@larkey03
You are correct that you cannot do this with a numeric quiz question.
Canvas has no question type that meets both of your requirements. Canvas does not understand mathematics (we've been asking for improved support for years). You might consider an external tool that is written specifically to understand the complexities of math or revise how you ask the question.
The Equation Editor requires the Rich Content Editor and that requires an essay question for Classic Quizzes. Essay questions are not auto-graded.
Furthermore, the equation editor returns an image, not a mathematical object or a number. Here is an example of what is returned for something as simple as 3/4.
<img class="equation_image" title="\frac{3}{4}" src="/equation_images/%255Cfrac%257B3%257D%257B4%257D?scale=1" alt="LaTeX: \frac{3}{4}" data-equation-content="\frac{3}{4}" data-ignore-a11y-check="" />
Note that it does return LaTeX as the title and alt tag. Even if you wrote a script that would go through and look at the student responses and autograde them, you're grading answers like \frac{3}{4} not the way we write 3/4.
While humans are really good at grading math, software that has not been designed to understand mathematics is not.
In the case of a fraction in lowest terms, you likely expect that there is just a single answer. That means that you could use a fill-in-the-blank question with the proper answer as the string to check against. With Classic Quizzes, you would have to allow for people to 3/4, 3 / 4, 3/ 4, 3 /4, etc, unless you tell them to enter it with no spaces. With New Quizzes, you can do a regular expression check to ignore spaces: /^3\s*\/\s*4$/
One approach is to use multiple-fill-in the blank questions and put the numerator in one blank with the denominator in the second. With this technique, you can also include units as a third blank. With some layout, you could make it look like a fraction.
Here's what the question looks like in the HTML view. I'm using the shortcut for LaTeX, you could also use the equation editor.
<p>Add \(\frac{1}{4}\) and \(\frac{5}{10}\) and reduce to lowest terms.</p>
<div style="text-align: center; border-bottom: thin solid black; margin-bottom: 7px; width: 10em;">[numerator]</div>
<div style="text-align: center; width: 10em;">[denominator]</div>
If you want to give partial credit for an unreduced fraction, then you are out of luck. Using a multiple-fill-in-the-blanks question could accept 6/8 as an answer, but the parts are independent of each other, meaning that if you allowed 3 and 6 for the numerator and 4 and 8 for the denominator, that someone could put 3/8 and it would be considered correct. Again, in the case of simplifying fractions, that's probably not a concern.
But numeric questions allow you flexibility and tolerance, which are not allowed with text answers. So, if you want a number that is judged as being close enough but want to include units in a classic quiz, you're out of luck.
I don't use New Quizzes except to test stuff for people in the Community, but they have a stimulus question. According to the documentation, you could create a stimulus question that asked what is 1/4 + 5/10 in lowest terms. Then you could add questions: one for the numerator, one for the denominator, and for the units -- however you wanted to set it up. The stimulus question doesn't work with formula questions as the stimulus, however. That is, you cannot generate random values that the answers then use.
Going back to Classic Quizzes, another approach is a multiple answers question. As a variation on multiple choice, you could have a bunch of fractions -- one of which is correct -- and a bunch of units -- one of which is correct. The student select a number and units to get the question correct. At least with multiple answers and multiple choice, you can use the equation editor to format the responses so they look like math.
You can also vary the type of question you ask. For example, "What is the numerator when 1/4 and 5/10 are added and reduced to lowest terms?" Then you could use a numeric type question and have it be auto-graded. You cannot ask for both the numerator and denominator since you can only have one numeric field per question.
Math and science teachers have had to get creative in how they ask questions. It's definitely a case of the technology defining how we assess, rather than the technology supporting how we want to assess. For my trigonometry and calculus courses, I use an external system that understands mathematics. For my statistics, finite, and differential equations courses, I use Canvas, but had to change the way I asked them from the way I would normally ask them in a paper-and-pencil setting.
