Simplifying Expressions

Food for the Indy-Cysiv Family

Essential Question

What are the most common errors people make when using the Distributive Property to simplify expressions?

The large Indy-Cysiv family is planning a family reunion and needs to order food for the reunion.

They’ve decided to order from their favorite restaurant, the D Prop Pizza Shop.

The only problem is that the restaurant only sells food in combos!

One combo is made up of three pizzas and an order of wings.

The family called at 12 pm and ordered 6 combos for the reunion that night.

At 1 pm, they called back and said that a couple of families couldn’t make it so they needed to remove 2 combo orders.

Then, at 3 pm they called back to say that more families decided to attend and they now needed many more pizzas but they had way too many wings because these families don’t eat chicken.

Remember, at this restaurant you can only order combo meals, so they had to be a little tricky.

The Indy-Cysiv family asked to order 5 more combos, but where the 3 pizzas are added on but the wings are subtracted off from the total.

What?!

The Indy-Cysiv family called back one last time at 4:15 pm to order 12 desserts.

You are the kitchen manager at the D Prop Pizza Shop and you need to make sure that the Indy-Cysiv family’s order is correct and ready.

Here are the notes the operator made about the order:6 orders of the combo (3 pizzas and 1 wing)Take away 2 combo orders (3 pizzas and 1 wing)5 more specialty combo orders (3 pizzas take

away 1 wing)With 12 desserts

How many of each food item should be cooked and ready for the family reunion?

Expression in Math Terms

Let p = pizzas, w = wings, and d = desserts

6(3p + w) – 2(3p + w) + 5(3p – w) + 12d

Essential Question

What are the most common errors people make when using the Distributive Property to simplify expressions?

Practice!

1) 5(3x – 2) + 6 2) 8 – 3(w + 4)

3) 7(y + 3) – 5(2y – 1) 4) ½(5x + 8) – 7

5) 8c + 9 – (3c – 2) 6) (-2a + 6)(-4) + 3a

7) x + 20) 8) 10h + 3(-6h + 2) - 4

15x – 4 -3w – 4

-3y + 26 x – 3

5c + 11 11a – 24

-4x – 19 -8h + 2