# Section C: Practice Problems The Size of Products

## Section Summary

Details

In this section, we learned how to compare the size of a product to the size of the factors. To compare with , for example, we can put them on a number line.
Since is 3 equal parts with 5 parts in the whole, it is to the left of , only part of the way there. We can also see this by writing as .

The product is less than because it is minus a fraction.

## Problem 1 (Lesson 16)

1. Andre ran of a 7 mile trail. Did Andre run more or less than 7 miles? Explain or show your reasoning.

2. Clare ran of a 7 mile trail. She ran more than 7 miles. Choose a number that could go in the box. Explain or show your reasoning.

## Problem 2 (Lesson 17)

The point J on the number line shows how many miles Jada ran. Label the points on the number line to show how far each of these students ran.

• Clare ran as far as Jada.

• Tyler ran as far as Jada.

• Lin ran as far as Jada.

## Problem 3 (Lesson 18)

The point A is labeled on the number line.

Label each of these points on the number line.

## Problem 4 (Lesson 19)

Use the equation to explain why .

## Problem 5 (Lesson 20)

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

## Problem 6 (Exploration)

A point P is labeled on the number line.

• P is of a number A. Plot A on the number line. Explain or show your reasoning.

• P is of a number B. Plot B on the number line. Explain or show your reasoning.

## Problem 7 (Exploration)

1. About people live in Michigan. About of the people in Michigan live in Flint.

• How many times as many people live in Michigan as in Flint?

• How many times as many people live in Flint as in Michigan?

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

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

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