Do you "reduce" fractions or put them in lowest terms?

In My Humble Opinion (IMHO)
#1

Q for mathematicians, teachers, and lovers of semantic arguments.

I’m not a math teacher, but once I had to teach it, so I took a class in teaching it. Our instructor said not to tell kids they are “reducing” fractions because that’s not correct. He said kids have a hard enough time as it is understanding equivalent fractions (a very necessary bit of knowledge, but VERY hard for kids to understand), and so to say a number is being “reduced” gives them the impression that the number is being made smaller, which, obviously, isn’t the case.

So now it bugs me when I hear someone talk about “reducing” fractions.

I’m sure an argument can be made either way, but what do y’all regularly say? What were you taught? Have you heard anyone express a preference?

I wish I were at school…I’d get out the fifth graders’ math books and see how the book puts it.

#2

When I think about it, it’s reducing or if I’m feeling particularly academic, reducing to lowest terms. I probably got confused when I first started doing it but at some point it clicked and the confusion disappeared.

#3

Huh? What do you mean? Thinking of 4/16 as 1/4 for example?

#4

I hate this kind of hair-splitting. When I was in High School, I had a teacher who hated it when someone referred to the elimination of a common factor in a fraction as “canceling”. What’s the problem? :mad:

#5

I think I heard both growing up. Though I think lowest terms was the term I heard most frequently.

#6

IANATorM, but I’ve always called it ‘simplifying’ or ‘reducing to the lowest terms’. ‘Simplifying’ is easier to say.

#7

Yeah. The argument is that if 4/16 is “reduced,” then it’s made into a smaller number.

Someone mentioned “reduce to lowest terms.” Not sure how the grammarmeticians would feel about that one :slight_smile:

#8

Is the actual question whether we do it, or how do we call it? I do it, but it’s one of those things I do in Spanish (never had a Math course in English). When taken to the end, it’s called “reducir al MCD,” lit. “reduce to the smallest value of the bottom number” (while keeping both numbers as whole numbers and the fraction at its original value).

#9

I am not a fan of hair splitting either. Besides you are reducing

For example I have 16 leggos and 4 are red, 4 are green, 4 are blue and 4 are yellow

I have 4/16 red leggos, this is correct

But suppose I combine (or join as it were) the 4 leggos, where once were 4 units there are now 1 unit. I reduced it from 4 small units to one larger unit.

And let’s say I do this for all the other colors. Now instead of having 16 small units I reduced the number of units to 4.

So I now have 1 red leggo unit and 4 total leggo units

Reducing can be used in many way. For instance, I have a bushel basket I half fill with leaves. I can make two trips or REDUCE the number of trips to empty the bushel basket by “increasing” the amount of leaves in the basket.

#10

Expressed them in the least common denominator. The act of mathematically doing so was referred to as reducing fractions, but it was always made very clear that the value was the same. That was the whole point of learning it.

Nothing changed except the way we expressed the fraction. We reduced it to it’s least common denominator, for simplicity.

#11

I have a vague memory of it being referred to as “simplifying” fractions. Does that ring any bells for anybody?

#12

In my eighth grade pre-algebra class, my students simplify fractions. At least, I encourage them to, sometimes they don’t and wonder why I’m having them work with large numbers and gasp not use a calculator. If they would just listen to me and simplify them, their problem solving would be so much easier…

What was the question again? Oh yeah, I use the term “simplify” and discuss in reference to the greatest common factor between the numerator and denominator. When reviewing the skill, I explain it as dividing both the numerator and the denominator by the GCF and show them how they’re really just dividing by the multiplicative identity. When I introduce variables, simplifying becomes factoring. We factor out numbers and variables and stop writing them if they equal one.

#13

Yeah, I was taught “simplifying”, too.

#14

Back in the pre-calculator era when I was learning math, it was called “reducing,” and it never occurred to me that that meant any change in the size of the number, just a reduction (sic) in the unwieldiness of it.

#15

We reduced fractions to the lowest terms. Back in my day, kids were smart enough to understand that “reducing fractions” meant something different than “reducing weight.” I would assume kids today are also smart enough, but that their teachers don’t think they are.

#16

I usually say, “Put it in lowest terms”.

Technically, you are not dealing with fractions but rational numbers. To be precise, 1/4 and 4/16 are different fractions but notations for the same rational number, as is .25.

But I have little patience with this hair splitting too.

#17

I volunteer as a math tutor. I use the word simplify. ‘Reduce’ works well for folks who have no trouble with the concept, but if you’re coming to me for tutoring, that might not be the case. I’m not going to say anything that might confuse you.

A fraction is almost like its own little equation - as long as you do the same things to the top and the bottom, it stays the same.

#18

I like “simplifying” over “reducing”, but I think I also might say “dividing out the common factors”.

Malienation, the purpose of this kind of hair splitting is to select ways of expressing ideas that help people understand it better. This is part of the general theme of teaching, which is helping people understand things. If you hate hair splitting, why are you joining a thread about it?

Markxxx, I don’t know if I just miscalculated my dosages this morning or what, but your proposal sounds to me nearly as bizarre as it is possible for a line of reasoning to be. If you had any arrangement other than equal numbers of each color, your reducing would change the value. Besides, it’s just a trick of the nature of Legos that you can join them together. And, couldn’t you also argue that you are “increasing” the fraction because the objects in question are larger afterwards?

#19

Well, that came out a bit more snitty than I really meant it to. Sorry - I didn’t especially want to be offensive. Perhaps one of you would like a free shot at me or something…

#20

Always. There’s something blasphemous about 5/30 or 14/63.