Let's break down each question from the image and provide the solutions:

5. Sara has fewer than ten $5 bills in her wallet. How much money might she have?

Sara has fewer than ten $5 bills, meaning she can have anywhere from 0 to 9 $5 bills. To calculate the possible amounts:

• 0 bills: $0
• 1 bill: $5
• 2 bills: $10
• 3 bills: $15
• 4 bills: $20
• 5 bills: $25
• 6 bills: $30
• 7 bills: $35
• 8 bills: $40
• 9 bills: $45

So, Sara could have any amount of money between $0 and $45, in increments of $5.

6. A clothing store employee is making a display of pairs of socks. Can the employee use 17 socks in all? Explain.

To determine if 17 socks can be used, we need to check if 17 can be divided into pairs. Since a pair consists of 2 socks: $\frac{17}{2} = 8 \text{ pairs with 1 sock left over}$ Since the division results in a remainder, the employee cannot use exactly 17 socks if they are arranging them in pairs. They would need an even number of socks to create full pairs.

7. Mike staples 10 sheets of paper together to make a packet. He makes fewer than 8 packets. He uses all of the paper. How many sheets of paper could Mike have used? Explain how you know.

Each packet consists of 10 sheets. If Mike makes fewer than 8 packets, he can make anywhere from 1 to 7 packets. To calculate how many sheets of paper he used, we multiply the number of packets by 10 (since each packet contains 10 sheets):

• 1 packet: $10 \times 1 = 10$ sheets
• 2 packets: $10 \times 2 = 20$ sheets
• 3 packets: $10 \times 3 = 30$ sheets
• 4 packets: $10 \times 4 = 40$ sheets
• 5 packets: $10 \times 5 = 50$ sheets
• 6 packets: $10 \times 6 = 60$ sheets
• 7 packets: $10 \times 7 = 70$ sheets

Therefore, Mike could have used any number of sheets from 10 to 70, in increments of 10.

8. Is it possible for a number to be a product of 2, a product of 5, and a product of 10? Explain.

For a number to be a product of 2, it must be divisible by 2. For a number to be a product of 5, it must be divisible by 5. For a number to be a product of 10, it must be divisible by both 2 and 5.

Since 10 is the least common multiple (LCM) of 2 and 5, any number that is a product of 10 is automatically divisible by both 2 and 5. Therefore, yes, it is possible for a number to be a product of 2, a product of 5, and a product of 10. Any multiple of 10, such as 10, 20, 30, etc., satisfies this condition.

Let me know if you need further clarification on any of these!

Here are 5 related questions to expand your understanding:

1. What is the total amount of money Sara could have if she had exactly 7 $5 bills?
2. How many socks would be needed to make 10 full pairs?
3. If Mike had 15 sheets of paper, how many packets could he make, and how many sheets would be left over?
4. What is the LCM of 2, 5, and 15? Is it possible for a number to be divisible by all three?
5. If Sara had a mix of $5 and $10 bills, how would the range of possible total amounts change?

Tip: When solving problems involving multiples or divisibility, identifying the least common multiple (LCM) often helps in answering questions involving multiple factors.