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MATH 104 Chapter 1

MATH 104 Chapter 1. Reasoning. Inductive Reasoning. Definition: Reasoning from specific to general Examples of Patterns. Deductive Reasoning. Definition: Reasoning from general to specific. Use Inductive or Deductive Reasoning. Example #1: What is the product of an odd and an even number?.

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MATH 104 Chapter 1

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  1. MATH 104 Chapter 1 Reasoning

  2. Inductive Reasoning • Definition: Reasoning from specific to general • Examples of Patterns

  3. Deductive Reasoning • Definition: Reasoning from general to specific

  4. Use Inductive or Deductive Reasoning • Example #1: What is the product of an odd and an even number?

  5. Divisible by 3 • Statement: If the sum of the digits of a number is divisible by 3, then the number is divisible by 3. True or false?

  6. Divisible by 4 • Statement: If the sum of the digits of a number is divisible by 4, then the number is divisible by 4. True or false?

  7. Example • Pick a number. • Multiply by 6. • Add 4. • Divide by 2. • Subtract 2. • What is your result?

  8. Use inductive reasoning 1.     Exponents: Notice that 21=2, 22=4, 23=8, 24=16, 25=32.  Predict what the last digit of  2100 is.

  9. Use inductive reasoning to predict Use inductive reasoning to predict the next three lines.  Then perform arithmetic to determine whether your conjecture is correct: 2.     111 / 3 = 37 222 / 6 = 37 333 /  9 = 37 3.     1 x 8 +         1 = 9 12 x 8 +       2 = 98 123 x 8 +     3 = 987 1234 x 8 +   4 = 9876 12345 x 8 + 5 = 98,765

  10. 4. Calculator patterns   a) Use a calculator to find the answers to     6x6= 66x66= 666x666= 6666x6666=   b) Describe a pattern in the numbers being multiplied and the resulting products.   c) Use the pattern to write the next three multiplications and their products   d) Use a calculator to verify.

  11. 5. 142,857 5.     Calculate the following: 142,857 x 2= 142,857 x 3=  142,857 x 4= What do you notice that all of your answers have in common?  Do you think this will continue indefinitely?

  12. 6.     Sections of a circle: If we draw a circle with two points on it and connected the points, I end up with 2 sections of a circle.       When I draw a circle with 3 points and connect the points,       I get 4 sections of the circle.       When I use 4 points, I get 8 sections.

  13. Sections– find a pattern and predict

  14. 7. Try inductive or deductive If you take a positive integer (1,2,3,4,5,…) that is NOT divisible by 3, then square that integer, and then subtract one, what happens? Is the result ALWAYS divisible by 3?

  15. 8.     Divisibility by 6: Show that anytime you take three consecutive positive integers and multiply them together that the resulting number is divisible by 6.

  16. 9.     Toothpicks: Consider the following pattern: 1x1 square --4 toothpicks        2x2 square--12 toothpicks 3x3 square (draw this…) How many toothpicks are needed to draw:          a 4x4 square? .

  17. 9. Toothpicks- data

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