# Help me help my brain learn how to scale up and down with precision in Adobe Illustrator.October 1, 2012 7:11 AM   Subscribe

If I scaled the artwork up by typing 173.95% into the scale dialog box in Adobe Illustrator, what percentage do I scale it down by in order to get it back to its original size. Is there a simple equation that will do this operation?

I am astonished and deeply embarrassed by my inability to figure this out. I have been using a combination of math skills that I haven't used for 20 years and trial and error--which seems like it should work. I can get it close scaling by hand, but I need it to be exact.

Also, I am going to be performing this operation probably 50+ times, which is why I need to figure out the equation--if there is one.

This is a shameless request, I know--but can anyone help?
posted by OlivesAndTurkishCoffee to Technology (9 answers total) 4 users marked this as a favorite

Scale by (10000 / 173.95) percent.
posted by qxntpqbbbqxl at 7:13 AM on October 1, 2012

Divide by 1.7395, e.g.

100 * 1.7395 = 173.95

173.95 / 1.7395 = 100
posted by devnull at 7:14 AM on October 1, 2012

Scale down by the inverse of the percentage you used to scale up.
1 / 1.7395 = 0.5749 or 57.49%
posted by twisted mister at 7:14 AM on October 1, 2012 [6 favorites]

All are correct, but maybe this will cast a bit more light:

When you scale something by 173.95%, you are scaling it (multiplying its current size) by 173.95÷100 (because per cent means 'divided by 100'). That's where the 1.7395 comes from.

Division is the inverse operation to multiplication, so you can take the new size and divide by the same number (173.95÷100, or 1.7395) to get back where you started.

It turns out that dividing something by 173.95÷100 is the same a multiplying it by 100÷173.95, which is 0.5749.
posted by pipeski at 7:45 AM on October 1, 2012 [6 favorites]

...and 0.5749 is 57.49÷100, so it's 57.49%
posted by pipeski at 7:46 AM on October 1, 2012

Best answer: Same thing, same explanation, different words...

100% is just 1 (or 1.00)
Yes?

So 173.99% is the same as 1.7399

Your_picture * 173.99% = new_picture
is the same as:
Your_picture * 1.7399 = new_picture

so:
your_picture = new_picture / 1.7399

but, as dividing is useless to you, this can be written as:
your_picture = new_picture * (1 / 1.7399)

and since 1/1.7399=0.5749 :
your_picture = new_picture * 0.5749

aaaand, 0.5749 is the same as 57.49%
posted by BadMiker at 8:27 AM on October 1, 2012 [1 favorite]

It might help to think of scaling as (original size of object)*(scaling factor) = (desired size of object)

You can pick whatever you like for the original size of your object; 1 is convenient, but you can pick the actual size of the object if that helps you keep track of things. So your original increase in size followed the following equation:

(1)*(1.7395) = 1.7395

And now you want:

(1.7395)*(X) = 1

So, X = 1/1.7395.

It might be useful to think of things this way in case you ever want to scale up/down to a different size than your original size.
posted by bluefly at 8:51 AM on October 1, 2012 [1 favorite]

If you remember it, the concept you're thinking of is the reciprocal, aka multiplicative inverse.
posted by bookdragoness at 1:45 PM on October 1, 2012

Response by poster: thanks all! huge help.
posted by OlivesAndTurkishCoffee at 8:49 PM on October 30, 2012

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