, 2019

(a) Seth wants to know how many positive whole numbers from one to one hundred are divisible by two or five. He thinks that the answer is 70 because there are fifty multiples of two and twenty multiples of five from one to one hundred. Explain why his answer is too large.

(b) Consider the list of 1800 fractions
$$\frac{1}{1800}, \frac{2}{1800}, \ldots, \frac{1799}{1800}, \frac{1800}{1800}.$$
How many are not in simplest form? Explain your reasoning.

[Note: The fraction $\frac{900}{1800}$ is not in simplest form because it can be simplified to $\frac{1}{2}$.]