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Pre-Algebra 1-6 Combining Like Terms Pre-Algebra: 1-6 HW Page 30 #19-45 all

Pre-Algebra 1-6 Combining Like Terms 1-6 Combining Like Terms Pre-Algebra Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

Pre-Algebra 1-6 Combining Like Terms Warm Up Solve Pre-Algebra 1-6 Combining Like Terms  20      5 + 3

Pre-Algebra 1-6 Combining Like Terms 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

Pre-Algebra 1-6 Combining Like Terms Today’s Learning Goal Learn to combine like terms in an expression.

Pre-Algebra 1-6 Combining Like Terms Vocabulary term like term equivalent expression simplify

Pre-Algebra 1-6 Combining Like Terms 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 power. Equivalent expressions have the same value for all values of the variables.

Pre-Algebra 1-6 Combining Like Terms Combine like terms. Additional Example 1: Combining Like Terms To Simplify Identify like terms. Combine coefficients: 14 – 5 = 9 A. 14a – 5a 9a9a B. 7y + 8 – 3y – 1 + y Identify like terms ; the coefficient of y is 1, because 1y = y. Combine coefficients: 7 – = 5 and 8 – 1 = 7 5y + 7

Pre-Algebra 1-6 Combining Like Terms Combine like terms. Try This: Example 1 Identify like terms; the coefficient of q is 1, because 1q = q. Combine coefficients: 4 – 1 = 3 Identify like terms; the coefficient of c is 1, because 1c = c. Combine coefficients: 5 – 4 – 1 = 0 and 8 – 2 = 6 6 3q3q A. 4q – q B. 5c + 8 – 4c – 2 – c

Pre-Algebra 1-6 Combining Like Terms Combine like terms. Additional Example 2A: Combining Like Terms in Two-Variables Expressions Identify like terms. Combine coefficients: 9 – 2 = 7 A. 9x + 3y – 2x + 5 7x + 3y + 5 9x + 3y – 2x + 5

Pre-Algebra 1-6 Combining Like Terms Combine like terms. Additional Example 2B: Combining Like Terms in Two-Variable Expressions Identify like terms. Combine coefficients: 5 – 2 = 3 and 7 – 3= 4 B. 5t + 7p – 3p – 2t 3t + 4p 5t + 7p – 3p – 2t

Pre-Algebra 1-6 Combining Like Terms Combine like terms. Additional Example 2C: Combining Like Terms in Two-Variable Expressions No like terms. C. 4m + 9n – 2 4m + 9n – 2

Pre-Algebra 1-6 Combining Like Terms Combine like terms. Try This: Example 2 Identify like terms. Combine coefficients: = 7 A. 2x + 5x – 4y + 3 7x – 4y + 3 2x + 5x – 4y + 3 Identify like terms. Combine coefficients: 9 – 4 = 5 and 7 – 2 = 5 B. 9d + 7c – 4d – 2c 5d + 5c 9d + 7c – 4d – 2c No like terms. C. 8g + c – 6 8g + c – 6

Pre-Algebra 1-6 Combining Like Terms To simplify an expression, perform all possible operations, including combining like terms.

Pre-Algebra 1-6 Combining Like Terms Simplify 6(5 + n) – 2n. Additional Example 3: Simplifying Algebraic Expressions by Combining Like Terms Distributive Property. 6n and 2n are like terms. 6(5 + n) – 2n n – 2n 6(5) + 6(n) – 2n n Combine coefficients 6 – 2 = 4

Pre-Algebra 1-6 Combining Like Terms Simplify 3(c + 7) – c. Try This: Example 3 Distributive Property. 3c and c are like terms. 3(c + 7) – c 3c + 21 – c 3(c) + 3(7) – c 2c + 21 Combine coefficients 3 – 1 = 2

Pre-Algebra 1-6 Combining Like Terms Solve x + 3x = 48. Additional Example 4: Solving Algebraic Expressions by Combining Like Terms Identify like terms. The coefficient of x is 1. Combine coefficients: = 4 x + 3x = 48 4x = 48 x = 12 Divide both sides by

Pre-Algebra 1-6 Combining Like Terms Solve 7c – c = 102. Try This: Example 4 Identify like terms. The coefficient of c is 1. Combine coefficients: 7 – 1 = 6 7c – c = 102 6c = 102 c = 17 Divide both sides by

Pre-Algebra 1-6 Combining Like Terms Lesson Quiz Combine like terms. 1. 3x x 2. 13k + 6  8k k Simplify. 3. 4(3x + 6)  7x 4. 6(x + 5) + 3x Solve. 5. 6y + y = 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? 6k + 15 y = 6 5x + 4 5x + 249x + 30 $3