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MATH 104 Chapter 1 Reasoning

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**Inductive Reasoning Definition: Reasoning from specific to general**

Examples of Patterns

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Deductive Reasoning Definition: Reasoning from general to specific

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**Use Inductive or Deductive Reasoning**

Example #1: What is the product of an odd and an even number?

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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? Number Sum of digits Sum div by 3? Number div by 3?

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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? Number Sum of digits Sum div by 4? Number div by 4?

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**Example Pick a number. Multiply by 6. Add 4. Divide by 2. Subtract 2.**

What is your result?

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**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.

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**Use inductive reasoning to predict**

Use inductive reasoning to predict the next three lines. Then perform arithmetic to determine whether your conjecture is correct: / 3 = / 6 = / 9 = x = 9 12 x = x = x = x = 98,765

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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.

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**5. 142,857 5. Calculate the following: 142,857 x 2= 142,857 x 3= **

What do you notice that all of your answers have in common? Do you think this will continue indefinitely?

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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.

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**Sections– find a pattern and predict**

Number of points Number of sections 2 3 4 5 6 7 10 100

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**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? n n 2 n

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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. Numbers Product Divisible by 6?

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**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? .

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**9. Toothpicks- data Square No. of toothpicks 1x1 2x2 3x3 4x4 5x5 6x6**

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