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Number sense????

Number sense????. Real numbers. Rational numbers. Irrational numbers. -0.666…. = -.6. Integers. -4. 0. 100. Whole numbers. 0.122333444…. -500. 1.25. Where do these numbers belong in the chart?. 293. 0.12112111211112…. 0.184. -0.42222…. -7. Rational numbers. Irrational numbers.

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Number sense????

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  1. Number sense????

  2. Real numbers Rational numbers Irrational numbers -0.666…. = -.6 Integers -4 0 100 Whole numbers 0.122333444…. -500 1.25

  3. Where do these numbers belong in the chart? 293 0.12112111211112… 0.184 -0.42222….. -7 Rational numbers Irrational numbers Integers -7 293 Whole numbers 0.12112111211112… 0.184 -0.42222…..

  4. Graph the real numbers: 2.7

  5. Properties of addition and multiplication: Let a, b, and c be real numbers. Property Addition Multiplication CLOSUREa + b is a real number. ab is a real number. COMMUTATIVEa + b = b + a ab = ba ASSOCIATIVE(a + b) + c = a + (b + c) (ab)c = a(bc) IDENTITYa + 0 = a, 0 + a = a a• 1 = a, 1 • a = a INVERSE a + (-a) = 0 a • = 1, a ≠ 0 DISTRIBUTIVEa(b + c) = ab + ac

  6. Identify the property: (3 + 9) + 8 = 3 + (9 + 8) x + 7 = 7 + x y + -y = 0 15 * 1 = 15 5(a – 6) = 5a - 30

  7. VOCAB! QUOTIENT ADD PRODUCT DIVIDE SUM SUBTRACT DIFFERENCE MULTIPLY

  8. VOCAB! QUOTIENT DIVIDE PRODUCT MULTIPLY ADD SUM SUBTRACT DIFFERENCE

  9. Please Excuse My Dear Aunt Sally • Grouping symbols • exponents • multiplication and division from left to right • addition and subtraction from left to right Evaluate: 3 + 2 * 5

  10. Examples • Evaluate the expression.

  11. You try these: (-2)6 -26 24 – 8 * 12 / 4 -8 + 5(1 – (-3))3

  12. Q: What does the zero say to the eight? 0 8 A: Nice belt!

  13. SimplifyingAlgebraic Expressions Terms Coefficient Like Terms Constant Terms

  14. Simplifying by Combining Like Terms 7x + 4x 3n2 + n - n2 2(x + 1) - 3(x - 4)

  15. You try these: 5x2 - 3x + 7x2 - 10x 7x - y + 9x - 2y 4(x - 5) - 3(2x + 7) 6(x - y) + 3(y + 2x)

  16. Evaluate -3x2 - 5x + 7 when x = -2. -3x2 - 5x + 7 = -3(-2)2 - 5(-2) + 7 Substitute -2 for x. = -3(4) - 5(-2) + 7 Evaluate power. = -12 + 10 + 7 Multiply. = 5 Add. YOU DO: x4 + 3y when x = 2 and y = -8 YOU DO:

  17. Examples • Write an expression for the area of the right triangle, then evaluate it for x=6.

  18. Examples • You want to buy either a CD or a cassette as a gift for each of 10 people. CD’s cost $13 each and cassettes cost $8 each. Write an expression for the total amount you must spend. Then evaluate the expression when 4 people get CDs.

  19. Q. Why was 6 scared of 7? A. Because 7-8-9!

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