Only if you forget that multiplication happens left to right and that a(b) is simply a different way to write a×b with no other extra steps or considerations. The P in PEMDAS just means resolve what’s INSIDE the parentheses first.
That only works if everyone agrees with you, which is clearly not true.
In academic math, there’s a thing called juxtaposition. It mostly exists because math people are lazy, so instead of putting parentheses around statement e.g. 5+(2*x) they’ll just write 5+2x.
This is fine as long as you know the context of that expression. If you take it out of the context and just ask any person what is the right order of operations - it becomes ambiguous. Because some people know PEMDAS. And other people know that PEMDAS is just a simplification for middle school, when real math notation is messy, non-standard and requires a lot of local domain knowledge.
I picked example without confusion on purpose, because most people will generally avoid patterns similar to what OP posted.
But if you want something more ambigious:
This is clearly 5/(2 * (a+9)). If we write this the form that the OP uses: 5/2(a+9) - it’s fucked beyond all recognition.
I think the issue comes with “division and multiplication”, and “addition and subtraction”
Here, I see people saying “Brackets/Parenthesis > Division > Multiplication > Subtraction > Addition” when I was taught “Brackets/Parenthesis > Division or multiplication, left to right > Subtraction or addition, left to right”
2x would be the multiplication, as we go left to right you would do the multiplication, then go back and do the addition. In what world would 2x not mean 2 multiplied by the value of x?
Its the cleanest thing ever when people understand the basics of math (like what symbol, or lack there of, means what).
I think it’s a little different when you’re working with variables. A variable with a coefficient is generally treated more as a single unit compared to two plain constants being operated on in some way. It’s an incomplete operation since there’s missing information.
Only if you forget that multiplication happens left to right and that a(b) is simply a different way to write a×b with no other extra steps or considerations. The P in PEMDAS just means resolve what’s INSIDE the parentheses first.
That only works if everyone agrees with you, which is clearly not true. In academic math, there’s a thing called juxtaposition. It mostly exists because math people are lazy, so instead of putting parentheses around statement e.g.
5+(2*x)they’ll just write5+2x.This is fine as long as you know the context of that expression. If you take it out of the context and just ask any person what is the right order of operations - it becomes ambiguous. Because some people know PEMDAS. And other people know that PEMDAS is just a simplification for middle school, when real math notation is messy, non-standard and requires a lot of local domain knowledge.
That’s not lazyness. Multiplication is always done before addition. No need for parenthesis for that.
I picked example without confusion on purpose, because most people will generally avoid patterns similar to what OP posted. But if you want something more ambigious:
This is clearly
5/(2 * (a+9)). If we write this the form that the OP uses:5/2(a+9)- it’s fucked beyond all recognition.I think the issue comes with “division and multiplication”, and “addition and subtraction” Here, I see people saying “Brackets/Parenthesis > Division > Multiplication > Subtraction > Addition” when I was taught “Brackets/Parenthesis > Division or multiplication, left to right > Subtraction or addition, left to right”
2x would be the multiplication, as we go left to right you would do the multiplication, then go back and do the addition. In what world would 2x not mean 2 multiplied by the value of x?
Its the cleanest thing ever when people understand the basics of math (like what symbol, or lack there of, means what).
I think it’s a little different when you’re working with variables. A variable with a coefficient is generally treated more as a single unit compared to two plain constants being operated on in some way. It’s an incomplete operation since there’s missing information.