The way I was taught, albeit sounding stupid, you flip one fraction and multiply across. So say we're doing 1/2 ÷ 3/4. Turn 3/4 into 4/3, and change the division symbol to multiplication. So your new problem is 1/2 x 4/3. Multiply the numerators (top numbers) and the denominators (bottom numbers). So 1 x 4 = 4. 2 x 3 = 6. Your answer is 1/2 ÷ 3/4 = 4/6.
Let me know if this helps!