1 7 Simplifying Expressions Purpose Students will be

1 -7 Simplifying Expressions Purpose Students will be able to use the Commutative, Associative, and Distributive Properties to simplify expressions and combine like terms. Holt Algebra 1

1 -7 Simplifying Expressions Holt Algebra 1

1 -7 Simplifying Expressions Example 1: Using the Commutative and Associative Properties Simplify. Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. 11(5) 55 Holt Algebra 1

1 -7 Simplifying Expressions Example 2: Using the Commutative and Associative Properties Simplify. 45 + 16 + 55 + 4 45 + 55 + 16 + 4 (45 + 55) + (16 + 4) (100) + (20) 120 Holt Algebra 1 Use the Commutative Property. Use the Associative Property to make groups of compatible numbers.

1 -7 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. Example: 15 + 18 + 5 easier (15 + 5) + 18 = 20 + 18 harder (15 + 18) +5 = 33 + 5 Holt Algebra 1

1 -7 Simplifying Expressions You Try! Simplify. Use the Commutative Property. Use the Associative Property to make groups of compatible numbers. 21 Holt Algebra 1

1 -7 Simplifying Expressions You Try! Simplify. 1 • 7 • 8 2 1 2 (12 • 8 • • 7 8) 7 4 • 7 28 Holt Algebra 1 Use the Commutative Property. Use the Associative Property to make groups of compatible numbers.

1 -7 Simplifying Expressions Note: The Distributive Property also works with subtraction because subtraction is the same as adding the opposite. Holt Algebra 1

1 -7 Simplifying Expressions Example 3: 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 Holt Algebra 1 Rewrite 59 as 50 + 9. Use the Distributive Property. Multiply. Add.

1 -7 Simplifying Expressions You Try! Write the product using the Distributive Property. Then simplify. 9(52) 9(50 + 2) 9(50) + 9(2) 450 + 18 468 Holt Algebra 1 Rewrite 52 as 50 + 2. Use the Distributive Property. Multiply. Add.

1 -7 Simplifying Expressions You Try! Write the product using the Distributive Property. Then simplify. 12(98) 12(100 – 2) 12(100) – 12(2) Holt Algebra 1 Rewrite 98 as 100 – 2. Use the Distributive Property. 1200 – 24 Multiply. 1176 Subtract.

1 -7 Simplifying Expressions The terms of an expression are the parts to be added or subtracted. Like terms are terms that contain the same variables raised to the same powers. Constants are also like terms. Like terms Constant 4 x – 3 x + 2 Holt Algebra 1

1 -7 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. Coefficients 1 x 2 + 3 x Holt Algebra 1

1 -7 Simplifying Expressions Using the Distributive Property can help you combine like terms. 7 x 2 – 4 x 2 = (7 – 4)x 2 = (3)x 2 = 3 x 2 Holt Algebra 1 Factor out x 2 from both terms. Perform operations in parenthesis.

1 -7 Simplifying Expressions You Try! Simplify by combining like terms. 3 a. 16 p + 84 p 100 p 3 b. – 20 t – 8. 5 t 2 3 c. 3 m 2 + m 3 Holt Algebra 1 16 p + 84 p are like terms. Add the coefficients. 20 t and 8. 5 t 2 are not like terms. Do not combine the terms. 3 m 2 and m 3 are not like terms. Do not combine the terms.

1 -7 Simplifying Expressions Example 4: Simplifying Algebraic Expressions Simplify 14 x + 4(2 + x). Justify each step. Procedure 1. 2. Justification 14 x + 4(2 + x) 14 x + 4(2) + 4(x) 3. 14 x + 8 + 4 x 4. 14 x + 8 5. (14 x + 4 x) + 8 6. Holt Algebra 1 18 x + 8 Distributive Property Multiply. Commutative Property Associative Property Combine like terms.

1 -7 Simplifying Expressions You Try! Simplify 6(x – 4) + 9. Justify each step. Procedure Justification 1. 6(x – 4) + 9 2. 6(x) – 6(4) + 9 Distributive Property 3. 6 x – 24 + 9 4. 6 x – 15 Multiply. Combine like terms. Holt Algebra 1

1 -7 Simplifying Expressions Exit Task Simplify each expression. 1. 165 +27 + 3 + 5 200 2. 8 Write each product using the Distributive Property. Then simplify. 3. 5($1. 99) 4. 6(13) Holt Algebra 1 5($2) – 5($0. 01) = $9. 95 6(10) + 6(3) = 78