How do you expand linear expressions that involve multiplication, addition, and subtraction with fractions? For example, how do you expand (2x + 6)?

In this lesson you will learn how to expand linear expressions with rational coefficients by using an area model and the distributive property.

Let’s Review Vocabulary: Linear expression Rational coefficient Combine like terms v v - 1 = v + 2

Let’s Review Properties of the Real Numbers: Commutative: = Associative: (4 + 3) + 9 = 4 + (3 + 9) Distributive: 5(6 + 2) = 5(6) + 5(2)

A Common Mistake Failing to distribute negative numbers completely: -9(4 + 3) = -9(4) + 9(3) -

Let’s Review A Common Mistake = Distributing multiplication over multiplication: 3(5 2) = 3(5) 3(2) - 3(10)

Let’s Review Core Lesson How do we expand (2x + 6)? xx x + 6 x 1 x X + 3 (2x + 6) = x + 3 x 1

Let’s Review Core Lesson Using the distributive property to expand (2x + 6): x 111 x 111 (2x + 6) 2x + 6 = (2x) + (6) = x + 3

Let’s Review Core Lesson Expand and combine like terms: (5n + 7) - 2( n - 1) = (5n) + (7)+ (-2)( n) + (-2)(-1) + + (- n)= n + 2 = n +

In this lesson you have learned how to expand linear expressions with rational coefficients by using an area model and the distributive property.

Let’s Review Guided Practice Simplify: ( w + 10) - 3(w - )

Let’s Review Extension Activities Use a diagram to show why (6y + 15) = 2y + 5.

Let’s Review Extension Activities Subtract one-half of a group of 8u + 3 from one-third of a group of 13u - 7.

Let’s Review Extension Activities Write at least two different linear expressions, using fractions, that expand and simplify to a value of 10x + 8.

Let’s Review Quick Quiz 1. Simplify: (9y-15) + (4y + 5) 2. Simplify: (6 - x) - 4(x - )