Final answer:
To express the product of 10/12 and 4/15 in lowest terms, multiply the fractions to get 40/180, which simplifies to 1/4.5 or 2/9 after dividing by the greatest common factor.
Step-by-step explanation:
The question requires multiplying two fractions and expressing the product in lowest terms. To find the product of 10/12 and 4/15, multiply the numerators together and then the denominators:
10/12 × 4/15 = (10 × 4)/(12 × 15) = 40/180.
Next, we simplify this fraction to its lowest terms. We can divide both the numerator and the denominator by their greatest common factor, which is 40:
40/180 = (40/40)/(180/40) = 1/4.5,
Since we want the denominator to be a whole number, we can further simplify 4.5 as 9/2:
1/4.5 = 1/(9/2) = 2/9.
The final answer in lowest terms is 2/9.