Math - Fraction Multiplication

I think there should be a video on why multiplying the numerators and the denominators works, because even with the visual exercises, it still doesn't make intuitive sense what all the numbers and the simplifications and the result really mean. Having 6/7 × 8/9 = 6×8/7×9 = 48/63 quickly calculated gives me no deeper understanding of what's going on. Having instead to think about what 6/7 of 8 is, it's very intriguing, and sends you on the path of discovering yourself how multiplying fractions works. You can't know what 6/7 of 8 is, because 7 doesn't go into 8 evenly. So we need to find and equivalent fraction for 8/9 that is divisible by 7. So 6/7 × 56/63. But what is 6/7 of 56? No idea. Ok, what's 1/7 of 56? Well, it's 8, our original numerator ( now I understand why multiplying numerators works ). Now we just need to multiply 6 × 1/7 of 56/63, and we just found out that 1/7 of 56/63 is 8/63, so 6 × 8/63 = 48/63