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Here is a Matchstick equation using Matchsticks as well as Points (dots).

Matchsticks and dots can be moved.

By moving only 1 Dot and 1 Matchstick make the equation equal.

No inequality or > or < allowed. You cannot remove the dot or sticks.

The equation 5.2/3.1= 51/8

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    $\begingroup$ If you turn it upside-down it's 1.3/2.5=8/15. That's almost correct. You'd need a dot on that 3 to make it exact... Of course the 3 is backwards though $\endgroup$ Commented Aug 22, 2017 at 21:26

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I think this is valid, let me know if it isn't:

 _ _ _ _ _ |_ _| / _| | = |_ | / |_ |_| |_ _| . | _| | |_| .

Explanation:

This is 62/3.1 = 5!/6. My moves were the top right vertical match in the 8 goes to make a 6 with the 5 from far left(originally), and the . from 5.1 is moved to make ! with the 1 from the right hand side of the equation. So 62/3.1 is 20, and 5!/6 is also 20.

Also, sorry about the formatting/picture I can't figure out how to do ascii art in the spoiler text.

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