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1-8 Simplifying Expressions

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1-8 Simplifying Expressions

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1. 427 + 35 2. 1.06 + 0.74

3.

Multiply.

4. 25(8)

6.

5. 1.3(22) 28.6200

10

462 1.80

1-8 Simplifying Expressions

MA.912.A.3.2 Identify and apply the distributive, associative, and commutative properties of real numbers….

Sunshine State Standards

1-8 Simplifying Expressions

Use the Commutative, Associative, and Distributive Properties to simplify expressions.

Combine like terms.

Objectives

1-8 Simplifying Expressions

termlike termscoefficient

Vocabulary

1-8 Simplifying Expressions

The Commutative and Associative Properties of Addition and Multiplication allow you to rearrange an expression to simplify it.

1-8 Simplifying Expressions

1-8 Simplifying Expressions

Additional Example 1A: Using the Commutative and Associative Properties

Simplify.

11(5)

55

Use the Commutative Property.

Use the Associative Property to make groups of compatible numbers.

1-8 Simplifying Expressions

Simplify.

Additional Example 1B: Using the Commutative and Associative Properties

45 + 16 + 55 + 4

45 + 55 + 16 + 4

(45 + 55) + (16 + 4)

(100) + (20)

120

Use the Commutative Property.

Use the Associative Property to make groups of compatible numbers.

1-8 Simplifying Expressions

Helpful Hint

Compatible numbers help you do math mentally. Try to make multiples of 5 or 10. They are simpler to use when multiplying.

1-8 Simplifying Expressions

Check It Out! Example 1a

Simplify.

21

Use the Commutative Property.

Use the Associative Property to make groups of compatible numbers.

1-8 Simplifying Expressions

Check It Out! Example 1b

Simplify.

410 + 58 + 90 + 2

410 + 90 + 58 + 2

(410 + 90) + (58 + 2)

(500) + (60)

560

Use the Commutative Property.

Use the Associative Property to make groups of compatible numbers.

1-8 Simplifying Expressions

Check It Out! Example 1c

Simplify.

28

Use the Commutative Property.

Use the Associative Property to make groups of compatible numbers.

12

• 7 • 8

12

• 8 • 7

( )12

• 8 7

4 • 7

1-8 Simplifying Expressions

The Distributive Property is used with Addition to simplify expressions.

The Distributive Property also works with subtraction because subtraction is the same as adding the opposite.

1-8 Simplifying Expressions

Additional Example 2A: Using the Distributive Property with Mental Math

Write the product using the Distributive Property. Then simplify.

5(59)

5(50 + 9)

5(50) + 5(9)

250 + 45

295

Rewrite 59 as 50 + 9.

Use the Distributive Property.

Multiply.

Add.

1-8 Simplifying Expressions

8(33)

8(30 + 3)

8(30) + 8(3)

240 + 24

264

Rewrite 33 as 30 + 3.

Use the Distributive Property.

Multiply.

Add.

Additional Example 2B: Using the Distributive Property with Mental Math

Write the product using the Distributive Property. Then simplify.

1-8 Simplifying Expressions

Check It Out! Example 2a

9(52)

9(50) + 9(2)

9(50 + 2)

450 + 18

468

Rewrite 52 as 50 + 2.

Use the Distributive Property.

Multiply.

Add.

Write the product using the Distributive Property. Then simplify.

1-8 Simplifying Expressions

Check It Out! Example 2b

12(98)

1176

Rewrite 98 as 100 – 2.

Use the Distributive Property.

Multiply.

Subtract.

12(100 – 2)

1200 – 24

12(100) – 12(2)

Write the product using the Distributive Property. Then simplify.

1-8 Simplifying Expressions

Check It Out! Example 2c

7(34)

7(30 + 4)

7(30) + 7(4)

210 + 28

238

Rewrite 34 as 30 + 4.

Use the Distributive Property.

Multiply.

Add.

Write the product using the Distributive Property. Then simplify.

1-8 Simplifying Expressions

The terms of an expression are the parts that are added together. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms.

4x – 3x + 2

Like terms Constant

1-8 Simplifying Expressions

A coefficient is a number multiplied by a variable. Like terms can have different coefficients. A variable written without a coefficient has a coefficient of 1.

1x2 + 3x

Coefficients

1-8 Simplifying Expressions

Using the Distributive Property can help you combine like terms. You can factor out the common factor to simplify the expression.

7x2 + 4x2 = (7 + 4)x2

= (11)x2

= 11x2

Factor out x2 from both terms.

Perform operations in parentheses.

Notice that you can combine like terms by adding the coefficients and keeping the variables and exponents the same.

1-8 Simplifying Expressions

Add only the coefficients.6.8y2 + (-y2) ≠ 6.8

Caution!

1-8 Simplifying Expressions

Additional Example 3A: Combining Like Terms

Simplify the expression by combining like terms.

72p – 25p

72p – 25p

47p

72p and 25p are like terms.

Subtract the coefficients.

1-8 Simplifying Expressions

Additional Example 3B: Combining Like Terms

Simplify the expression by combining like terms.

A variable without a coefficient has a coefficient of 1.

Write 1 as .

Add the coefficients.

and are like terms.

1-8 Simplifying Expressions

Additional Example 3C: Combining Like Terms

Simplify the expression by combining like terms.

0.5m + 2.5n

0.5m + 2.5n

0.5m + 2.5n

0.5m and 2.5n are not like terms.

Do not combine the terms.

1-8 Simplifying Expressions

Check It Out! Example 3

Simplify by combining like terms.

3a. 16p + 84p

16p + 84p

100p

16p + 84p are like terms.

Add the coefficients.

3b. –20t – 8.5t

–20t – 8.5t 20t and 8.5t are like terms.

–28.5t Add the coefficients.

3m2 + m3 3m2 and m3 are not like terms.

3c. 3m2 + m3

Do not combine the terms.3m2 + m3

1-8 Simplifying ExpressionsAdditional Example 4: Simplifying Algebraic Expressions

Simplify 14x + 4(2 + x). Justify each step.

14x + 4(2) + 4(x) Distributive Property

Multiply.

Commutative Property

Associative Property

Combine like terms.

14x + 8 + 4x

(14x + 4x) + 8

14x + 4x + 8

18x + 8

14x + 4(2 + x)1. 2. 3. 4. 5. 6.

Procedure Justification

1-8 Simplifying Expressions

6(x) – 6(4) + 9 Distributive Property

Multiply.

Combine like terms.

6x – 24 + 9

6x – 15

6(x – 4) + 91. 2. 3. 4.

Procedure Justification

Check It Out! Example 4a

Simplify 6(x – 4) + 9. Justify each step.

1-8 Simplifying Expressions

–12x – 5x + x + 3a Commutative Property

Combine like terms.–16x + 3a

–12x – 5x + 3a + x1. 2. 3.

Procedure Justification

Check It Out! Example 4b

Simplify −12x – 5x + 3a + x. Justify each step.

1-8 Simplifying Expressions

Standard Lesson Quiz

Lesson Quizzes

Lesson Quiz for Student Response Systems

1-8 Simplifying Expressions

Lesson Quiz: Part I

Simplify each expression.

1. 165 +27 + 3 + 5

2.

Write each product using the Distributive Property. Then simplify.

3. 5($1.99)

4. 6(13)

200

8

5($2) – 5($0.01) = $9.95

6(10) + 6(3) = 78

1-8 Simplifying Expressions

Lesson Quiz: Part II

Simplify each expression by combining like terms. Justify each step with an operation or property.

7. 301x – x

8. 24a + b2 + 3a + 2b2

5.

300x

27a + 3b2

6. 14c2 – 9c 14c2 – 9c

1-8 Simplifying Expressions

1. Which property states that you can add or

multiply in any order?

Lesson Quiz for Student Response Systems

A. Associative

B. Commutative

C. Multiplicative

D. Grouping

1-8 Simplifying Expressions

2. Simplify

A. 5

B. 6

C. 10

D. –5

Lesson Quiz for Student Response Systems

1-8 Simplifying Expressions

3. Which of the following are like terms?

A. 3x and 2y

B. 3x and 2x

C. 3x and x2

D. 3x and 2x

Lesson Quiz for Student Response Systems

1-8 Simplifying Expressions

4. Simplify by combining like terms.

2x2 + x2

A. 2x4

B. 3x4

C. 3x2

D. 4x2

Lesson Quiz for Student Response Systems