My immediate thought is definitely “no”… Your follow-up is exactly how I would do that, 2a/3, but perhaps that doesn’t exactly teach a concept to a learning-age child? Otherwise I would use parentheses, (2/3)a. But I admit to programming bias, there.
(2/3)a is acceptable, I believe? Hard to misread it that way. Or just write it ‘fully typeset’, only smaller so it fits in line.
According to the link above, out of 60 students (in Harvard, 2014) asked to compute “2x/3y-1 with x=9 and y=2 ,” 58 got 2, and two got 18/5. That is the reality you must deal with.
You’re not wrong. But I still prefer to at least attempt to teach the students what they need to know, even if our culture encourages them to immediately forget it.
And teaching right now is hard enough, with high schoolers. Anyone who manages to get meaningful education to kindergartners under these conditions deserves a Nobel Prize.
I don’t use any computer math systems so I can’t speak to those, but that would be a syntax error in all programming languages that I’m familiar with. All of them require the explicit multiplication, so 2/3*a. That looks different to my eyes than the implicit version.
Of course, in many languages, that expression is exactly equivalent to “a”. Evaluating left-to-right, the 2/3 is performed first in integer math, resulting in 1, which gets multiplied with a. a*2/3 is more likely to give the result you want.
Huh–turns out that some (once popular) calculators treat 2/3a as 2/(3a):
Solution 11773: Implied Multiplication Versus Explicit Multiplication on TI Graphing Calculators.
Does implied multiplication and explicit multiplication have the same precedence on TI graphing calculators?
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/(2X), while other products may evaluate the same expression as 1/2X 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™ Handheld in TI-84 Plus Mode. Implied and explicit multiplication are given the same priority.
That said, I’m not sure TI did students any favors when their own products can’t be trusted to behave consistently across the lineup.
Doing my best…
(7/2 - 2) = (7/2 - 4/2) = 3/2, so the equation is now 8 +4^2 ÷ 3/2
4^2 = 16, 16+8 = 24, so the equation is now 24 ÷ 3/2
24 ÷ 3/2 = 24 x 2/3 = 48/3 = 16
My answer is 16. I followed the convention of doing everything in parentheses first. I considered the 16+8 to be the numerator of a fraction and the 2/3 to be the denominator. Right or wrong, if I were being tested, I would answer 16.
I hope I have helped you
Uh, I can’t math today. 2/3 gets rounded down to zero in most languages. Still not the result you probably want, though 
.
This just illustrates what I wrote a few posts up: The / is used instead of the horizontal bar in order to write a fraction on one line, BUT the problem is that / doesn’t really have the same semantics as the horizontal-line format of a fraction.
When I learned algebra, starting in 9th grade in 1965, we learned the symbols of grouping: ( ), (that’s supposed to be left and right square brackets), and { } AND also, that a horizontal bar above or below part of an expression is also a symbol of grouping.
The book had many sample problems to work that made use of that, in ways that you would NEVER EVER see elsewhere. But the point (that the textbook never explicitly mentioned) was the use of the horizontal bar in fractions, and also the horizontal bar in writing radicals with the entire radicand under the bar. In those uses, the horizontal bar does serve double-duty as a symbol of grouping, while the slash / does not.
The issue is always opportunity cost. Complex abstract concepts can be taught, but they take time. So what do you cut out of Alg 1 to make a couple weeks to really dig into notation?
To the wider point: Google Classroom and Google Forms have basically no formating options. You can’t bullet, bold, anything. You can attach a Google doc, but then you have to grade by hand (which this teacher may well be doing for other assignments). Of she’s using Google as her main platform (and I think most of us are), it really sucks for math.
Agreed. I don’t expect them to be able to teach this to all kids at the primary school level. I think if you can, and if your child takes to it, its a fantastic form of additional enrichment you can take-- deep dive into this kind of stuff.
Does this help the OP in any way?
The OP’s question was answered a long time ago and the discussion moved past that already. Who shat in your cornflakes?
Sorry, I don’t follow what point you’re making here - it seems to me the vast majority are getting the ‘correct’ answer on that basis, and the 2 that didn’t have interpreted the calculation in a way that isn’t entirely unreasonable. Either way there is no reason not to add some parentheses to make things unambiguous.
The point is that none of the 60 humans got the computerised answer, even though ‘everyone nowadays uses computers.’ Secondarily, that not everyone got the same answer. Therefore, absolutely, some parentheses or some reformatting may be necessary.
Oh, sure, a few extra sets of parentheses never hurt anyone. When in doubt, make things less ambiguous.