Final answer:
To find the product of fractions, multiply the numerators and denominators and simplify the result. To find the amount of soil needed to fill all the pots, multiply the number of pots by the capacity of each pot. To find the product of mixed numbers, convert them to improper fractions, multiply the fractions, and simplify the result.
Step-by-step explanation:
To find the product of 13/14 and 10/9, multiply the numerators and denominators: (13 x 10) / (14 x 9) = 130 / 126. Simplify the fraction by dividing both the numerator and denominator by the greatest common divisor, which is 2. So, the final answer is 65/63, which can be further simplified to 5/7. Therefore, the answer is option C: 2/7.
To find out how much soil Andy needs to fill all the pots, multiply the number of pots (5) by the capacity of each pot (3/8 pound): 5 x (3/8) = 15/8. Convert 15/8 to a mixed number by dividing 15 by 8: 15 ÷ 8 = 1 with a remainder of 7. So, the answer is option D: 1 7/8 pounds.
To find the product of 4 2/3 and 3 3/4, convert the mixed numbers to improper fractions: 4 2/3 = (4 x 3) + 2 = 14/3 and 3 3/4 = (3 x 4) + 3 = 15/4. Multiply the fractions: (14/3) x (15/4) = 210/12. Simplify the fraction by dividing both the numerator and denominator by the greatest common divisor, which is 6. So, the final answer is 35/2, which can be further simplified to 17 1/2. Therefore, the answer is option D: 17 1/2.