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Math 010 – Lots of math

Math 010 – Lots of math. October 2, 2013. 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. Recap from Monday: Rounding.

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Math 010 – Lots of math

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  1. Math 010 – Lots of math 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 numerator denominator

  9. 3.6 - Taking the square of a fraction • What is • Squared means multiplied by itself. • So, = • “One half of one half is one fourth” • What is ? • =

  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) • Addition Property of Zero • Any number plus zero is that number. 8 + 0 = 8 • Multiplication Property of Zero • Any number times zero is zero. -9(0) = 0 • Multiplication Property of One • Any number times one is that number. 5(1) = 5 • Inverse Property of Addition • a + (-a) = 0 • Inverse Property of Multiplication • a= 1

  14. Now let’s do some algebra. • Don’t get scared/angry! • We can use our properties here. 3x(y)(4) + 2x + 5y – 7x

  15. Using the multiplication properties • Rule of thumb: Constants (numbers) go before variables (letters). • 5 ∙ (4x) = (5 ∙ 4)x = 20x • (5y)(3y) = 5 ∙ y ∙ 3 ∙ y = 5 ∙ 3 ∙ y ∙ y = (5∙ 3)(y ∙ y) = 15 • -9 ∙ (6y) = (-9 ∙ 6)y = -54y • (7x)(-5y) = (7)(-5)(x)(y) = -35xy • (-20)(-c) = (-20)(-1c) = (-20 ∙ -1)(c) = 20c • (-8)(-x) = (-8)(-1x) = (-8 ∙ -1)x = 8x

  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 • A term of a variable expression is one of the addends. • Terms are added together. • has four terms. What are they? • , , , and • The constant in each term is called the coefficient • What is the coefficient of each term in ? • 4, -3, 1, -9 • The first three terms are variable terms • 9 is a constant term

  19. Simplify by adding like terms • What is 3x + 2x? • Think about cats – or something else • 3 cats plus 2 cats is 5 cats • So, 3x + 2x = 5x • Match terms that have the same variable part • 10y - 5y = 5y • 3xy - 4xy = -1xy = -xy • Constant terms also add together • 5 + 9 = 14

  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

  22. Simplify: • Rewrite: • Group like terms: • Add like terms:

  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 #7Show work & answers on a sheet of paper. You can leave when you’re done. • Evaluate • What is one-third squared? • Simplify: 3(2a + 4b) • Simplify: x + 2x + 3 + 4 • How well did you understand today’s lesson?

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