BebuLamar

We know that you can't enlarge a 6x7 image to exactly fit an 8x10 frame but..
Suppose that the 6x7 negative contains an image of 60mm x 70mm (which isn't exactly true) and you add equal borders around the image how big should the image be enlarged to in order to exactly fit the 8x10 frame with equal border around it?

axiesdad Loc: Monticello, Indiana

You can't get there from here. You can't have equal borders all around without changing the ratio of length to width or distorting the image. You can have a .333" border top and bottom with nothing on the sides or you can crop the sides to create a 5.6 x 7 which can be enlarged to 8 x 10 with no border.

anotherview Loc: California

Yes, it is about ratios.

blackest Loc: Ireland

unless the ratio of the two formats is the same you cant have equal borders.
the easiest way to compare the two ratios is divide one side by the other

e.g 8/10 and 6/7 (0.8) and (0.85 something)

You could calculate the needed border width if say you went for a 1cm border top and bottom you could figure the side width to make it fit the 8 by 10 frame.

Easier is to open a new document of the required size or larger paste in the image in the middle or slightly higher some people prefer to have the bottom border wider than the top. Then do an 8 by 10 crop. A lot of programs will indicate when a pasted image is centred on a page Horizontally or Vertically or both.

In affinity designer , and others there is the possibility to create a rectangle at 8 by 10 and paste the image into the rectangle you can grab the handles of the image and resize to a similar size to the rectangle drag the image till the cropped image suits and then you have a perfect 8 by 10 crop as you want it. You can group the rectangle and image and copy to the clipboard and open a new image from the clipboard and save that say as a jpeg file and you have your perfect 8 by 10. No math required.

big-guy Loc: Peterborough Ontario Canada

A ratio is constant... always! You can call it 1/2 or 2/4 or 3/6 or 4/8 or 5/10 etc. But regardless, you still have ½ a whatever. A ratio of 6x7 does not = 8x10 but does = 8x9.333331, close but no cigar. Assuming a print of 8x10 with borders around the 6x7 photo you would end up with a 1" border on both the 6" dimensions and a 1.5" border on both the 7" dimensions.

Cdouthitt Loc: Traverse City, MI

if you scale up a 6x7 133%, it will fit within an 8x10.

Bill_de Loc: US

I hope this is a joke.

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rehess Loc: South Bend, Indiana, USA

If you have a 1" matte, then you are taking a total of 2" off each dimension, so a 6" x 8" image would fit into a 8" x 10" frame.

axiesdad Loc: Monticello, Indiana

Fit, yes. Equal borders all around, no. Enlarging by 1.33 will give you no border on the sides and .33" border top and bottom.

BebuLamar

No you can't. You can do the reverse fitting an 8x10 image in a 6x7 frame with equal border.

BebuLamar

Adding equal border around an image changes its ratio. For example a 4:3 image adding 1 to each dimension makes it 5:4. But the ratio becomes smaller and not greater.

jerryc41 Loc: Catskill Mts of NY

When I see the term "math problem," I tend to avoid the article or post, but I thought I'd take a look, anyway.

There's a very slight difference in proportions between the two, but mixing inches and mm adds to the confusion. As for a mathematical solution, I'll be interested in seeing if anyone comes up with a good answer. I suspect the "equal borders" might be a problem.

jerryc41 Loc: Catskill Mts of NY

Sounds good!

billnikon Loc: Pennsylvania/Ohio/Florida/Maui/Oregon/Vermont

I have always preferred full crop of the 2X3 format. This is what I see through the viewfinder, 4X6, 8X12, 16X24. Yes, life is simple if you just let it be.

jcboy3

It cannot be done.

You want to add an equal border to a 6x7 ratio image to get an 8x10 image. Let K be the width of the border. Then what you want is:

(8-K) / (10-K) = 6 / 7

or

56 - 7K = 60 - 6K

or

K = -4

Which means there is no solution to the problem.