Fraction bars
Make two fractions with the + and − buttons. Each bar is one whole, cut into equal pieces. Then press Cut smaller. Both bars are cut again until their pieces are the same size, and now you can add them or take one away from the other.
What's going on
The bottom number of a fraction says how many equal pieces the whole is cut into. The top number says how many of those pieces you have. So the bottom number is really a size: thirds are bigger than quarters.
You can only count things together when they are the same kind of thing. One third and one quarter are two pieces, but two pieces of what? They are different sizes, so "two" tells you nothing yet.
The fix is to cut both bars into smaller pieces that match. Cut each third into 4 and each quarter into 3, and both bars are in twelfths. Look at the shading while you press the button: it does not move. One third and four twelfths are the same amount with two different names.
Once the pieces match, adding is just counting: 4 twelfths and 3 twelfths make 7 twelfths.
Sheets: The same fraction in disguise and Why you cannot add thirds to quarters.