1. Andre ran \(\frac{4}{5}\) of a 7-mile trail. Did Andre run a distance greater than or less than 7 miles? Explain or show your reasoning.
2. Clare ran \(\frac{\boxed{\phantom{\frac{0}{000}}}}{\Large{10}}\) of a 7-mile trail. She ran a distance greater than 7 miles. Find a number that makes this statement true. Explain or show your reasoning.

Point J on the number line shows how many miles Jada ran. Label the points on the number line to show each runner’s distance, in miles.

1. Clare ran \(\frac{8}{5}\) as far as Jada.
2. Tyler ran \(\frac{4}{3}\) as far as Jada.
3. Lin ran \(\frac{1}{2}\) as far as Jada.

Point A is labeled on the number line.

Label each of these points on the number line.

• \(\frac{2}{5} \times A\)
• \(\frac{13}{10} \times A\)
• \(\frac{7}{4} \times A\)

Use the equation \(\frac{5}{7} = \left(1 - \frac{2}{7}\right)\) to explain why \(\frac{5}{7} \times \frac{11}{3} < \frac{11}{3}\).

Explain why multiplying a fraction by a number less than 1 makes the fraction smaller.

Point P is labeled on the number line.

1. Point P is \(\frac{3}{4}\) of a number A. Plot A on the number line. Explain or show your reasoning.
2. Point P is \(\frac{5}{9}\) of a number B. Plot B on the number line. Explain or show your reasoning.

1. About \(10^6\) people live in Michigan. About \(10^4\) of the people in Michigan live in Flint.

   1. How many times as many people live in Michigan as in Flint?

   2. How many times as many people live in Flint as in Michigan?

2. There are about 10¹¹ stars in the Milky Way. There are about 10²⁴ stars in the universe.

   1. How many times as many stars are there in the universe than in the Milky Way?

   2. How many times as many stars are there in the Milky Way than in the universe?