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7/24.

If the question were what number is halfway between 3 and 4 we would simply add the numbers together and divide by 2. (3 + 4) / 2 = 7/2 = 3.5

We can do exactly the same thing with fractions.

So, we have (1/4 + 1/3) / 2. To start we convert both fractions so that they have the same denominator which allows us to add them; we will change both fractions into twelfths = (3/12 + 4/12) / 2 = 7/12/2 = 7/(2*12) = 7/24.

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Q: What number is halfway between 1 over 4 and 1 over 3?
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