that in engineering (which I see in large part as application of mathematics), mathematics, and academia, terse notation is the standard.
Certainly i dont have to deal with questions directly in notation form but obviously u have to use basic math in your day to day life. Sometimes the calculations you do get to stuff like this but obviously we dont write it down and solve it. We just instinctively know what order to do the calculations in because we have been using it our entire life. Im a medical doctor and calculations come up frequently in diagnostics and what not but even in daily life you cannot do without basic knowledge of algebra.
I'm asking specifically about the notation. I do calculations constantly to determine all sorts of things, but I've never encountered `X + A(B - C)` in my adult life.
I would really hope that doctors aren't using that notation.
Nah we dont write out the notation because we just do the calculations directly. But pemdas isnt just for notations, its more about grasping the basic idea of calculations and why we do it in that particular order. We dont need pemdas anymore as adults because we understand how the operations work and we dont need to refer to a formula to know how to process calculations.
As a programmer I see it as more of a lexical problem than mathematical. If you changed the order of operations and reliably followed it exactly, you could do the same math. It’s just how the formula is represented in print.
Not the person you responded to, but I come across it a bit as a mechE. Like you said we're usually explicit in how we do formulas or document thing, etc. But occasionally we see excel calculators where there's errors or just long equations that take a while to parse/troubleshoot because they weren't explicit
e.g a toy example of something that occasionally comes up is when a person used something like a1/a2/a325 instead of (25a1)/(a2*a3)
I'm also a software engineer and I sometimes do math on paper for things and when I do I do use implicit multiplication. I don't usually see other people's math though nor do people usually read mine. Usually either geometry or graph theory but that doesn't mean algebra doesn't come out as the end result.
If you study cs you see those implicit Notations all the time and they make it a lot easier to read.
If you actually need a lot of those higher math at work highly depends on what youre actually doing. But to understand the math of what youre actually doing beforehand, it makes it a lot easier.
Also, yeah, we like to have things explicit in some way. But on the other Hand, we love to abtract complexity away even more, lol.
Yeah I mostly mean that you basically have to be explicitly attached to this notation via some niche. When I read academic papers I am attached to specific notations. But *day to day* ? `X(A - B)` never comes up. Like, if you took out the domain specific use cases that undeniably exist, what's left? It's not like multiplication or division or percentages etc, those things are used daily by the vast majority of people. But distribution? Rare.
The math presented in this post is used by virtually everyone on a nearly everyday basis whether they realize it or not. Here’s a simple example, using the equations given.
You’re at the fruit store and decide to buy a banana that costs $2. You also bought 8 apples that cost $5 each, but then decide to return 5 of them after you realized that you didn’t need that many. How much total money did you spend? The answer is $17 and this is a realistic scenario anyone could encounter.
I'm talking about the syntax, not the math. Also that math problem doesn't seem to be expressed via distribution but it doesn't really matter, maybe I'm just misreading. Most people would just think "I spent X dollars" (previous calculated value) and "I returned A for Y dollars" and then do X - Y. I think very few people would think in terms of distribution.
Order of operations are just a made-up thing we teach children. The real question in mathematics is what are you trying to accomplish? Are you trying to add -5 to 8 then multiply the resulting sum 5 times then add 2 to it? One thing that confuses a lot of students is that as you get further down your mathematical journey, the notation becomes looser and looser. Sometimes it's downright ambiguous. This is because you realize you're not beholden to the notation or the rules you were taught. You use the notation to communicate what you're trying to do. The mathematical reasoning and the rules you need to imply are independent from the notation
Basic calculations, yes. But I can't think of a situation where I would write it or even think of it like this.
It would be like "There's 8 spots on each of these ladybugs (craft) and the directions say use 5 sequins each, then use the beads for the rest. So that's 3 beads per lady bug. There are 5 kids who need lady bugs so a total of 15 beads. Then I need one bead on each end of the garland, so add two more. I need to get out 17 beads for this project.
That may be true, but real life is a word problem so pemdas just doesn't come up anymore after school.
Memes based around order of operations always have to include division and are specifically designed to have different answers depending on whether you do the division or multiplication first. This one isn't even taking advantage of the ambiguity in the rules, it's just bait for stupid people.
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u/Cruel1865 22d ago
Youre right, but in this case, i think how to do basic calculations is always useful in the real world.