7 1 Simplifying Algebraic Expressions Warm Up Problem

7 -1 Simplifying Algebraic Expressions Warm Up Problem of the Day Lesson Presentation Lesson Quizzes

7 -1 Simplifying Algebraic Expressions Warm Up Simplify. 1. 2. 3. 4. 9 + 13 5 + 3 20 16 8 + 4 1 11 6 + 9 10 + 3 8 17 + 8 20 2 3

7 -1 Simplifying Algebraic Expressions Problem of the Day Ray and Katrina are wandering through the wildlife preserve. They observe and count a total of 15 wild turkeys and deer and a total of 46 legs. How many of each did they see? 7 turkeys, 8 deer

7 -1 Simplifying Algebraic Expressions Learn to combine like terms in an expression.

7 -1 Simplifying Algebraic Expressions Vocabulary terms like terms equivalent expressions simplify

7 -1 Simplifying Algebraic Expressions Terms in an expression are separated by plus or minus signs. Like terms can be grouped together because they have the same variable raised to the same exponents. Helpful Hint Equivalent expressions same Constants such as 4, 0. 75, have and the 11 are like value all values ofof the variables. termsfor because none them have a variable.

7 -1 Simplifying Algebraic Expressions To simplify an expression, perform all possible operations, including combining like terms.

7 -1 Simplifying Algebraic Expressions Additional Example 1: Combining Like Terms To Simplify Combine like terms. A. 14 a – 5 a 9 a B. 7 y 2 +8– Identify like terms. Combine coefficients: 14 – 5 = 9 3 y 2 4 y 2 + y + 7 Identify like terms; the – 1+y coefficient of y is 1, because 1 y = y. Combine coefficients: 7 – 3 = 4 and 8 – 1=7

7 -1 Simplifying Algebraic Expressions Additional Example 2 A: Combining Like Terms in Two -Variables Expressions Combine like terms. 5 t 2 + 7 p – 3 p – 2 t 2 3 t 2 + 4 p Identify like terms. Combine coefficients.

7 -1 Simplifying Algebraic Expressions Additional Example 2 B: Combining Like Terms in Two -Variable Expressions Combine like terms. 4 m 3 + 9 n – 2 No like terms.

7 -1 Simplifying Algebraic Expressions Remember! The Distributive Property states that a(b + c) = ab + ac for all real numbers a, b, and c. For example, 2(3 + 5) = 2(3) + 2(5).

7 -1 Simplifying Algebraic Expressions Additional Example 3: Using the Distributive Property to Simplify 6(5 + n) – 2 n 6(5) + 6(n) – 2 n Distributive Property. 30 + 6 n – 2 n Multiply. 30 + 4 n Combine coefficients: 6 – 2 = 4.

7 -1 Simplifying Algebraic Expressions Additional Example 4: Combining Like Terms to Solve Algebraic Equations Solve x + 3 x = 48 Identify like terms. The coefficient of x is 1. 4 x = 48 Combine coefficients: 1 + 3 = 4 4 x = 48 4 4 Divide both sides by 4. x = 12

7 -1 Simplifying Algebraic Expressions Lesson Quizzes Standard Lesson Quiz for Student Response Systems

7 -1 Simplifying Algebraic Expressions Lesson Quiz Combine like terms. 1. 3 x 2 + 4 + 2 x 2 5 x 2 + 4 Simplify. 2. 13 k + 6 – 8 m + 9 + k 14 k – 8 m + 15 3. 4(3 x + 6) – 7 x 5 x + 24 4. 6(x + 5) + 3 x 9 x + 30 Solve. 5. 6 y + y = 42 y = 6 6. The Accounting Department ordered 15 boxes of pens. The Marketing Department ordered 9 boxes of pens. If the total cost of the combined order was $72, what is the price of each box of pens? $3

7 -1 Simplifying Algebraic Expressions Lesson Quiz for Student Response Systems 1. Combine like terms. 4 p + 13 + 11 p A. 15 p 2 + 13 B. 15 p + 13 C. 28 p D. 28

7 -1 Simplifying Algebraic Expressions Lesson Quiz for Student Response Systems 2. Combine like terms. 15 t + 9 – 7 s + 10 + 5 t A. 15 t – 7 s – 1 B. 15 t – 7 s + 1 C. 20 t – 7 s + 19 D. 20 t + 7 s + 19

7 -1 Simplifying Algebraic Expressions Lesson Quiz for Student Response Systems 3. Simplify 7(4 m + 9) – 9 m. A. 19 m + 9 B. 19 m + 63 C. 37 m + 9 D. 37 m + 63

7 -1 Simplifying Algebraic Expressions Lesson Quiz for Student Response Systems 4. Solve 11 v + 2 v = 65. A. v = 2 B. v = 5 C. v = 7 D. v = 11