Priya is sharing 24 apples equally with some friends. She uses division to find out how many people can have a share if each person gets a particular number of apples. For example, \(24 \div 4 = 6\) means that if each person gets 4 apples, then 6 people can have apples. Here are some other calculations:

1. Priya thinks the “?” represents a number less than 24. Do you agree? Explain or show your reasoning.

2. The value of \(24 \div \frac{1}{2}\) tells us how many people can enjoy the apples that Jada has if each person gets half an apple. What is that value?

Here is a centimeter ruler.

1. Use the ruler to find \(1 \div \frac{1}{10}\) and \(4 \div \frac{1}{10}\).

2. What calculation did you do each time?

3. Use this pattern to find \(18 \div \frac{1}{10}\).

4. Explain how you could find \(4\div \frac{2}{10}\) and \(4\div \frac{8}{10}\).

A portion of a ruler with the top labeled inches and the bottom of the ruler labeled centimeters. The top of the ruler has the numbers 1 and 2 indicated. There are 15 evenly spaced tick marks between the beginning of the ruler and 1 and between 1 and 2. The bottom of the ruler has the numbers 1 through 5 indicated. There are 9 evenly spaced tick marks between the beginning of the ruler and 1, 1 and 2, 2 and 3, 3 and 4, and 4 and 5.

Find each quotient.

1. \(5 \div \frac{1}{10}\)

2. \(5 \div \frac{3}{10}\)

3. \(5\div \frac{9}{10}\)

Use the fact that \(2\frac12 \div \frac18=20\) to find \(2\frac12 \div \frac58\). Explain or show your reasoning.

Consider the problem: It takes one week for a crew of workers to pave \(\frac35\) kilometer of a road. At that rate, how long will it take to pave 1 kilometer?

Write a multiplication equation and a division equation to represent the question. Then find the answer and show your reasoning.

A box contains \(1\frac{3}{4}\) pounds of baking soda. Jada used \(\frac{7}{8}\) pound for a science project. What fraction of the baking soda in the box did she use? Explain or show your reasoning. Draw a diagram if you find it helpful.

Calculate each percentage mentally.

1. 25% of 400
2. 50% of 90
3. 75% of 200
4. 10% of 8,000
5. 5% of 20