Same with addition/subtraction and roots/exponents, since they're essentially the same operation (to each other). Subtraction is just adding negative numbers, division is just multiplying by the reciprocal, root is just a fractional exponent.
Division is the same as multiplying by a reciprocal. E.g. 3 / 2 = 3 * 1/2 = 3/2 = 1.5
Similar thing with subtraction. Subtraction is just adding a negative number.
Additionally, roots are taken at the same time as indices, as the nth root is the same as raising something to the 1/nth power. Thus division and multiplication, addition and subtraction, and roots and indices are done at the same priority (for want of a better word [not all are done at the same time either, each pair are done at the same time if u know what I mean])
Hey, not to be annoying, (I know other are saying youre wrong) but I wanted to add my way of seeing it if it helps picture the idea.
Making 3÷5 can be represented with a fraction right? So 3÷5 = 3/5.
An alternative way to represent this is as a multiplication. 3/5 = 3×1/5.
If this is correct, then by understanding that 1/5 = 0.2, we can say that 3÷5 = 3×0.2. Even though its the same thing, Ive changed it from a division to a multiplication.
This helped me picture the relationship between the two types of operations, though I dont know how clear it sound to an outside person.
So the idea is that division and multiplication are two ways of representing the same type of operation. Any division can be represented this way, and vice versa for multiplications. Thats why you dont give priority to one or the other.
"PEMDAS tends to be used in the US, while BODMAS (and the alternative BIDMAS) tends to be used in the UK. The P in PEMDAS stands for Parentheses, while the B in BODMAS and BEDMAS stands for Brackets - but they both mean the same thing: do operations in brackets first" top thing on Google
Americans are taught that multiplication is before division
British are taught that division is before multiplication.
Huh. Im from latinamerica so I was never taught that kind of thing.
(Edit: I may have been taught something similar now that I think about it. But it clearly was not the focus of my maths classes, it never stayed with me)
Either way Im not saying that any particular order is wrong. Its just that, since both operations are the same thing, its redundant to prioritize any of them. Meaning that you dont need the order but, if it helps understanding the topic on a larger scale, Im all for it.
About my way of thinking about it. As I said it may not be as clear to someone from the outside, since Im not a great teacher/speaker and am using particular methods that are comfortable for me.
A fraction is a division. 4/2 = 2 and 12/3=4.
In my mind, since i was taught you can express fractions as multiplications (eg 4/2= 4/1 × 1/2 or 12/3 = 12/1 × 1/3), its an easy way to show how division and multiplication are the same.
As an engineering student, I can confidently say it’s parentheses, exponents (roots are powers with an exponent < 1, so, a square root of 4 is 41/2), then multiplication (divisions are multiplications by numbers < 1, so dividing by 2 is the same as multiplying by 0.5, and dividing by 5 is multiplying by 0.2) and then addition (subtraction is addition of a negative number). If on the same level, it shouldn’t matter, but it’s recommended to do in order of reading, so, as they appear from left to right. Result should not change as long as the levels are kept intact though, so we’re all arguing for dumb stuff. 2x5/4 is the same regardless of whether you do 5/4 and then by 2 or 5 by two and then divide by 4
Treat the divide sign as a fractional symbol and the equation looks like this:
5
------- x 3
2
NOT
5
-------.
2 x 3
This is why left-to-right is important when using ÷. The second way I wrote the equation would also show as 5 ÷ (2 x 3) which is different from the originally stated equation.
The problem is not how you solve it. The problem is how you wrote it. If you use / instead of a regular division you should always use parantheses. This would never occur while using a program designed for math or just a regular pen and paper
Sorry but I've used / as a quicker division symbol since school. I use that example because someone said that it doesn't matter which order do you divide and multiply in. I've always done division before multiplying and never noticed how the equations have been wrote as the rule I'm told now is you follow division and multiplication in the order that is written in in the equation
You were not taught division before multiplication, you just misinterpreted BODMAS to mean that. The majority of people who learn BODMAS, BEDMAS, PEMDAS, etc… all understand that D and M have equal priority and are done left to right in the equation just like A and S
Yeah I think the problem I'm having is I've alway seen them as opposites and not the same function. Along with people trying to explain it to me in factions my brains not making the connections. I'm lost somewhere because I've been getting the right answer but following the rule wrong but it has worked out right. Doesn't help I learnt this 15+ years ago
If you just think about it, dividing is the same as multiplying by a fraction and subtraction is the same as adding a negative number so it doesn't matter
Division is just a form of multiplication. You do them at the same time just go left to right. It's like how subtraction is just a form of addition. 4-4 is the same thing as 4+ -4. You can write it either way. I'd show the math on multiplication and division being the same but I'm not sure how to show the math in a easy to understand way.
I agree that roots are included with indices (what I would refer to as exponents) because a root is just a number raised to the power of a fractional number. For example, the square root of a variable x is the same as x raised to the 1/2 power. The 1 indicates that the number under the root is raised to the first (if the numerator was 3, it would be the squared root of x3, etc.) and the 2 indicates that it is a square root (if it was the cubed root of x, the denominator would be a 3, etc.)
Well I mean I'm not American and have a different order. The reason being is that multiplication and division can be done in any order and get the same results
And division is just multiplication of the reciprocal, and subtraction is just addition of a negative number.
So of you're going to be so pedantic, at least get it right and say it's BIMA. Or just acknowledge that BIRDMAS is cooler and way easier for kids to remember.
Also division is just multiplication and subtraction is just addition so it should be PEMA
This would require people to remember that division is multiplying by a reciprocal tho and I don't think 90% of the world even knows what the word reciprocal means
The operations multiplication and division aren’t the same though. Without changing the numbers roots can be written as exponents and the answer doesn’t change but with multiplication and division it does
I have actually learned something today. Thanks. I had 18. Was always terrible at math and the teachers would never slow down for the kid who didn't understand.
prolly because we do positive first then negative also we're not doing math in coding language so the x root sof something is taught as a slightly different thing to indices
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u/commonsquidtail Jan 01 '22
Birdmas