California Standards Preview of Grade 7 AF1.3 Simplify numerical expressions by applying properties of rational numbers (e.g., identity, inverse, distributive, associative, and commutative) and justify the process used. Also covered: 6AF1.2, 6AF3.1, 6AF3.2

Vocabulary term coefficient

In the expression 7x + 9y, 7x and 9y are called terms In the expression 7x + 9y, 7x and 9y are called terms. A term can be a number, a variable, or a product of numbers and variables. Terms in an expression are separated by plus or minus signs. In the term 7x, 7 is called the coefficient. A coefficient is a number that is multiplied by a variable in an algebraic expression. Coefficient Variable 7 x

Like terms are terms with the same variable raised to the same power Like terms are terms with the same variable raised to the same power. The coefficients do not have to be the same. Constants, like 5, , and 3.2, are also like terms. 1 2 w 7 Like Terms Unlike Terms 3x and 2x w and 5 and 1.8 5x2 and 2x 6a and 6b 3.2 and n Only one term contains a variable The exponents are different The variables are different

Teacher Example 1: Identifying Like Terms Identify like terms in the list. 3t 5w2 7t 9v 4w2 8v Look for like variables with like powers. 3t 5w2 7t 9v 4w2 8v Like terms: 3t and 7t 5w2 and 4w2 9v and 8v Use different shapes or colors to indicate sets of like terms. Helpful Hint

Student Practice 1: Identify like terms in the list. 2x 4y3 8x 5z 5y3 8z Look for like variables with like powers. 2x 4y3 8x 5z 5y3 8z Like terms: 2x and 8x 4y3 and 5y3 5z and 8z

To simplify an algebraic expression that contains like terms, combine like terms. Combining like terms is like grouping similar objects. x x x x x x x x + = x x x x x x x x x x = 9x 4x + 5x To combine like terms that have variables, use the Distributive Property. 4x + 5x = (4 + 5)x = 9x

Teacher Example 2A & 2B: Simplifying Algebraic Expressions Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. A. 6t – 4t 6t – 4t 6t and 4t are like terms. 2t Subtract the coefficients. B. 45x – 37y + 87 In this expression, there are no like terms to combine.

Teacher Example 2C: Simplifying Algebraic Expressions Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. C. 3a2 + 5b + 11b2 – 4b + 2a2 – 6 Identify like terms. 3a2 + 5b + 11b2 – 4b + 2a2 – 6 Commutative Property. 3a2 + 2a2 + 5b – 4b + 11b2 – 6 (3 + 2)a2 + (5 – 4)b + 11b2 – 6 Distributive Property. 5a2 + b + 11b2 – 6

Distributive Property. Student Practice 2A & 2B: Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. A. 5y + 3y 5y + 3y 5y and 3y are like terms. 8y Add the coefficients. B. 2(x2 – 13x) + 6 2x – 26x + 6 2 Distributive Property. There are no like terms to combine.

Student Practice 2C: Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. C. 4x2 + 5y + 3x2 – 4y + 2x2 + 5 4x2 + 5y + 3x2 – 4y + 2x2 + 5 Identify like terms. 4x2 + 3x2 + 2x2 + 5y – 4y + 5 Commutative Property. Distributive Property. (4 + 3 + 2)x2 + (5 – 4)y + 5 9x2 + y + 5

Teacher Example 3: Geometry Application Write an expression for the perimeter of the triangle. Then simplify the expression. 2x + 3 3x + 2 x Write an expression using the side lengths. 2x + 3 + 3x + 2 + x (2x + 3x + x) + (3 + 2) Identify and group like terms. (2 + 3 + 1)x + (3 + 2) Distributive Property. 6x + 5

Write an expression using the side lengths. x + 2x + 1 + 2x + 1 Student Practice 3: Write an expression for the perimeter of the triangle. Then simplify the expression. 2x + 1 2x + 1 x Write an expression using the side lengths. x + 2x + 1 + 2x + 1 x + 2x + 2x + 1 + 1 Identify and group like terms. (1 + 2 + 2)x + (1 + 1) Distributive Property. 5x + 2

Lesson Quiz: Part I Identify like terms in the list. 1. a5 2a2 a3 3a 4a2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. 2. 4a + 3b + 2a 5n, 8n 2a2, 4a2 6a + 3b 9x2 + 2y

Lesson Quiz: Part II 3. Write an expression for the perimeter of the given figure. 2x + 3y x + y x + y 2x + 3y 6x + 8y

Lesson Quiz: Part I Identify like terms in the list. 1. 3n2 5n 2n3 8n 2. a5 2a2 a3 3a 4a2 Simplify. Justify your steps using the Commutative, Associative, and Distributive Properties when necessary. 3. 4a + 3b + 2a 4. x2 + 2y + 8x2 5n, 8n 2a2, 4a2 6a + 3b 9x2 + 2y