Final answer:
To multiply and simplify the fractions (5by)/(3y) * (12y)/(15b), cancel out common factors to get (5b * 12)/(3 * 15b). After simplification, the resulting fraction is 4.
Step-by-step explanation:
To multiply the fractions (5by)/(3y) * (12y)/(15b), first multiply the numerators together and then the denominators together. To simplify the expression, first cancel out the common factors. In the numerators, there is a common factor of y, which can be cancelled out. In the denominators, there is a common factor of 3 and 15, which reduces to 5. After cancelling and simplifying, you are left with the simplified expression (5b * 12)/(3 * 15b). Now divide both numerators and denominators by their greatest common divisor, which is b in this case. The b's cancel out in the numerator and the denominator. After simplification, the resulting fraction is 4/1 or simply 4. Hence, when multiplied and simplified, (5by)/(3y) * (12y)/(15b) equals 4.