Pre-Algebra

1-6 Combining Like Terms1-6 Combining Like Terms

Pre-Algebra

Warm UpWarm Up

Problem of the DayProblem of the Day

Lesson PresentationLesson Presentation

Pre-Algebra

1-6 Combining Like Terms

Warm UpSolve.

2011

8

3

Pre-Algebra

1-6 Combining Like Terms

4. 17 + 8 20 23. 6 + 9 10 + 3

2. 16 8 + 4 11. 9 + 13 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

Learn to combine like terms in an expression.

Pre-Algebra

1-6 Combining Like Terms

Vocabularytermlike termequivalent expressionsimplify

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

9a

B. 7y + 8 – 3y – 1 + y Identify like terms ; the coefficient of y is 1, because 1y = y.

Combine coefficients: 7 – 3 + 1 = 5 and 8 – 1 = 7

5y + 7

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

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

30 + 6n – 2n

6(5) + 6(n) – 2n

30 + 4n Combine coefficients 6 – 2 = 4

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: 1 + 3 = 4

x + 3x = 48

4x = 48

4x = 48

x = 12

Divide both sides by 4.4 4

Pre-Algebra

1-6 Combining Like Terms

Lesson Quiz

Combine like terms.

1. 3x + 4 + 2x 2. 13k + 6 8k + 9 + k

Simplify.

3. 4(3x + 6) 7x 4. 6(x + 5) + 3x

Solve.

5. 6y + y = 42

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?

6k + 15

y = 6

5x + 4

5x + 24 9x + 30

$3