The document discusses inductive and deductive reasoning. Inductive reasoning involves making a conclusion based on examples, while deductive reasoning makes a conclusion based on statements that are known to be true. It then provides examples to determine whether inductive or deductive reasoning is being used. The last part involves using inductive reasoning to perform a number trick with three different starting numbers and make a conjecture based on the results.

1. inductive reasoning: when you make a conclusion
based on several examples
deductive reasoning: when you make a conclusion
based on statements that are assumed or have
been shown to be true.
Conjecture: a statement that is believed to be true
but not yet shown to be true
2.8 USE PROPERTIES OF REAL NUMBERS
AND LOGICAL REASONING

2. PROPERTIES OF EQUALITY

3. inductive or deductive reasoning
a.
While shopping at a mall, you notice that the
first three stores you visit are having a sale.
You conclude that every store in the mall is
having a sale.

4. INDUCTIVE OR DEDUCTIVE REASONING
At a furniture store in a mall, you are looking at
the top of a triangular corner table. The corner
angle of the table has a measure of 90° and the
other angles are equal in measure. Because the
sum of the measures of the angles in a triangle
is 180° and 90 + 45 + 45 = 180, you conclude that
the other two angles must each measure 45°.

5. Guided Practice
Determine whether inductive or deductive
reasoning is used.
ANSWER deductive
for Example 1
1. You are in a carpeted square room with a side length
of 18 feet. You conclude that the room contains 324
square feet of carpeting.
ANSWER inductive
2. You observe that Jose wore white sneakers every
day for the last 10 days. You decide that Jose will
wear white sneakers tomorrow.

6. Use inductive reasoning
Your friend asks you to perform the
following number trick: Choose any
number. Then double the number. Then
add 8. Then multiply by 3. Then divide by
6. Then subtract 4. Perform the number
trick for three different numbers. Then
make a conjecture based on the results.
Example 2

7. Use inductive reasoningExample 2
STEP 2 Double the
number.
2810 12–
STEP 3 Add 8. 3618 4–
STEP 4 Multiply by 3. 10854 12–
STEP 5 Divide by 6. 189 2–
STEP 6 Subtract 4. 145 6–
SOLUTION
Choose 14.Choose 5. Choose –6.STEP 1 Choose any
number.

8. Use inductive reasoningExample 2
Notice that the number in Step 6 is equal to
the number chosen in Step 1 for each of the
three trials. You can make a conjecture
based on these results.
Conjecture: The result of Step 6 will always equal the
number in Step 1.
ANSWER