Lesson 2.5 Apply the Distributive Property Essential Question: How do you use the distributive property to simplify expressions?

Before we start…

Properties of Addition

The identity property states that the sum of a number a and 0 is a The identity property states that the sum of a number a and 0 is a. The number 0 is the additive identity. The inverse property states that the sum of a number a and its opposite is 0. The opposite of a is its additive inverse.

Identify the property

Properties of Multiplication

The Multiplicative Identity The identity property states that the product of a number a and 1 is a. The number 1 is called the multiplicative identity.

Identify the property 𝑥∙7 ∙0.5=𝑥 7∙0.5 8∙0=0 −6∙𝑦=𝑦∙ −6

Identify the property

What is the distributive property? It allows you to rewrite an expression as an equivalent expression to find the product of a number and a sum or difference. This combines multiplication and addition.

When you use the distributive property, you distribute, or multiply, the number outside the parentheses to each number inside the parentheses:

The Distributive Property

Another Way to Look at Distributive Property

How do you use the distributive property? You multiply the term on the outside with each term on the inside. Then simplify if necessary.

What are equivalent variable expressions? Two variable expressions that have the same value You can use the distributive property to write equivalent variable expressions.

What is a term? The parts of an expression that are added together terms

What is a coefficient? The number part of a term with a variable part

What are … 15 12𝑥 and 6𝑥 Constant terms? Like terms? A number part but no variable Have the same variable part Constant terms are also like terms. 15 12𝑥 and 6𝑥

Identify the terms, like terms, coefficients, and constant terms of the expression:

Identify the terms, like terms, coefficients, and constant terms of the expression:

How do you use the distributive property to simplify variable expressions? Use the distributive property if necessary. Combine like terms. Add the coefficients of the variable terms Add the constant terms

Simplify 4𝑎−1 2+𝑎 6𝑟+2 𝑟+4

Simplifying Expressions You can simplify expressions that are being divided by the same number. To simplify, divide each term by the number.

Simplify 36𝑥−24 6 16𝑥−8 −4

Simplify −6𝑦+18 3 −10𝑧−20 −5

Simplify −8𝑥−80 −8 15𝑥+30 −5

Simplify 2 𝑥−6 −1 4 𝑥−10 −2

Simplify −6 𝑦+8 −2 12 𝑥−3 −4

Simplify −4 𝑦+2 +8 𝑦−3 −2

Exercise Your daily workout plan involves a total of 50 minutes of running and swimming. You burn 15 calories per minute when running and 9 calories per minute when swimming. Let r be the number of minutes that you run. Find the number of calories you burn in your 50 minute workout if you run for 20 minutes.

Pizza Party You are buying 10 pizzas for a party Pizza Party You are buying 10 pizzas for a party. Cheese pizzas cost $11 each, and single topping pizzas cost $13 each. Write an expression that gives the total cost in terms of the number, c, of cheese pizzas that you buy. Find the total cost if 4 of the pizzas you buy are cheese.

Movies Once a week, you either rent a movie for $4 or see a movie in a theater for $9. Let r represent the number of movies you rent in a year. Write and simplify an expression in terms of r for the total amount you spend on movies during the year. How much do you spend if you go to the theater 20 weeks of the year?

How do you use the distributive property to simplify expressions?

Ticket Out the Door Simplify. Place your name on the paper and place it in the basket.