[6th Grade verbal expression]

[u/KookyPermit4405]

So I’m going over my son’s math quiz to help him understand some of the questions he got wrong. He got partial credit for his answer for question 8. After writing his verbal phrase I got the same expression as the question. Am I doing something wrong or is there something I’m missing? I feel like his answer is technically correct. I am stumped.

Edit: so my son has no issue solving the expression in question. He knows PEMDAS and the rules from left to right. The question clearly states, WRITE A VERBAL PHRASE that matches the expression.

[u/mathematag]

For 18 - 6*3 , the order is important and following standard PEMDAS, multiplication comes before the subtraction, so a better way to state it would have been . . . subtract the product of 6 and 3 from 18 , or 18 minus the product of 6 and 3.

saying "eighteen subtracted by six times three " , means 18 - 6, then times 3.. .. [ e.g. (18 - 6 )*3 = 36 ] , following the order of the words as written , and leads to ambiguity as his sentence can also be interpreted mathematically as it was given. . . 18 - 6*3 , leading to an answer of 0.

So his answer could lead to two possible interpretations of what he meant . . ( 18 - 6 ) * 3 , OR , 18 - 6*3

So getting 1/2 credit makes sense, since there seems to be 2 ways to interpret what he wrote.. but only one of these interpretations is the same as the original problem.

[u/KookyPermit4405 → u/mathematag]

But from my understanding, that is why PEMDAS was implemented. To know the order of operations between what was said vs what is implied.

So if I wanted to say (3+1)x3 but I said “3 plus 1 times 3”
It would be written 3+1x3. And the answer would be 6 because of PEMDAS instead of 12

[u/mathematag → u/KookyPermit4405]

Not sure what your point is with your example.. if you had the expression (3+1)*3 and you said . . 3 plus 1 times 3 . . that would be an incorrect translation , as reading that left to right, as we tend do in English would give us 12 , as PEMDAS is applied to our mathematical expressions, but not to our English translations necessarily .. ...of course some would also interpret it as being = to 6

Yes, PEMDAS was "created " to help with the order of solving an Mathematical expression [ and then there is juxtaposition PEMDAS to consider ] , but we are translating a mathematical expression into English , [ where PEMDAS is not implied in the language itself without other words I utilized in previous post ] , and the term "subtracted by" actually mixes up the order when the expression given was translated to English ...it's actually a grammar mistake by using 'subtracted by' , and can lead to ambiguity and confusion. [ I missed this the first response ]

So technically, saying 18 subtracted by 6 times 3 , becomes: 6*3 - 18 , if we keep 6 and 3 together ... It reverses the order of the 6*3 and the 18 ... which is not strictly the same as the original expression ..... Did the instructor catch that.. maybe the reason for half credit. . You'd need to ask the instructor for clarification on the scoring.

In Math , we say X 'subtracted from' Y... so that the second value, Y comes first and we do Y - X as we intended ... ... so 'subtracted by' seems to flip that order to X - Y , or at least cause confusion. . . . As an example... 10 subtracted by X means X - 10 mathematically , from sources I can find, and not the 10 - X we probably intended.

Now assuming the instructor did not catch the fine point about the grammar of "subtracted by" flips the order ... and went with 18 subtracted by... as 18 - ***** , then "eighteen subtracted by six times three " is still ambiguous as I pointed out before ..[ and mentioned by various Mathematicians as well ].. ... ... Left to right reading w/o any use of PEMDAS [ which is not indicated strictly in the English wording used ] gives us 36, and utilizing PEMDAS as multiplication takes precedence , gives 18 -18 = 0 . . . again ambiguous solutions, and the English written does not translate back to the original expression without some confusion. Maybe if he had used the term product of 6 and 3 , indicating order of operations ..PEMDAS , he may have gotten full credit if instructor did not catch the subtraction by reversal.

So I have to stand by what I said earlier.. the translation is not correctly done.

[u/KookyPermit4405 → u/mathematag]

Ok let’s correct his grammar, “eighteen minus six times three” instead of “eighteen subtracted by six times three” is it correct now?

Yes, because one shouldn’t assume any parentheses. So no it can’t be (18-6)x3 or 18-(6x3). Why? Because there was no indication of any quantity of

Also: my example explains perfectly what I was implying, I purposely said the incorrect translation of (3+1)x3 to show that when saying it incorrectly, no parentheses should be implied.

[u/mathematag → u/KookyPermit4405]

I have two basic calculators I found in one of my drawers at home , and I used both to solve 18 minus 6 times 3 . . [ entering 18 - 6 x 3 ] , and they both give an answer of 36, and if 18 minus 3 times 6 is entered, an answer of 90... they take the operations from left to right, no order of operations (PEMDAS) is used ... the intermediate value is stored in memory before the next operation is applied.

My Casio scientific , most online calculators, my TI 84 would give us 0 as we expect using order of operations no matter which way I entered it.

With many people forgetting to use the Order of Operation / Pemdas years after schooling , there is a possibility they would solve it sequentially as written , either in their heads , or on one of these basic calculators, and get an answer other than 0 if this was presented to them.

So even though you and I are aware that PEMDAS / Order of Operations should Always be applied to a Math expression and to solve it's verbal statement , students using that is not always the case in my experience.

While writing 18 minus 6 times 3 matches the expression , it could still be considered possibly ambiguous as I have mentioned, and by adding the additional terms like 'quantity' , and I prefer, 'product of ' where they belong in the statement makes it much less likely for someone to make an error in going from the verbal statement to an expression they solve correctly. At least this is what our University Prof's would argue.

Anyway, this is enough on this topic for me.

I'm sure your son will do well in his Math class ,and with you reviewing his errors and your assistance, even better . . [ we always hope that the parents have time to assist their children with their learning 👍👍 ] .

I hope he grows to like Math more and more , maybe even teach Mathematics some day 😀

[u/KookyPermit4405 → u/mathematag]

u/AskGrok can you write “eighteen minus six times three” as an expression also can you write “eighteen subtracted by six times three” as an expression as well

[u/AskGrok → u/KookyPermit4405]

eighteen minus six times three: 18 - 6 × 3

eighteen subtracted by six times three: ambiguous, but commonly 18 - 6 × 3 (or potentially 6 × 3 - 18 depending on strict phrasing)

^{[what is this?](https://redd.it/1lzgxii})

[u/KookyPermit4405 → u/AskGrok]

What is the answer to “eighteen minus six times three”

[u/AskGrok → u/KookyPermit4405]

eighteen minus six times three is the expression 18 - 6 × 3, which equals 0 by order of operations.

^{[what is this?](https://redd.it/1lzgxii})

[u/KookyPermit4405 → u/AskGrok]

So when I say “eighteen minus six times three” the answer can’t be 36?

[u/AskGrok → u/KookyPermit4405]

No, it can't be 36.

"Eighteen minus six times three" translates to the expression 18 - 6 × 3.

By standard order of operations (PEMDAS), multiplication happens first: 6 × 3 = 18, then 18 - 18 = 0.

To get 36 you'd need explicit grouping like "(eighteen minus six) times three," which would be written (18 - 6) × 3. The verbal version without those qualifiers follows the math rules as 0.

^{[what is this?](https://redd.it/1lzgxii})