Final answer:
The product of 5/6 and 2 2/5, using the distributive property and converting the mixed number into an improper fraction, is 2. This is obtained by multiplying the numerators and denominators and then simplifying the fraction.
Step-by-step explanation:
To find the product of 5/6 x 2 2/5 using the distributive property, we first need to convert the mixed number into an improper fraction. The mixed number 2 2/5 becomes 12/5 when converted to an improper fraction since 2 2/5 is equal to (2 x 5) + 2 = 10 + 2 = 12, and we keep the original denominator of 5.
Next, we use the distributive property to multiply these two fractions. To multiply fractions, you multiply the numerators together and the denominators together. So, the multiplication of 5/6 and 12/5 is:
(5 x 12) / (6 x 5) = 60 / 30
Finally, we simplify the fraction by finding the greatest common divisor of 60 and 30, which is 30. Dividing both numerator and denominator by 30 gives us:
60 / 30 = 2 / 1, or simply 2.
Therefore, the product of 5/6 x 2 2/5 is 2.