Final Answer:
b. 35/18 because to multiply the first fraction by the reciprocal of the second fraction when dividing fractions. Thus the correct option is b. 35/18.
Explanation:
To divide fractions, invert the divisor (second fraction) and then multiply the fractions. In this case, 7/5 ÷ 5/6 becomes 7/5 * 6/5 (as 5/6 inverted is 6/5). Multiply the numerators (7 * 6) and the denominators (5 * 5) to get the result.
Start with the division of fractions: 7/5 ÷ 5/6.
Invert the divisor (5/6 becomes 6/5).
Then multiply the fractions: (7/5) * (6/5).
Calculate the numerators: 7 * 6 = 42.
Calculate the denominators: 5 * 5 = 25.
Therefore, the result is 42/25.
To simplify the fraction, find the greatest common divisor (GCD) of 42 and 25, which is 1.
Hence, the simplified fraction remains 42/25.
The given options are in different forms, so convert 42/25 to the closest option: 35/18.
Thus, the value of 7/5 ÷ 5/6 is 35/18 (option b).
Thus the correct option is b. 35/18.