Why learn to identify and use properties of real numbers to evaluate expressions and equations?

Have you ever planned a party or gathering where you had a budget, and you had to buy everything you needed for the party while not spending more than you set aside?

As the treasurer for his college’s Aspiring Entrepreneurs Club, Jose is responsible for keeping track of membership dues, fundraising money, and club expenses. He’s excited because it’s time to plan the spring end-of-term party, and that means he gets to go shopping for snacks and drinks. He’s planning to buy chips, cookies, and sodas. The club’s budget for the party is $76.

At the store, Jose checks the prices on what he needs to buy:

• A bag of chips costs $3.
• A package of cookies costs $2.
• A 12-pack of soda costs $5.

Jose knows he wants to buy five 12-packs of soda to make sure there’s enough for everyone. Then he wants to get two more bags of chips than cookies with the remaining money. So how many packages of each snack should Jose buy?

While Jose stares at the snacks in the grocery store aisle, let’s explore real numbers and some of the properties that can help us figure out this problem.