What do fractions multiply integers and fractions multiply fractions have in common

What do fractions multiply integers and fractions multiply fractions have in common

They are all the same. The denominator of an integer is 1. Because an integer divided by 1 is equal to itself, the denominator of 1 is omitted for convenience
("A / b" stands for "the fraction whose numerator is a and denominator is B")
Fraction multiplied by fraction = (numerator multiplied by numerator) / (denominator multiplied by denominator)
For example: fraction times fraction: 1 / 2 times 1 / 3 = (1 × 1) / (2 × 3) = 1 / 6
: fractional times integer: 1 / 2 times 5 = 1 / 2 times 5 / 1 = (1 × 5) / (2 × 1) = 5 / 2