Algebra 1 Notes

1. 1. If y = 16, y – 3.6 = ____ 3. = ____ 2. 45 – (- 14) = ___4. -3 + 17 = ____ Warm Up 14 12.4 16 – 3.6 Algebra 1 Notes 59 14 GOAL USE THE DIST. PROP. TO EVALUATE/SIMPLIFY EXPRESSIONS; RECOGNIZE AND USE THE COMMUTATIVE AND ASSOCIATIVE PROP.; FIND SQUARE ROOTS; CLASSIFY AND ORDER REAL NUMBERS. KEY WORDS & PROPERTIES COEFFICIENT, EQUIVALENT EXPRESSIONS, IRRATIONAL NUMBERS, LIKE TERMS, PERFECT SQUARE, PRINCIPAL SQUARE ROOT, RADICAL SIGN, RATIONAL APPROXIMATION, REAL NUMBERS, SIMPLEST FORM, SQUARE ROOT, TERM,

2. Properties • Commutative • Associative • Distributive • Identity Order of the terms does not change your answer 3 + 5 = 5 + 3 a + b = b + a 4 * 3 = 3 * 4 x * y = y * x Moving grouping symbols does not change your answer 3 + (5 + 7) = (3 + 5) + 7 (6 * 5) * 9 = 6 * (5 * 9) a + (b + c) = (a + b) + c a * (b * c) = (a * b) * c Multiply your outside term times all terms inside the parentheses a(b + c) = ab + ac 5(7 + 9) = 5(7) + 5(9) Of Addition: 3 + 0 = 3 x + 0 = x Of Multiplication: 5 * 1 = 5 x * 1 = x

3. Example 1 Use the Distributive Property to simplify the expressions. 5(6m + 4n – 3n)  3(2x + 6)

4. Example 2 Use the distributive property to write this product in another way.

5. Example 3 Simplify by collecting like terms.

6. Example 4 Simplify. 3.2(x + y) + 2.3(x + y) + 4x

7. Example 5 Evaluate.