I am looking for a good antonym for reducing/simplifying equivalent fractions: 'reduce' and 'simplify' both make sense to me when dividing, but I'm struggling to name what it is we do when we multiply a fraction by 2/2, or 7/7, or any of their Unity Sisters!

Ideas that came to mind: increasing? complexifying?

  • $\begingroup$ I talk about my goal as I do it: I'm going to multiply by 1 aka 2/2, which just makes this look different, so that this can be added to this. I never thought about wanting a name for it. $\endgroup$ – Sue VanHattum Jun 20 '16 at 20:52
  • $\begingroup$ Why is this down-voted? Could the dv-er please provide further information so that the question can be strengthened? $\endgroup$ – Benjamin Dickman Jun 20 '16 at 21:14
  • $\begingroup$ One note: all of these ideas are great, but as you know there isn't one way to do it. (Nor is there one way to reduce, but there is the concept of reduced fraction, whereas there isn't any limit to the "unreduced"/"expanded" fractions.) So if you use this terminology to teach it (which could be good) you'll need to deal with that at some point, whether with terminology or warnings. $\endgroup$ – kcrisman Jun 22 '16 at 18:37

I thought the standard terminology was expanding fractions, at least it is in my language.

Some support for this term found by googling:

Expanding and Reducing Fractions

Expanding Fractions

  • $\begingroup$ Super Boss Dag! Love the way it labels what's happening when you show pie slices. 'Reducing' clearly reduces the number of slices. 'Expanding' clearly expands the number of slices. Subtle, and surely not a fit for everyone, but perfect for me. Thank you! $\endgroup$ – user2802450 Jun 22 '16 at 2:47

How about saying "find equivalent fractions to"? For example, to find equivalent fractions to $\frac13$ means giving examples of $\frac{n}{3n}$ for different values of integers $n$.

Now, if we are asked to find equivalent fractions to, say, $\frac69$, this would include $\frac23$ (which is in simplest form) and, say, $\frac{10}{15}$ (where the numerator $10$ is not an integer multiple of $6$) so perhaps more clarifications are needed if this is what you intend to mean.

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    $\begingroup$ Or maybe: reducible equivalent fractions. $\endgroup$ – Joseph O'Rourke Jun 21 '16 at 1:26
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    $\begingroup$ Finding equivalent fractions is the language that I have seen used in elementary classrooms. When we wanted to find only those with larger numerators and denominators we would find equivalent fractions by multiplying. $\endgroup$ – Amy B Jun 21 '16 at 12:36
  • $\begingroup$ While this is certainly standard terminology, the problem is that technically "finding equivalent fractions" must be a strict superset of "reducing fractions" (so, not symmetric). $\endgroup$ – Daniel R. Collins Jun 22 '16 at 15:57

How about : rescaling the fraction. This could refer to going in either direction.

  • $\begingroup$ Love it! Definitely going to use rescaling to introduce both reducing and to expanding fractions. Thanks so much! $\endgroup$ – user2802450 Jun 22 '16 at 14:19

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