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

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?

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

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]

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]

When you scale something by 173.95%, you are scaling it (multiplying its current size) by 173.95÷100 (because

Division is the inverse operation to multiplication, so you can take the new size and

It turns out that dividing something by 173.95÷100 is the same a

posted by pipeski at 7:45 AM on October 1, 2012 [6 favorites]

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]

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]

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

posted by bookdragoness at 1:45 PM on October 1, 2012

thanks all! huge help.

posted by OlivesAndTurkishCoffee at 8:49 PM on October 30, 2012

posted by OlivesAndTurkishCoffee at 8:49 PM on October 30, 2012

This thread is closed to new comments.

posted by qxntpqbbbqxl at 7:13 AM on October 1, 2012