1. October 2, 2013

2. Announcements If you were absent last class, sign up for a conference time. This is required and worth 8 quiz grades! Check your RIC e-mail Quiz today will be on today’s material

3. Recap from Monday: Rounding Find the digit in the place you are trying to round to. This will be the last digit. This digit will either stay the same, or round up. To figure out which, look at the digit to the right. 5 or greater: round up 4 or less: round down (stay the same) If you need to round up a 9, change it to a 0 and increase the digit to the left by 1.

4. Rounding examples Round $4.256 to the nearest cent, that is the nearest hundredth. So our last digit will be in the hundredths place. Will the 5 round up or down? 6 ≥ 5, so $4.256 to the nearest cent is $4.26 Round 3.71 to the nearest tenth. So our last digit will be in the tenths place. Will the 7 round up or down? 1 < 5, so 3.71 to the nearest tenth is 3.7

5. Rounding up from a 9 Round 2.495 to the nearest hundredth. Last digit will be in the hundredths place. Does the 9 round up or down? 9 becomes a zero. Increase the tenths place by 1. 2.50 = 2.5 Round 6.9997 to the nearest thousandth. Round up the 9, look at digits before Tip: 6.999 + 0.001 = 7.000 = 7

6. Does rounding a decimal keep the number the same, or change it? The purpose of rounding is to get an approximation of a number. We want an approximation when we don’t need the exact value, just something close. π = 3.14159265….. but we round to the nearest hundredth and say π ≈ 3.14, or “Pi is about 3.14.” We don’t know what π is exactly, so we have to round. So technically, the value of the decimal does change.

7. 3.6 - Complex Fractions (Fractions inside fractions) Do you remember what the fraction bar means? A fraction bar means division.

8. Working from the inside out First need to perform the operations inside the numerator and the denominator Then it becomes a simpler complex fraction Now it becomes a fraction division problem numeratordenominator

9. 3.6 - Taking the square of a fraction

10. 4.6 – Graphing Inequalities

11. Meanings of inequalities (A) The minimum value of x is -2, and x is less than 3. (B) x is between -4 and 2. (C) The minimum value of x is -2. (D) x is less than 3.

12. 5.1 Properties of Real Numbers Commutative Property of Addition a + b = b + a Commutative Property of Multiplication ab = ba Associative Property of Addition (a + b) + c = a + (b + c) = a + b + c = (a + b + c) Associative Property of Multiplication (ab)c = a(bc) = abc = (abc)

13. 5.1 - More Properties (p. 308)

14. Now let’s do some algebra. Don’t get scared/angry! We can use our properties here.

15. Using the multiplication properties

16. Using the addition properties -4t + 9 + 4t = -4t + 4t + 9 = (-4t + 4t) + 9 = 0 + 9 = 9 5 + 8y + (-8y) = 5 + 0 = 5 -5y + 5y + 7 = -5y + 5y + 7 = 0 + 7 = 7 -3z + 8 + 3z = -3z + 3z + 8 = 0 + 8 = 8

17. The Distributive Property Used to remove parentheses from a variable expression a(b + c) = ab + ac 2(3 + 5) = 2(8) = 16 2(3) + 2(5) = 6 + 10 = 16 3(5a + 4) = 3(5a) + 3(4) = 15a + 12 -4(2a + 3) = -4(2a) + -4(3) = -8a + (-12) = -8a -12 -5(-4a – 2) = -5(-4a) – (-5)(2) = 20a + 10 6(5c – 12) = 6(5c) – 6(12) = 30c - 72

18. 5.2 – Simplest Form: Terms

19. Simplify by adding like terms

20. Simplify: 6a + 7 - 9a + 3 It helps a lot to rewrite subtracted terms as addition of a negative term. This way they can move around freely. 6a + 7 + (-9a) + 3 Next, rearrange terms so like terms are together. 6a + (-9a) + 7 + 3 Now, add like terms. -3a + 10

21. Simplify: 9y - 3z - 12y + 3z + 2 Can change to 9y + (-3z) + (-12y) + 3z + 2 Group like terms: 9y + (-12y) + (-3z) + 3z + 2 Add like terms: -3y + 0z + 2 -3y + 2

23. Simplify with Distributive ppty 5x + 2(x + 1) Distribute: 5x + 2x + 2 Like terms already together, so add them: 7x + 2

24. One more of these 9n – 3(2n – 1) Distribute: 9n – 3(2n) – 3(-1) = 9n – 6n – (-3) = 9n – 6n + 3 Add like terms: 3n + 3 Keeping track of negative signs is important

25. Topics to know so far for the EXAM Complex fractions Taking the square of fractions Decimals – order relation Convert decimals to fractions Rounding decimals Set up decimal addition, subtraction, multiplication Solve equations with decimals Square roots Graphing inequalities What inequalities mean Simplifying expressions with all properties Need help? E-mail me or stop by office before class

26. Quiz #7 Show work & answers on a sheet of paper. You can leave when you’re done.