1. Algebra 1 Shelby Ferreira

2. Group Activity Half a number plus 5 is 11.What is the number? Explain your reasoning and create an equation that represents the problem.

3. Vocabulary Variable Coefficient Exponent Base Like terms

4. Addition and Subtraction Like terms Add/subtract coefficients Ex: p. 145 #1, 12, 20

5. Exponential Notation Even number of negative signs = + answer Odd number of negative signs= - answer No exponent, assume 1 p. 146 Exercise 6.3.1 #1

6. Multiplying Numbers in Exponential Notation To multiply expressions with the same base: 1. Add the exponents. 2. The base stays the same. Ex: p.147 Exercise 6.3.2 # 1, 8 To multiply expressions without the same base: 1. Multiply coefficients. 2. Add exponents of like bases. 3. Always make sure the bases are the same before you add exponents. Ex: p. 148 Exercise 6.3.3 # 1, 6

7. Power to a Power To raise a power to a power: 1. Multiply the exponents. 2. The base stays the same Ex: (a 2 ) 3 = a( 2x3) = a 6 Ex: p. 149 Exercise 6.3.4 # 1, 6

8. Product to a Power 1. Use the distributive property 2. Distribute the exponent to each of the factors inside the parentheses Ex: (ab) c = a c b c Ex: p. 150 # 1, 2

9. Division of Exponential Terms To divide expressions with the same base: 1.Write the division problem as a fraction 2. Subtract the exponents 3. The base stays the same Ex: a m / a n = a m-n Ex: p. 151 Exercise 6.4.1 #1, 7

10. Division of Algebraic Terms with a Coefficient To divide expressions with the same base: 1.Write the division problem as a fraction 2. Divide the coefficients 3. Subtract the exponents 4. The base stays the same Ex: p. 152 #1, 6

11. Zero as a Power Any expression to the “Zero” power =1 0 0 is undefined Ex: z z /z z =1 Ex: p. 153 Exercise 6.4.3 #1, 8

12. Negative Exponents A number with a negative exponent equals its reciprocal written with a positive exponent. Ex: t 3 / t 5 = t -2 = 1/t 2 Ex: p. 155, Exercise 6.4.4 #1

13. The Distributive Principle for Multiplication Distribute the items outside of the parentheses to all terms inside the parentheses Ex: a(b+c)= ab+ac

14. The Distributive Principle for Division 1. Distribute the denominator 2. Divide the like terms 3. a/a =1, so cancel it out Ex: (ab + ac )/a = ab/a+ac/a =b+c Ex: p. 158 Exercise 6.5.1, # 1, 12, 20

15. Factoring Ex: 24 = 2 x 3 x 4 To factor algebraic expressions, look for a common factor in all the terms in the expression. Ex: 3a + 9c = 3(a+3c) Like reverse distribution Ex: p. 160 Exercise 6.6.1 # 1, 5, 10

16. Evaluating Expressions Replacing letters with numerical values in an algebraic expression NOTE!! This is only done when the numerical value is known! Ex: If a=1 and b=6, then a+b= 1+6 = 7 A good habit it to place parentheses around numbers when you substitute them for letters so that you remember the operation. Ex: If a=5 and b=2, ab ≠ 52, ab= (5)(2)=10 Ex: p. 162, Exercise 6.7.1 # 1, 8 When expressions are complex, simplify as far as you can before substituting the variables. Ex: p. 162, Exercise 6.7.2 #1

17. Group Problems 1. Subtract 15 times a number n from twice the square of the number. Write this as an algebraic expression. Explain your reasoning. 2. Simplify 9(x + 2y) + 4(x – 6y). Explain your reasoning.