When I taught maths, I taught kids they should almost always simplify their fractions. I also use the phrase “express/put in lowest terms.” Although it is somewhat vague, I like simplify because it can be used analogously in other topics and it reminds students what they are doing - expressing their answer in a neater and more understandable way.
I don’t have a huge problem with reduce but I suppose it is better to remove any potential source of confusion. Maybe one or two kids would be confused by “reduce” but I can’t image it would be a major obstacle to understanding fractions.
I’m not a math teacher or mathematician or the like, but I always do it. If my fiance is talking about using two - 1/4 cups of something, I cringe and say, “Hun, that’s a half cup.” I hate non-reduced reducible fractions.
I agree. If a person gets the concept, then you can use the term. But the semantics can really confuse others.
I believe the same thing applies to descriptions of English as a language. It’s a disservice to learners to say that English has “five vowels.” (It’s also a disservice to say “long E” / “short E,” which implies that English has only 10 vowels.) It may have five letters which are used to represent vowel sounds, but to understand one of the more prominent characteristics of English is to understand how expansive and numerous its vowel are.
If you have four cups, and one of them is full of sugar, you don’t have 1/4 cup of sugar; you have 1 cup of sugar.
The number of red Legos you have is 4. The proportion of your Legos which are red is 4/16.
If somebody gives you two more Legos, one of which is red, then the proportion of your Legos which are red will be 5/18. But, considering fractions as numbers, it is certainly wrong to say that
4/16 + 1/2 = 5/18.
As for the OP’s question, now that you mention it, I probably talk about “reducing to lowest terms”—whether the things being reduced are fractions, like 4/16, or fractional expressions, like
(x[sup]2[/sup] – 4)/(x[sup]2[/sup] + 4x + 4).