It’s BE(D=M)(A=S). Different places have slightly different acronyms - B for bracket vs P for parenthesis, for example.
But, since your rule has the D&M as well as the A&S in brackets does that mean your rule means you have to do D&M as well as the A&S in the formula before you do the exponents that are not in brackets?
But seriously. Only grade school arithmetic textbooks have formulas written in this ambiguous manner. Real mathematicians write their formulas clearly so that there isn’t any ambiguity.
Grade school is a US synonym for primary or elementary school; it doesn’t seem to be used as a term in England or Australia. Apparently, they’re often K-6 or K-8; my elementary school was K-4; some places have a middle school or junior high between grade school and high school.
I don’t know why you’re getting lost on the pedantry of defining “grade school”, when I was clearly discussing the fact that you only see this kind of sloppy formula construction in arithmetic textbooks where students are learning the basics of how to perform the calculations. Once you get into applied mathematics and specialized fields that use actual mathematics, like engineering, chemistry and physics, you stop seeing this style of formula construction because the ambiguity of the terms leads directly to errors of interpretation.
I was taught that division is just inverse multiplication, and to be treated as such when it came to the order of operations (i.e. they are treated as the same type of operation). Ditto with addition and subtraction.
afair, multiplication was always before division, also as addition was before subtraction
It’s BE(D=M)(A=S). Different places have slightly different acronyms - B for bracket vs P for parenthesis, for example.
But multiplication and division are whichever comes first right to left in the expression, and likewise with subtraction.
Although implicit multiplication is often treated as binding tighter than explicit. 1/2x is usually interpreted as 1/(2x), not (1/2)x.
a fair point, but aren’t division and subtraction are non-communicative, hence both operands need to be evaluated first?
It’s commutative, not communicative, btw
whoops, my bad
1 - 3 + 1 is interpreted as (1 - 3) + 1 = -1
Yes, they’re non commutative, and you need to evaluate anything in parens first, but that’s basically a red herring here.
ok, i guess you’re right
But, since your rule has the D&M as well as the A&S in brackets does that mean your rule means you have to do D&M as well as the A&S in the formula before you do the exponents that are not in brackets?
But seriously. Only grade school arithmetic textbooks have formulas written in this ambiguous manner. Real mathematicians write their formulas clearly so that there isn’t any ambiguity.
That’s not really true.
You’ll regularly see textbooks where 3x/2y is written to mean 3x/(2y) rather than (3x/2)*y because they don’t want to format
3x ---- 2yproperly because that’s a terrible waste of space in many contexts.
That’s what I said.
You generally don’t see algebra in grade school textbooks, though.
12 is a grade. I took algebra in the 7th grade.
Grade school is a US synonym for primary or elementary school; it doesn’t seem to be used as a term in England or Australia. Apparently, they’re often K-6 or K-8; my elementary school was K-4; some places have a middle school or junior high between grade school and high school.
I don’t know why you’re getting lost on the pedantry of defining “grade school”, when I was clearly discussing the fact that you only see this kind of sloppy formula construction in arithmetic textbooks where students are learning the basics of how to perform the calculations. Once you get into applied mathematics and specialized fields that use actual mathematics, like engineering, chemistry and physics, you stop seeing this style of formula construction because the ambiguity of the terms leads directly to errors of interpretation.
Multiplication VS division doesn’t matter just like order of addition and subtraction doesn’t matter… You can do either and get same results.Edit : the order matters as proven below, hence is important
If you do only multiplication first, then 2×3÷3×2 = 6÷6 = 1.
If you do mixed division and multiplication left to right, then 2×3÷3×2 = 6÷3×2 = 2×2 = 4.
Edit: changed whitespace for clarity
2nd one is correct, divisions first.
4 would be correct since you go left to right.
I was taught that division is just inverse multiplication, and to be treated as such when it came to the order of operations (i.e. they are treated as the same type of operation). Ditto with addition and subtraction.